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A. NRG flows and fixed points Figure 4 plots the schematic renormalization-group flows of the couplings λ entering Eq. ( 15) and ∆ defined in Eq. ( 50) for a symmetric impurity (U = -2ǫ d ) coupled to bath described by an exponent 0 < s < 1. These flows are deduced from the evolution of the manybody spectrum with increasing iteration number N , i.e., with reduction in the effective band and bath cutoffs D = Ω ≃ DΛ -N/2 . A separatrix (dashed line) forms the boundary between the basins of attraction of a pair of stable fixed points, regions that correspond to the two phases shown in Fig. 3. | cond-mat.str-el |
The use of computer models of liquids has played an important role for understanding glass forming-liquids. Computationally undemanding models are attractive, since long simulation times are important. Further more, the model does not have to be specific since the glass transition is universal. A simple model for molecular interactions is the the famous Lennard-Jones pair potential, U ij (r ij ) = 4ε((r ij /σ ij ) 12 -(r ij /σ ij ) 6 ). It is not possible to investigate a single component Lennard-Jones liquid close to the glass transition since the structural relaxation time is of the same order as the crystallization time. This can be avoided by using a binary Lennard-Jones liquid where the liquid consists of two kind of particles with differend radii σ ij and binding energy ε ij [1,2]. | cond-mat.mtrl-sci |
The local self-energy is then defined by the Dyson equation [(G -1 0,σ -Σ σ ) * G σ ](t, t ′ ) = δ C (t, t ′ ),(15) where the noninteracting (U = 0) single-site Green function and its inverse are given by G 0,σ (t, t ′ ) = -i c σ (t)c † σ (t ′ ) S0 ,(16a) G -1 0,σ (t, t ′ ) = δ C (t, t ′ )(i∂ t + µ) -Λ σ (t, t ′ ),(16b) [G -1 0,σ * G 0,σ ](t, t ′ ) = δ C (t, t ′ ),(18) for G 0,σ are inhomogeneous integro-differential equations on the contour C when Eq. (16a) is inserted. They have a unique solution because G 0,σ and G satisfy the boundary condition (9). The solution of such integral equations on C is discussed in detail in Sec. IV. In order to determine the hybridization function Λ σ (t, t ′ ) one must equate the self-energy Σ σ (t, t ′ ) and the Green function G σ (t, t ′ ) of the single-site problem with the local self-energy Σ jjσ (t, t ′ ) and the local Green function G jjσ (t, t ′ ) of the lattice problem at the given site j, respectively, G jjσ (t, t ′ ) = G σ (t, t ′ ), Σ ijσ (t, t ′ ) = δ ij Σ σ (t, t ′ ). | cond-mat.str-el |
Doping of a single edge shifts the band energies of the orbitals which are strongly localized at this edge. Such a shift provides an opportunity to obtain another useful property which is important for spintronics -the halfmetallicity of graphene. For the HOMO or LUMO orbitals, which are shown to be localized at the edges, doping can create a strong non-degeneracy of the α-and β-spin states, because these states are spatially separated and localized at the opposite edges. Moreover, the HOMO α and LUMO β orbitals are localized at one edge, while HOMO β and LUMO α at the other. If doping increases the bandgap ∆ α for the α-spin state, then the bandgap ∆ β for the β-spin state, in contrast will be reduced, and vice versa. Therefore, doping induces the spin gap asymmetry in graphene. | cond-mat.mtrl-sci |
One simplification occurs for cylindrical geometries, whereby outof-plane shear waves decouple from in-plane waves. However, in-plane shear and pressure waves remain inherently coupled. Earlier proposals for neutral inclusions include using asymptotic and computational methods to find suitable material parameters for coated cylindrical inclusions [13]. The latter has proved successful in the elastostatic context in the case of anti-plane shear and in-plane coupled pressure and shear polarizations. However, neutrality breaks down for finite frequencies. Other avenues to elastic cloaking should therefore be investigated. | cond-mat.mtrl-sci |
The phonon modes are described by the free phonon Hamiltonian H ph = k ω k b † k b k , where b k , b † k are bosonic operators of the phonon modes and ω k are the corresponding frequencies. Interaction of carriers confined in the DQD with phonons is modelled by the independent boson Hamiltonian H c-ph = (|1 1| + |3 |3|) k f (1) k (b † k + b -k ) + (|2 2| + |3 |3|) k f (2) k (b † k + b -k ),(2)where f (1,2) k are system-reservoir coupling constants. For Gaussian wave functions, the coupling constants for the deformation potential coupling between confined charges and longitudinal phonon modes have the form f(1,2) k = f k e ±ikzD/2, where f k = (σ e -σ h ) k 2̺vc l exp - l 2 z k 2 z + l 2 k 2 ⊥ 4 . Here v is the normalization volume, k ⊥/z are momentum components in the xy plane and along the z axis, σ e/h are deformation potential constants for electrons/holes, c l is the speed of longitudinal sound, and ̺ is the crystal density. We assume that off-diagonal carrier-phonon couplings are negligible due to small overlap of the wave functions confined in different dots. The third component in our modeling is the radiative reservoir (modes of the electromagnetic field), described by the HamiltonianH rad = k,λ w k c † k,λ c k,λ , where c k,λ , c † k,λ are photon creation and annihilation operators and w k are the corresponding frequencies (λ denotes polarizations). | cond-mat.mes-hall |
This is in contrast to t ′ = 0.8t, for which the weaker hopping amplitude displays ferromagnetic correlations whereas spins with the larger hopping amplitude are antiferromagnetically coupled, indicating a row-wise AF Neel arrangement of spins. Thus, t ′ = 0.8t induces a much stronger tendency towards magnetic order than t ′ = t, which explains why the reentrant behavior occurs for t ′ = 0.8t, but not for t ′ = t (see Fig. 1). At low T , the electron entropy is suppressed for t ′ = 0.8t as compared to t ′ = t. As T is increased for t ′ = 0.8t, the system lowers its free energy by transforming to a metal since the entropy of the metal exceeds that of the ordered insulator. At even higher temperatures the system gains entropy of log(2) by transforming back into a paramagnetic insulator. This result is analogous to the one found for the unfrustrated square lattice. | cond-mat.str-el |
Typically, NMR signal enhancement is associated with the domain walls which are swept out with H resulting in the disappearance of the enhancement effect. In this regard, the usual enhancement of the signal with large H suggests the persistence of the domain motions at least up to 4 T. Since the domains of the long-range ordered phase are expected to be frozen-in at low fields, the enhanced high-field signal might be related to the domain motions of the short-range ordered state. Above we have ascribed the short-range order to the orbital ordering induced by the structural phase transition. Specifically, the V ions form the antiferromagnetic chain with the exchange coupling constant of an order of 1000 K [3]. In this situation, the short-range ordered component of the V spins is frustrated. Thus, in the studied field range the short-range ordered state undergoes a minor change in the spin directions accompanying the domain motions. | cond-mat.str-el |
Singlequbit operations can be implemented by rotating the single spins using a magnetic field. Two-qubit operations, which are needed in order to implement logical gates, can be realized by means of a pulsed (gate-controlled) exchange interaction between neighboring dots by lowering the inter-dot potential barrier and allowing the electron wave functions to overlap. Remote two-qubit operations can be realized by swapping the two qubits next to each other, again assisted by pulsing on and off exchange interaction between neighboring quantum dots. The LDV scheme involves a system of symmetric dots since, in general, no electrical bias is applied between the adjacent dots at any time. Indeed small bias about the symmetric point will only reduce the exchange splitting J. 9 The model potential is symmetric and the best choice for the two-dot scenario is the quartic potential introduced in Sec. | cond-mat.mes-hall |
Transport measurements in the presence of the magnetic field were performed in a 14/16T Oxford He-3 cryostat. Magnetic fields up to 10T were applied both parallel and transverse to the sample plane at temperatures of 5K, 1K and 400mK. The voltage sweep rate was 0.5 -1.2 mV/s. IV. RESULTS AND DISCUSSION A. Non-Ohmic Regime We first focus on the regime of finite applied bias. Here the transport properties are highly non-Ohmic. | cond-mat.mes-hall |
The parameter λ is used to reproduce the correct splitting ∆ 1 of the valence bands A and B. As discussed in Ref. 17 , the small CF splitting ∆ cf of the wurtzite crystal differentiates the p z orbital from the p x and p y orbitals. Pseudo-potential calculations in local density approximation indicate that for the studied InN [eV] GaN [eV] ∆ cf = 0 ∆ cf = 0 ∆ cf = 0 ∆ cf = 0 ∆ cf = 0 ∆ cf = 0 ∆so = 0 ∆so = 0 ∆so = 0 ∆so = 0 ∆so = 0 ∆so = 0 E(s,a) -6.791 -6.5134 - materials the bulk crystal field splitting between the A and C valence bands, schematically shown in Fig. 2, cannot be reproduced from first principles, unless thirdnearest-neighbor interactions are taken into account 20 . The TB model discussed in Ref. | cond-mat.mtrl-sci |
It turns out that, as the temperature increases, the descending rate of w d (T )/w d (0) is much lower than ∆(T )/∆(0) from the numerical calculation. Such a result has two consequences. The first one is the transition temperature by analytical calculation is higher than the numerical result since a slower descending w d (T )/w d (0) will lead to a higher crosspoint with a given w n (T ); Still another is the extremely high transition temperature in the weak coupling regions shown in the inset of Fig. 4. It is found that, in the weak coupling regions, the slow descending w d (T )/w d (0) can still survive to some high temperature, at where ∆(T ) from the numerical calculation has died out, bringing about an artifact high transition temperature. On the other hand, As one can see from Fig. | cond-mat.mes-hall |
B 55 (6), 3445 (1997). 33 As quasicrystals show non-periodic translational order we generate periodic approximants to apply periodic boundary conditions. The 4 to 5 million atoms of our sample then form the unit cell. Because of this high number of atoms the configuration should mechanically behave like the perfect quasicrystal. 34 Here we use equation (2) of Gumbsch et al. 32 with a "filled stadion damping" f ≡ 1. | cond-mat.mtrl-sci |
(82) This is built from Q by just adding an extra incoming index i, where index i has fixed particle number n and no degeneracy (i.e., i is associated to a trivial space V [i] C). We refer to both invariant and covariant tensors as symmetric tensors. By using the above construction, in this work we will represent all U(1) symmetric tensors by means of U(1) invariant tensors. In particular, we represent the non-trivial components (Ψ n ) t n of the covariant vector |Ψ n in Eqs. 31-32 as an invariant matrix T of size |t n |×1 with components Tt n 1 = (Ψ n ) t n . Consequently, from now on, we will mostly consider only invariant tensors. | cond-mat.str-el |
2(a). As seen there, for both V = 1.0 and V = 2.0, we obtain a finite value of D ∞ . 2,4,6,7 The results presented so far were obtained at a very high temperature (β = 0.001), where finite size effects are the smallest, but transport properties are still nontrivial. In Fig. 2(b), one can see that for T > 10, the actual value of T is not essential since quantities such as D L T , D * L T , and ΓT become almost independent of T . Figure 2(b) also shows that, for the considered temperatures and system sizes, Γ is independent of the system size, while D L and D * L still exhibit finite size effects. | cond-mat.str-el |
As in the preceding section (R, θ, φ) will be the spherical coordinates of R and (r 1 , θ 1 , φ 1 ) those of r 1 . In order to express the previous expression as a function of 1/R, we use following expansion of solid spherical harmonics (for simple derivation see ref. P M L (cos θ -) e iMφ± R L+1 - = ∞ n=0 r n 1 R L+n+1 m L + n -m L -M × (-1) M-m P m L+n (cos θ) e imφ × P M-m n (cos θ 1 ) e i(M-m)φ1 (21) where the sum over m spans all integer values. Neverthe-less, only a finite number of terms will contribute, since P m l = 0 if |m| > l. Setting l = L + n and introducing spherical harmonics leads to : Y M L (θ -, φ -) R L+1 - = ∞ l=L m Y m l (θ, φ) R l+1 × (-1) M-m l -m L -M l + m L + M 1 2 × r l-L 1 Y M-m l-L (θ 1 , φ 1 )(22) Considering R + in this equation instead of R -is equivalent to the transformationθ 1 -→ π -θ 1 φ 1 -→ π + φ 1 that results in an overall (-1) l-L factor. Inserting relation 22 into eq. 20 and inverting the summation over l and L leads to the expansion : ∆V n ( r 0 , r 1 ) = R ∈ En ∞ l=0 l m=-l Y m l (θ, φ) R l+1 A lm(23)with : A lm = l L=0 L M=-L M LM ( r 0 ) l -m L -M l + m L + M 1 2 ×(-1) M-m r l-L 1 Y M-m l-L (θ 1 , φ 1 ) × 1 -(-1) l-L (24) Considering the parity of Y lm , one can see from eq. | cond-mat.str-el |
Inserting this into Eqs. (27,28) leads to the simple and general result S = 1 2 tanh 1 2 β∆ with ∆ = 2 S |a ⊥ |(31) This means that in the ordered phase the molecular field splitting ∆ of spins is field independent up to h c and hence the total moment S is also field independent, i. e. the moment can only be rotated by the field as long as the transverse staggered order exists. This fact has striking consequences for the thermodynamic quantities below h c . For the thermodynamics we also need the temperature derivatives ∂ S i /∂T = -k B β 2 (∂ S i /∂β) (i = , ⊥). They are obtained from Eq. ( 27) in a straightforward but lengthy calculation and the resulting explicit expressions are given in appendix A. | cond-mat.str-el |
(Note that the prefactors of j * m (r) and j m (r) in Eq. (2.8) must be complex conjugate since J (3) (r) t is a real quantity). The problem is to get a compact expression for γ m (t). In the next section, we are going to show why the "brute force" calculation of the triple commutator appearing in S m (t 1 , t 2 , t 3 ; t) raises a major technical problem which let it open for decades. Thanks to the many-body theory for composite-bosons we constructed [20,21], we were able to overcome this difficulty [25,26] and to derive a compact expression of J (3) (r) t in terms of the Pauli and Coulomb scatterings of this theory. While the expression of J (3) (r) t we then obtained is fully correct, it turns out that, in preparing the present manuscript, we have found a way to greatly simplify our first calculation. | cond-mat.mes-hall |
4, the K(T ) data fit rather well to Eq. 2 in the temperature range 9 K ≤ T ≤ 300 K. Using A hf ≃ 4400 Oe/µ B (obtained from the K vs χ analysis) we obtained K 0 ≃ -890ppm, J 1 ≃ (141 ± 5)K, and g ≃ 2. 2. Below about 8 K, K(T ) show a significant deviation from the fit (see lower inset of Fig. 4) which shall be discussed later. The temperature dependence of 31 P 1/T 1 is presented in Fig. | cond-mat.str-el |
Hence the observed systematics in the behaviour of binary systems on the ∆ , ∆ / map is not anticipated from the current understanding of the alloying of metals. In a recent paper 17 , we have shown that the above observations call for a reinterpretation of Eq. (1) as the energy of the nearest neighbour unlike atom-pair bond. It also follows that the bond remains identical in all the intermetallic compounds occurring in the same binary system at different compositions. A 'bond energy' can then be defined in alloys as for a conventional chemical bond 18 which remains more or less the same irrespective of the nature of the functional groups attached to the atoms on the bond. Metallic elements do not have enough electrons to form conventional chemical bonds. | cond-mat.mtrl-sci |
We obtain the spinon vertex-distribution function Λ f (k f F , ω) = 1 2 Γ f (k f F , ω)A f (k f F , ω) + Γ b f,cos (k f F , ω)A c (k c F , ω) Γ b f (k f F , ω) + Γ a f,1-cos (k f F , ω) -Γ b f,cos (k f F , ω) Γ c,cos (k f F , ω) Γ c (k c F , ω) -1 ,(29)where 2Γ a f,1-cos (k f F , ω) ≡ 3 2Λ 3 Λ 0 dqq 2 1 -1 d cos θ f f [1 -cos θ f f ] Quantum Boltzman equation study for the Kondo breakdown quantum critical point 12 ∞ 0 dν π [v f 2 F cos 2 (θ f f /2)]ℑD a (q, ν) [n(ν) + f (ω + ν)]A f (k f F + q, ω + ν) -[n(-ν) + f (ω -ν)]A f (k f F + q, ω -ν)(30) is identified with [τ a tr (ω)] -1 as shown in the U(1) gauge theory of the previous section. 3.2.3. Conductivity in the decoupling limit In the vertex-distribution function for spinons [Eq. ( 25)] we neglect the coupling term Λ c (k c F , ω) as the zeroth order approximation for the transport study, named as the decoupling limit. One may understand validity of this approximation, based on the fact that spinons are heavily massive denoted by α ≪ 1 and scattering with conduction electrons will not affect their dynamics much. Then, we find Λ f (k f F , ω) = 1 2 Γ f (k f F , ω)A f (k f F , ω) Γ f (k f F , ω) + Γ a f,1-cos (k f F , ω) . | cond-mat.str-el |
Again, if these regions correspond to edges of the NW (that is for θ = π/6), localization is enhanced for these two edges, while the other four edges are charge depleted. On the other hand, if θ = 0 carriers tend to be confined in the center of the two facets where the field is perpendicular, and all edges of the NW are charge depleted. Note the different slopes of the energy levels with field intensity for different orientation θ of the field. In fact, only the orthogonal component cos(θ)B ⊥ is effective, and the Landau-level energy is correspondingly smaller. For higher energies, the succession of peaks is repeated. A discussion of these states in a related cylindrical systems is given in Ref. | cond-mat.mes-hall |
The number of bands is reduced as the interaction increases. In the insulating phase, all fine gaps of the Hofstadter butterfly are closed, but the Mott-Hubbard gap opens at the Fermi level. In a long-range ordered phase, the electron correlation induced gap, such as the checkerboard charge ordering gap in the FKM, preserves the fine structure of the Hofstadter butterfly. However, the Hofstadter butterfly is separated into two wings by the long-range ordering gap. In the present paper we have only considered the rational magnetic field. In the noninteraction case an irrational magnetic field induces the Hofstadter butterfly in the form of a Cantor set. | cond-mat.str-el |
1(b) in simple shear and 1(c) in pure shear, and from an obvious flow pattern in equibiaxial loading. Differentiations wrt. x and y provides those enjoyed by ε ij . The symmetry group of the constitutive law carries them unchanged over σ ij . For v = u or u * and for a = ε or σ:• In PS loading:• In SS loading: A2c) a ii (x, y) = -a ii (-x, y) = -a ii (x, -y), i = x, y, (A2d) a xx (x, y) = a yy (y, x), (A2e) a xy (x, y) = a xy (-x, y) = a xy (x, -y), (A2f) a xy (x, y) = a xy (y, x);(A2g) • In equibiaxial loading: v x (x, y) = -v x (-x, y) = v x (x, -y), (A3a) v y (x, y) = v y (-x, y) = -v y (x, -y), (A3b) v x (x, y) = v y (y, x), (A3c) a ii (x, y) = a ii (-x, y) = a ii (x, -y), i = x, y, (A3d) a xx (x, y) = a yy (y, x), (A3e) a xy (x, y) = -a xy (-x, y) = -a xy (x, -y), (A3f) a xy (x, y) = a xy (y, x). (A3g) | cond-mat.mtrl-sci |
Therefore, we have the ground state|Ψ 0 = q C † q,2 |0 ,(5)with the ground-state energy E 0 = - q ǫ 2 q + ∆ 2 q = - q E q . (6) The two-site reduced density matrix can be expressed as [25] ρ(r 1 , r 2 ) = Tr ′ (|g g|) = 1 4 3 α,α ′ =0 g σ α 1 σ α ′ 2 g σ α 1 σ α ′ 2 ,(7) where σ α (σ α ′ ) are Pauli matrices σ x , σ y , and σ z for α (α ′ )= 1 to 3, and the unit matrix for α (α ′ )= 0. Now we consider the nearest-two-site reduced density matrix, (i.e., the reduced density matrix of an x-bond. It can be proved that all but two parts of the density matrix are nonzero: ρ(r, r + x)= 1 4 g σ x r σ x r+x g σ x r σ x r+x + 1 4 I r I r+x . (8) If we assume the system has translational symmetry, we can calculate the average g σ x r σ x r+x g = 1 L 2 g |H x | g = - 1 L 2 ∂E 0 ∂J x . (9) Combining Eqs. | cond-mat.str-el |
Several general observations can be made about the energy resolved transmission spectra: (i) there are regions of pseudo-gaps and pseudo-bands where transmissivity is relatively opaque and transparent respectively, (ii) within the pseudo-bands, there are camel-back structures which increases in number with increasing roughness frequency (i.e. decreasing λ) and (iii) a delayed 'turn-on' of transmission called 'enhanced threshold', which increases with increasing roughness frequency. The enhanced threshold energy is a geometrically derived property due to 2D quantization effects of the roughened morphology. The enhanced threshold is zero for an unroughened quantum well channel. Note that the energy scale are referenced from the subband energy of the first mode in the lead, previously defined as κ 1 . In addition, due to the symmetry of the problem, Φ mn =0 if and only if both m and n are odd/even numbers. | cond-mat.mes-hall |
In such devices electrons are constrained to move in a two-dimensional space (Ox-Oŷ) forming a 2D gas. The asymmetry of the quantum well generates an electric field, along the ẑ-direction, perpendicular to the plane containing the electrons. This causes electrons to be subject to an effective magnetic field B ef f ∝ p × E coupling to their spin. Such coupling gives rise to the well known Rashba potential 4 : V Rashba = λ N i=1 [p y i σ x i -p x i σ y i ] ,(1) where p i is the momentum of the i -th electron, and σ x i and σ y i are the Pauli matrices acting over the spin of particle i. Neglecting the Coulomb interaction among the electrons the Hamiltonian is a sum of one body terms, and the problem is analytically solvable. Single particle solutions are given by plane waves with k-dependent spinors. | cond-mat.str-el |
The classical phase transition at J ′ 2 = 1 2 J 1 is of continuous (second-order) type, with the gs energy and its derivative both continuous. In the limit of large J ′ 2 /J 1 the above classical limit represents a set of decoupled 1D HAF chains (along the diagonals of the square lattice) with a relative spin orientation between neighboring chains that approaches 90 • . In fact, of course, there is complete degeneracy at the classical level in this limit between all states for which the relative ordering directions of spins on different HAF chains are arbitrary. Clearly the exact spin-1/2 limit should also be a set of decoupled HAF chains as given by the exact Bethe ansatz solution. 17 However, one might expect that this degeneracy could be lifted by quantum fluctuations by the wellknown phenomenon of order by disorder. 18 Just such a phase is known to exist in the J 1 -J 2 model 4,5 for values of J 2 /J 1 0.6, where it is the so-called collinear stripe phase in which, on the square lattice, spins along (say) the rows in Fig. | cond-mat.str-el |
Our time steps thus each represent ~200 ns in the experiments. One obvious limitation of the present experiments and models should be mentioned here. In the LLG simulation we watch the actual dynamical switching process in detail, while the domain walls are moving. This process involves not only a simple Ising-like up and down flipping of polarization but also a development of in-plane component of polarization, which arises prior to the complete polarization reversal. However, it is difficult to verify this via direct PFM experiment for at least two reasons. First, the actual domain switching measurements using PFM are quasi-static. | cond-mat.mtrl-sci |
Then, the conservation of energy requires ∆p R = ∆p L = p F . In the end, the energy balance for the right-moving electrons consists of a loss of ǫ F due to removal of one particle from the Fermi level and a gain of ∆Q R = v F p F = 2ǫ F due to the redistribution of momentum. As a result, for every right-moving electron that changes direction, ∆N R = -1, the right-movers' energy increases by an amount ∆E R = ǫ F . It is easy to check that the difference between the chemical potential µ and the Fermi energy ǫ F is irrelevant for our discussion, so we concludeĖR = -µ Ṅ R . (49) It is important to point out that this result is independent of a specific equilibration mechanism, or the degree to which equilibration has occurred. The result (49) can be also expressed in the formQR = -2µ Ṅ R ,(50) cf. | cond-mat.mes-hall |
We define a := ∂ log (F ) ∂ log (p) R(18)= - 1 i * 2 (i * + 1) + d + ∂ ∂ log p log Û d  ĉ(x, β) i * +1 R ,(19) with the help of which the behavior of the transition point can be expressed asp ∝ F χ/2+1/a . (20) As the important information is contained in the exponent we additionally introduceb := χ 2 + 1 a ,(21) which is discussed in detail by means of numerical as well as analytical methods in section IV C 1. Analogously, the relation between R and p at constant flux is obtained from f := ∂ log (R) ∂ log (p) F (22a) = -i * a . (22b) This relation provides a useful means of comparison to the simulation data discussed in section IV C 2 with special respect to figure 8. B. One-dimensional pattern Analytical results The one-dimensional case can be interpreted as a pattern of parallel stripes with spacing p between them and a width of 2 s as depicted in figure 3. In the dimensionless notation of equation ( 13) the value of s is of no relevance, however, as the boundary conditions are supplied by the sinks with ĉ(x = 0) = ĉ(x = 1) = 0. | cond-mat.mtrl-sci |
The influence of the embedded length is most pronounced for a fracture energy of 30 J/m 2 . However, this fracture energy is much less than fracture energies of PP reported in the literature [16,15,18], which range between 300 and 3000 J/m 2 . The decrease of the average shear strength with decreasing fracture energy is explained by the damage distribution in the ITZ along the fibre, which is presented together with the shear stress distribution in Fig. 9. In the present work, the influence of radial stresses and the fracture process on the average shear strength determined by the microbond test were investigated by nonlinear finite element analysis. The work resulted in the following conclusions: CONCLUSIONS • Radial stresses generated by the knife blades and the droplet geometry have a small influence on the average shear strength. | cond-mat.mtrl-sci |
In Eq. ( 23), d α is a phenomenological non-radiative decay rate, representing processes as e. g. exciton annihilation via impurities, escape into the wetting layer, or Auger processes. These processes are not treated explicitly in the present theory. The acoustic phonon scattering rates γ αβ are defined as γ αβ = 2π h q |t q αβ | 2 [(n B (hω q ) + 1)δ(E β -E α -hω q ) + n B (hω q )δ(E β -E α + hω q )] (25) where n B (hω q ) is the Bose-Einstein distribution of acoustic phonons with dispersion hω q = hsq (s -sound velocity). They obey the relation of detailed balance between in-and out scattering of a given state, γ βα = γ αβ e (Eα-E β )/kB T ,(26) with the phonon (i.e. lattice) temperature T . | cond-mat.mes-hall |
At the lowest temperature a negative MCE is possible. A. Calculation of mean field order parameters and thermodynamics In this section the magnetothermal properties will be investigated in mean field approximation to have a reference for the spin wave and numerical exactdiagonalization methods. The results of the former are, however, not expected to give a realistic description of the MCE. For a unified treatment of AF phases it is advisable to use a four-sublattice description (α, β = A, B, C, D) with each sublattice having N/4 sites for both NAF and CAF. Since we consider only isotropic exchange we may assume without loss of generality that the field is perpendicular to the (xy) plane of the square lattice, i. e., h = hẑ. | cond-mat.str-el |
For the effective impurity model entering the DMFT, this means that only one of the impurity orbitals connects to the rest of the system through an effective hybridization function defined by D 2 2 Ĝloc (z) 11 . In the following, this quantity is represented by an auxiliary set of dynamical degrees of freedom, which we will call an effective bath. The Hamiltonian representing the effective impurity model can now be written as H = k ǫ k a † kσ a kσ + kσ γ k a † kσ c 1σ + c † 1σ a kσ + ασ E α n ασ + H local ,(5) where a kσ are the auxiliary annihilation operators with quantum number k and spin σ defining the effective bath, E α = -µ is the energy level for the impurity site, n ασ = c † ασ c ασ and H local the local interaction term as defined in (3). The set of parameters for the effective bath {ǫ k , γ k } must be determined self-consistently through the DMFT condition eq. ( 4). The Hamiltonian (5) represents a quantum impurity model, which is a challenging theoretical problem on its own account. | cond-mat.str-el |
Therefore, the Mie-Grüneisen equation of state with cubic shock velocity as a function of particle velocity defines pressure as p = ρ 0 c 2 µ 1 + 1 -Γ 2 µ -Γ 2 µ 2 1 -(S 1 -1) µ -S 2 µ 2 µ+1 -S 3 µ 3 (µ+1) 2 2 + + (1 + µ) • Γ • E, µ > 0; ρ 0 c 2 µ + (1 + µ) • Γ • E, µ < 0; ,(4)c = K ρ 0 , (5) where E is the internal energy per initial specific volume E = e ρ 0 , K is the classical bulk modulus, S 1 , S 2 , S 3 are the intercept of the U -u p curve. Parameters c, S 1 , S 2 , S 3 , γ 0 , a represent material properties which define its EOS. Parameters have been defined to cover a large number of isotropic materials [19]. AN ANISOTROPIC EQUATION OF STATE Before discussing an anisotropic equation of state, the generalized decomposition of the stress tensor is summarized in [10]. The generalized decomposition framework will provide a useful point of construction an anisotropic equation of state. Generalized decomposition of the stress tensor: α-β decomposition The definition of pressure in the case of an anisotropic solids should be the result of stating that the "pressure" term should only produce a change of scale, i.e. | cond-mat.mtrl-sci |
One might argue, on similar grounds, that for our s = 1 model a first-order transition for the stripe phase might be more likely than for the Néel phase. We stress again, however, that our own results do indicate a direct second-order transition between these two phases below the QTCP. In a similar vein one might wonder too whether for the present spin-1 J 1 -J ′ 1 -J 2 model there might exist a narrow strip of some intermediate phase, which could perhaps also act to reconcile our results with standard Ginzburg-Landau theory. Again, such a possibility cannot be ruled out with complete certainty by any numerical calculation such as ours. However, we have shown that our own extrapolation schemes are sufficiently robust and show sufficient internal consistency to rule out any but a very narrow strip of an intermediate phase for 0 < J ′ 1 /J 1 0.66. We estimate that the width of such a strip cannot exceed by more than a factor of three or so that shown in fig. | cond-mat.str-el |
These Green's functions may be computed by standard methods. 25 A general expression is presented in Appendix A; for our actual computations we will use the infinite bandwidth limit in which the level broadening is independent of ω so that G </> 0 (t ′ , t ′′ ) = ±i α=L,R Γ α dω 2π e -iω(t ′ -t ′′ ) 1 ∓ tanh ω-µα 2T (ω -ǫ d -U/2) 2 + Γ 2(20) with the upper sign pertaining to G < 0 and the lower sign to G > 0 . B. Detailed balance and fast updates The algorithm samples auxiliary Ising spin configurations {(t K,1 , s 1 ), (t K,2 , s 2 ), . . . | cond-mat.mes-hall |
F-D-N SYSTEM We start by considering a F-D-N system, i.e., only one of the leads is ferromagnetic with spin polarization p. To set a reference, we first consider the case of noninteracting electrons, U = 0. Afterward, we study the limit of strong Coulomb interaction, U = ∞. For the latter limit, the direction of electron transfer, from ferromagnet to normal lead or vice versa, will have an import influence on the FCS. In both limits we constrain ourselves to the shot-noise regime, in which only unidirectional transport is possible. Hence, the Fermi functions are f r (ε) = 1 and 0 if r refers to the source and drain leads, respectively. Furthermore, in the limit of strong Coulomb interaction, we put f r (ε + U ) = 0. | cond-mat.mes-hall |
There is a minor narrowing of the t 2g and e g bands of ∼ 0.2 and 0.1 eV, respectively, as well as a slight up-shift of the center of gravity of the t 2g bands (∼ 0.1 eV) with decreasing JT distortion. In Fig. 2 we display our results for the GGA total energy as a function of the JT distortion δ JT . Notice that, in agreement with previous studies, 6,44 the electron-lattice interaction alone is found insufficient to stabilize the orbitally ordered insulating state. The non-magnetic GGA calculations not only give a metallic solution, but its total energy profile is seen to be almost constant for δ JT < 4 %, with a very shallow minimum at about 2.5 %. This would imply that KCuF 3 has no JT distortion for temperature above 100 K, which is in clear contradiction to experiment. | cond-mat.str-el |
An interesting property of mixed states is that they present the "wrong" curvature; that is, the electronic compressibility ∂ 2 f e /∂φ 2 is negative. Generally, this does not imply a thermodynamic instability since the usual stability condition of positive compressibility must be formulated for the global neutral system thus including the background compressibility. Since in frustrated phase separation analysis, the inverse background compressibility is assumed to be an infinite positive number (the background density is fixed to the uniform average value φ), it follows from this point of view that the system is in a stable MS. An important difference with ordinary phase separation resides in the behavior of the local densities of the domains. In unfrustrated phase separation the two phases have a constant density independently of the global density. In frustrated phase separation the local density of the domains decreases with an increase of the global density [42,40]. Assuming that the Curie temperature is an increasing function of the local density, rather than the global density (controlled by doping), this could explain [12] the puzzling maximum of the Curie temperature in the three-dimensional perovskite manganite La 1-x Ca x MnO 3 at x = 0.35 Ca doping [45] not predicted by the conventional double-exchange mechanism [46,47,48]. | cond-mat.str-el |
For the moment we assume an interface configuration with the semi-infinite electrode at right and the film at left. The situation is sketched in Fig. 3, which also illustrates the following discussion. We first compute the planar average of the local electrostatic potential, V H (r), further convoluted with a Gaussian filter of width α to suppress the short-range oscillations, V (d, z) = 1 √ παS V H (d, r ′ )e -(z-z ′ ) 2 /α 2 d 3 r ′ . (20) Next, we identify two z coordinates on either side of the interface, z F in the film and z M in the metal. Both z F and z M must be located far enough from the interface that the short-range structural distortions related to interface bonding have already relaxed back to the regular 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Potential z ∆V ∆V 0000000000000000 0000000000000000 0000000000000000 1111111111111111 1111111111111111 1111111111111111 00000000000 11111111111 V B z 3c δ M V(z) F z M 5 E c F M bulk φ f FIG. | cond-mat.mtrl-sci |
16 Third, the randomness causes relaxation of the spin component along the growth axis observed in Ref. [17] in GaAs (011) QW, investigated now for spintronics applications. 17,18 Fourth, the most recent example of the system with random SO coupling is graphene, where the randomness and spin relaxation appear due to the rippling of the layers 19 and due to the disorder and electronphonon coupling in the substrate. 20 In this paper we study the effects of randomness on the spin relaxation and spin injection. We show that spin relaxation reveals interesting quantum effects arising from the non-commutativity of the momentum and coordinate-dependent randomness. The calculated spin injection can be observed in a wide range of frequencies, extended up to the electron Fermi energy. | cond-mat.mes-hall |
This work made quantitative predictions about properties of the carrier density distribution, both at and away from the Dirac point, and enabled Ref. 45 to develop an effective medium theory to calculate the graphene's conductivity through these inhomogeneous puddles, capturing quantitatively the minimum conductivity plateau that is seen in experiments. 1,19,46 We mention that underlying the existence of this minimum conductivity plateau is the high transmission of graphene p-n junctions, which has been the subject of theoretical 47,48 and experimental study. 49,50,51 For the purposes of this paper we do not discuss quantum interference effects (see Ref. The remainder of this paper is structured as follows. In Section II we discuss the problem of the screening of a single Coulomb impurity in the sub-critical regime as a useful toy model to understand the many impurity problem that we address in Section III where we study the case of many Coulomb impurities that are uncorrelated and distributed uniformly in order to study the ground state properties of graphene. | cond-mat.mes-hall |
However, in the intermediate temperature range ω saddle πT < ω drift [note the π prefactor difference in Eqs. ( 16) and (17)], important spatial redistribution of the spectral weight occurs at the saddle-points, so that tunneling structures broader than the magnetic length become visible, see the wide "bridge" connecting tunneling trajectories in Fig. 3 at finite temperature. An important remark concerns how accurate is Eq. ( 13) for an arbitrary potential V (r), since two assumptions were made in our derivation: (i) large Landau level separation ω c ≫ l 2 B ∆ r V , i.e., ω c ≫ ω 0 for the model (15); (ii) local description of V (r) up to second order spatial derivatives. Condition (i) is well satisfied in the experiments, as the analysis of the typical spatial variations of the LDoS maxima lead to a rough estimate ω 0 3meV, while ω c = 70meV at B = 12T for InSb. | cond-mat.mes-hall |
Blue (black in Fig. 1) and red (grey in Fig. 1) balls correspond to the atoms in the icosahedral binary model. Atoms on the border, which are not allowed to move, are coloured in yellow and green. On the left the atomically sharp seed crack can be seen. Due to the high deformation near the crack tip, blue atoms loose their neighbours and show up for short instances. | cond-mat.mtrl-sci |
For ω = 0 and q = 0, the intra-band and inter-band scatterings also yield different contributions. The effective low-energy Lagrangian density of the smectic Goldstone mode φ Φ (a real field in position space and time) takes the form (see Appendix D) L φΦ = g 2 S | Φ| 2 N S (0) B(ϕ q ) ω 2 k F g S | Φ| + iA(ϕ q ) |ω|q k F g S | Φ| -κ S (ϕ q )q 2 |φ Φ ( q, ω)| 2 ,(7.2) where ϕ q is the angle between q and the stripe direction and N S (0) is the density of states in the smectic phase. A(ϕ q ), B(ϕ q ), and κ S (ϕ q ) are coupling constants that depend on microscopic details and the direction of q, which reflects the anisotropic nature of the smectic phase. We will neglect the direction dependence of these three coefficients since they result in irrelevant contributions at low energies and long distances. The first term ∝ ω 2 in Eq. ( 7.2) is due to inter-band scattering, while the second, ∝ i|ω|q, is due to intra-band scattering. | cond-mat.str-el |
for H⊥ab and H||ab. This behavior may be ascribed to the FM preordered zigzag chain fragments with considerable AFM coupling already above T N . At the Néel transition only the stacking of the zigzag chains becomes better dened. In this sense the AFM transition may be considered as an order disorder one. 32 The ratio between M ⊥ and M || agrees with the expectations for an AFM order of moments aligned within the ab planes due to an easy-plane anisotropy. Below T ≈ 135 K M ⊥ is larger than M || , whereas the opposite is observed in the paramagnetic phase. | cond-mat.str-el |
When g ≪ 1, g is approximately related to the longitudinal conductivity σ xx by σ xx ∼ (e 2 / )g. [24] We also calculate the Hall conductivity by substituting the eigenstates of the disordered system to Kubo formula, Eq. ( 5). For every quantity, we take an average over a number of samples with different configuration of the disorder potential and boundary phase factors φ x , φ y . The absolute value of σ xy generally depends on the k-space cut-off. This is because σ xy can be expressed as the summation of the contribution from all the occupied states below the Fermi energy, unlike σ xx which only depends on the states at the Fermi energy. In the clean limit, the cut-off at ε = ±ε c leads to overall shift of σ xy (ε) by a constant, (e 2 /h)∆/ε c , which is the contribution from the missing states out of the cut-off. | cond-mat.mes-hall |
Ledges seem to be produced only for the smallest angles measured from the crack propagation direction. Fourth, less clusters are intersected by the fracture surfaces than by the flat seed cracks. Fifth, a seed crack at a low energy cleavage plane deviates to a parallel plane to reduce the number of cluster intersections in spite of the higher energy required to form the fracture surfaces. In contrast, a crack built-in at this new position does not show such a deviation. Another observation of the simulations is that the plane structure of the quasicrystal also influences fracture. The fracture surfaces that are located perpendicular to the twofold and fivefold symmetry axes show constant average heights. | cond-mat.mtrl-sci |
The term proportional to M in Eq. 1 produces the anomalous Hall voltage and, in transition metal ferromagnetic films, it is usually orders of magnitude larger than the ordinary Hall term. The robustness of the AHE signal offers one a potentially important probe of localization effects as manifest in the three predominant AHE channels: intrinsic inter-band scattering, skew scattering, and side-jump scattering [5]. The theoretical treatment of the AHE has a long and contentious history, but in recent years there has been a significant interest in how disorder-enhanced quantum correlations affect the low-temperature behavior of the AHE and, in particular, how such corrections are related to the well-established weak-localization corrections to the longitudinal transport [1]. This remains an open issue, particularly in the regime of moderate to strong disorder [6,[9][10][11]. In this Letter, we present a study of the lowtemperature anomalous Hall effect as a function of the sheet resistance of homogeneously disordered CNi 3 films. | cond-mat.str-el |
These break the (ss/ot)/(os/st) symmetry, but act to restore other symmetries broken in the VB ansatz. At α = 1, the energy and degeneracy from the VB ansatz are exact, showing that the orbital sector is classical andintroduces no resonance effects. Figure 11(a) shows the complete spectrum of the triangular cluster for all ratios of superexchange to direct exchange, and in the absence of Hund coupling. Frustration of spin-orbital interactions is manifest in rather dense energy spectra away from the symmetric points, and in a ground-state energy per bond significantly higher than the minimal value -J. At α = 0 the spectrum is rather broad, with a significant number of states of relatively low degeneracy due to the strong fluctuations and consequent mixing of VB states in this regime. However, even in this case the ground state is well separated from the first excited state. | cond-mat.str-el |
We reproduce all the values of Eq. 15 with errors bounded by 3 × 10 -4 . Discussion.-In this paper we have explained how to compute the ground state of a critical Hamiltonian using the scale invariant MERA and how to extract from it the properties that characterize the system at a quantum critical point. Our results, which build upon those of Ref. [3,4,5,6,7,8], also unveil a concise connection between the scale invariant MERA and CFT. This correspondence adds significantly to the conceptual foundations of entanglement renormalization. | cond-mat.str-el |
(28) The factor of 2 here is due to the sublattice pseudospin degree of freedom. As already stated above, real spin and valley degrees of freedom enter our calculations only through the trivial degeneracy factors they imply. Given a value of k c the Kohn-Sham-Dirac matrix H KSD k,k has d H eigenvalues, labeled by the discrete index λ = 1, . . . , d H . | cond-mat.str-el |
Since we are interested in the morphology of fracture surfaces we apply a sample form that allows us to follow the dynamics of the running crack for a long time. For this purpose, a strip geometry is used to model crack propagation with constant energy release rate 32 . The samples consist of about 4 to 5 million atoms, with dimensions of approximately 450r 0 ×150r 0 ×70r 0 . Periodic boundary conditions 33 are applied in the direction parallel to the crack front. For the other directions, all atoms in the outermost boundary layers of width 2.5r 0 are held fixed. An atomically sharp seed crack is inserted at a plane of lowest surface energy, from one side to about one quarter of the strip length. | cond-mat.mtrl-sci |
We have previously shown however, that good agreement with experimental data is achievable by assuming T e = T +20 K. 16 In fig. 4, we show the average intersubband scattering rate as a function of subband separation at T =4 K, T e =24 K. For L=0 nm and subband spacing closer than 10 meV, ionized impurity and electron-electron scattering domi- nate, while at spacings between 10 meV and 55 meV, interface roughness and intravalley acoustic phonon scattering are fastest. As the subband spacing becomes comparable to the energy of the g-LO phonons, the emission rate exceeds the intravalley acoustic phonon scattering rate. Alloy disorder scattering is again shown to increase significantly with interdiffusion and becomes dominant for subband spacing above 10 meV and L=2 nm. B. (111) n-type single QW Several important changes are introduced by moving to the (111) orientation. | cond-mat.mes-hall |
So in case I-b), µ = 5 × 10 -6 . Thus, assuming either regime I-a) or I-b), the experimental results could be explained by an extremely weak pinning potential, V 0 K ⊥ = 10 -6 ∼ 10 -5 . Heating effect in metallic samples has indeed been found to be crucially important. 57 Use of short pulsed current of ns order could be useful in avoiding heating. Sub ns pulse was reported to be quite efficient in driving the wall at low current density of ∼ 10 10 A/m 2 . 65 This could be due to the fact that damping does not affect much for such short timescale. | cond-mat.mes-hall |
This value suggest that the electron-hole puddles are quite small. However a closer inspection reveals that, close to the Dirac point, the density profile is characterized by two distinct types of inhomogeneities 45 : wide regions (i.e. big puddles spanning the system size) of low density containing a number of electrons (holes) of order 10; and few narrow regions, whose size is correctly estimated by ξ, of high density containing a number of carriers of order 2. This picture is confirmed by the results shown in Fig. 4 in which the disorder averaged area fraction, A 0 , over which |n(r) -n | < n rms /10 is plotted as a function of n imp . We see that A 0 is of order 1/3 and we also find that the area fraction over which |n(r) -n | is less than 1/5 of n rms is close to 50% for n imp 10 11 cm -2 . | cond-mat.mes-hall |
The results show that significant percentage of uncorrelated H frustrated domains are easily formed in the early stages of the hydrogenation process leading to lattice decreased values and extensive membrane corrugations. These results also suggest that large domains of perfect graphane-like structures are unlikely to be formed, H frustrated domains are always present. The molecular dynamics simulations of the hydrogenation showed that one formed hydrogenated domains are very stable. Table 1. DMol 3 results for the crystalline structures shown in figure 1. The energy per atom in the unit cell, the cell parameter values and the carbon-carbon distances are displayed. | cond-mat.mtrl-sci |
The current at contact, say, 1, I 1 (t) = R C I 1A (t)+ T C I 1B (t) (here T C = 1 -R C = |t C | 2 ) , consists of a current coming from source A (B) reflected (transmitted) at the central QPC and passed through the interferometer L. At zero temperature, the partial current I 1α (t), α = A, B, comprises a classical part due to the current generated by the capacitor, I α (t) = e 2 2πi ∂Uα ∂t S (0) * α (t) ∂ ∂E S(0) α (t), and an interference part, I 1α (t) = R l L R r L I α (t -τ d Lα ) + T l L T r L I α (t -τ u Lα )(3) + eγ L /π τ u Lα -τ d Lα Im S (0) * α (t -τ u Lα )S (0) α (t -τ d Lα )e -iΦL . The current in contact 2 is found analogously. Here we introduced the instantaneous scattering matrix of the cavity α at the Fermi energy µ, Sα (t) = S α (µ -eU α (t)(0) ). The transmission probability at each MZI beam splitter is T j β = 1 -R j β = |t j β | 2 and γ β = (R l β R r β T l β T r β ) 1/ 2 is a product of the reflection and transmission coefficients. Furthermore the flux enclosed by the interferometer β is given by Φ β = Φu β -Φd β , in units of Φ 0 /(2π), where Φ 0 = h/e is the magnetic flux quantum. As the coherent emission of quantized charge attracts our special attention, we now treat the case of small transmission of the cavities' QPCs, where the current emitted by a cavity is a series of well separated pulses of opposite sign for the emission of electrons and holes. | cond-mat.mes-hall |
In the region of |E| <1.0V/m, the shift ∆ k in the nonequilibrium Green's function in Eq. ( 7) is about 0.01t c , which is about 1/100 of the band gap of θ d -(ET) 2 X obtained in the tight-binding approximation. Although ∆ k is small, there is an error in the replacement of G <(2) (k, ω) in (8) into G < (k, ω) in (9). This error can be estimated by, δ = G <(2) (k, µ) -G < (k, µ) G <(2) (k, µ) ,(11) which is about 10 -3 for |E| < 1.0V/m. However, when |E| is larger than 1.0V/m, the error exceeds 0.3, since β∆ k appearing in n F (ω -∆ k ) becomes close to 1 at the low temperature (5K, for example). This means that in the higher electric fields, the error becomes larger, and higher order correlations in (8) become necessary. | cond-mat.str-el |
The width dependence of the strength of the low energy peak for ZZ-BLGNRs is given in Figure 6. For very narrow ribbons with p < 6 the peak quickly decreases in magnitude at a decreasing rate. For p > 6 however, the peak magnitude increases steadily reflecting the low energy subband shape. As the width increases, the low energy subbands remain lower, which increases the DOS, allowing more transitions between subbands. For very narrow width ZZ-BLGNRs however, the curvature in the subbands is so high that the velocity operator allows strong coupling between the subbands, which makes the low energy magnitude very strong. In summary, we have shown that the interplay of ribbon's chirality and the inter-ribbon coupling can lead to significant enhancement in optical response. | cond-mat.mes-hall |
The detection principle relies on the exponential current sensitivity of the switching of a JJ from a metastable zero-voltage branch to a dissipative one. When biased at a current I J slightly below its critical current I 0 , the rate of switching is therefore very sensitive to noise in the current. The first detection of asymmetric noise with a JJ was reported in Refs. [7,8]. However, the detector JJ, which was placed in an inductive environment, had a very large plasma frequency, and the dynamics of the junction changed regime as the noise intensity increased, from macroscopic quantum tunneling (MQT) to retrapping [10] through thermal activation. The measured asymmetry in the escape rates could only be compared to an adiabatic model [11], using empirical parameters. | cond-mat.mes-hall |
The MS states exist for defect potentials in between two gapclosings, indicated as a function of U0 by the shaded regions in the inset. (The red solid and blue dashed curves show, respectively U0 + δU0 and U0 + δUπ. The label T indicates the topologically trivial phase.) has dispersion relation E 2 = [U 0 + 2β(2 -cos ak x -cos ak y )] 2 + γ 2 sin 2 ak x + γ 2 sin 2 ak y . (2) (We have defined the energy scales β = 2 /2ma 2 , γ = ∆/a.) The spectrum becomes gapless for U 0 = 0, -4β, and -8β, signaling a topological phase transition [25]. | cond-mat.mes-hall |
3 (a) we have summarized these observations, plotting the behavior of the resistance steps against the current bias. The measurements done in scheme B deliver an additional curve for F4; this electrode is now under positive bias, and the sign of both the spin valve signal as well as I DC is reversed. These experiments indicate, that biasing the injector electrodes yields a dramatic change in their spin injection efficiencies, enhancing the spin valve signal to a saturation value or suppressing it completely. Applying Equation (1) for the spin valve signal we measured in scheme B, at +5 µA bias we calculate a spin polarization P inj = 43% for the contact between F4 and graphene. To do this, we keep the spin polarization of the unbiased detector/graphene contact P det at the original 25%. In case of maximum reverse bias on the other hand, the AC measurements show a reversed spin valve behavior (see panels (i) on Fig. | cond-mat.mes-hall |
There are further attempts [24,25] at bridging polynuclear and/or heterometallic units by halogens. Hundreds of MX compounds have thus been synthesized and studied, but they all have single-chain-assembled structures. In such circumstances, several chemists designed MX ladders [26,27]. Platinum-halide doublechain compounds, (µ-bpym)[Pt(en)X] 2 X(ClO 4 ) 3 •H 2 O (X = Cl, Br; en = ethylendiamine = C 2 H 8 N 2 ; µ-bpym = U M U X t MM t MX α u n:l 1 M u n:l 1 X ( ) u n:l M u n:l X K MX ( ) u n 2:l M u n 1:l M β X ε X β M ε M ( ) u n 3:l X u n 2:l X V MM V MX V XX V MM V MM V XX V MX V XX V XX V MM M dz 2 pz X Fig. 1: (Color online) Modelling of an MX quadratic prism, where heavily and lightly shaded clouds denote M d z 2 and X pz orbitals, the electron numbers on which are given by n n:lM s ≡ a † n:lM s a n:lM s and n n:lXs ≡ a † n:lXs a n:lXs , respectively. The on-site energies of isolated atoms are given by εM and εX , while the electron hoppings between these levels are modelled by t MX and t ⊥ MM . | cond-mat.str-el |
The introduction of the interaction term λm in the Eq. ( 1) modifies the character of relaxation. Namely, under magnetization reversal this term becomes time dependent as it comprises the magnetization m(t). This means that the overall magnetization relaxes not to the above real equilibrium magnetization M ∞ = M ∞ (H, T ), but to certain (so far unknown) self-consistent equilibrium magnetization value, dictated by the effective magnetic field H + λm(t) at each time point. We denote this new hypothetical equilibrium magnetization as m * ∞ (t), and its normalized value as M * ∞ (t r ) = m * ∞ (t r /f 0 )/m p . Here we note, that M * ∞ (t r ) = M * ∞ [H, T, M(t r ) ] so that the kinetic equation for magnetization assumes the form: ∂M(t r ) ∂t r = 1 τ r [M * ∞ -M(t r )],(2a) where M * ∞ (t r ) is determined by the equation M * ∞ (t r ) = tanh m p [H + λm(t r /f 0 )]V p kT = tanh 2[h + λ red M(t r )] T red . | cond-mat.mes-hall |
(15) The present analysis readily suggests a correspondence between the scaling operators φ α of the scale invariant MERA, defined on a lattice, and the quasi-primary fields φ CFT α of a CFT, defined in the continuum. Together with the algorithm described below, this correspondence grants us numerical access, given a critical Hamiltonian H on the lattice, to most of the conformal data of the underlying CFT, namely to scaling dimensions and OPE coefficients. The central charge c can also be obtained e.g. [14] from the von Neumann entropy S(ρ) ≡ -tr(ρ log 2 ρ), which for a block of L sites scales, up to some additive constant, as S = c 3 log 2 L [15]. We then have S(ρ) -S(ρ (1) ) = c 3 (log 2 2 -log 2 1) = c 3 , or simply c = 3 S(ρ) -S(ρ (1) ) . (16) Algorithm.-Given a critical Hamiltonian H for an infinite lattice, we obtain a scale invariant MERA for its ground state |Ψ by adapting the general strategy discussed in Ref. | cond-mat.str-el |
In particular, the mechanisms inducing curvature and the nature of the cross-linking sites are still unclear. As already mentioned, in the case of pure C films, the window of processing parameters yielding a FL structure is very narrow, with the FL structure being difficult to control. However, in CN x the formation and control of the FL structure is much easier since, for example, occurs at lower substrate temperatures. This suggests that N incorporation plays a key role for the promotion of buckling of the graphene sheets [13]. The N-induced modification can be attributed to changes in the bonding length and bond angle distortions due to the formation of C-N bonds instead of C-C and, additionally, to the capability of N to accommodate different local atomic arrangements and coordination such as substitutional sites in graphite, pyrrole-like, pyridine-like or nitrile-like configurations [14,15]. These different bonding environments can be identified in Figure 3. | cond-mat.mtrl-sci |
Some weak reflections were observed. Fig. 9 shows the thermal evolution of one of these peaks and, for comparison, also that of the (0,0,4) peak. As evident, the intensity of the (0,0,4) peak, being due to magnetic and nuclear contributions, decrease smoothly and goes to the value of the nuclear intensity as the temperature reaches T c . In particular there is no visible variation in the (0,0,4) intensity when T is varied across T m , indicating that the event at this temperature, does not belong to the main phase. On the other hand, the intensity of the other peak decays very fast as the temperature increases and is almost within the experimental uncertainty when T > 2 K. Such a thermal evolution is similar to the features observed in the magnetization hysteresis (Fig. | cond-mat.str-el |
4. Alternatively, we can use the quantum point contact QPC2, placed near the QD(r2), which measures charge q(r2) of QD(r2). The results of the present calculations allow us to predict the measurement outcomes. For both the nanodevices A and B, we obtain either q(r1) = 0 or q(r1) = -e and either q(r2) = -2e or q(r2) = -e for two different output charge states (Fig. 4). This means that both the nanodevices A and B operate as spin-charge converters. | cond-mat.mes-hall |
V. II. CHERN-SIMONS TRANSFORMATIONS We consider a quantum Hall system with κ internal states, hereafter referred to as "components". In the simplest case of a two-dimensional electron gas at a GaAs/AlGaAs interface, one has κ = 2 for the two possible orientations of the electron spin. The case κ = 4 is relevant for bilayer quantum Hall systems, where a second pseudospin mimics the layer index, or in graphene due to its two-fold valley degeneracy, in addition to the physical spin of the electrons. Higher values of κ are rarely discussed in the literature, but may play a role in the context of multilayer systems or of bilayer graphene, where the zero-energy level consists of the n = 0 and n = 1 Landau levels. 20 The Chern-Simons transformation 2,23 is defined by the relation between the κ original electronic fields ψ α (r) and the κ transformed fields ψ CS α (r) as ψ α (r) = exp -i d 2 r ′ θ(r -r ′ ) κ β=1 K αβ ρ β (r ′ ) ψ CS α (r),(2.1) where θ(r) = arg(x + iy) indicates the angle between the vector r = (x, y) and the e x direction, and ρ β (r) = ψ † β (r)ψ β (r) = ψ CS † β (r)ψ CS β (r) is the density operator of the particles of component β. | cond-mat.mes-hall |
In this paper, we present a doping dependent hard x-ray photoemission study on bilayered LSMO, La 2-2x Sr 1+2x Mn 2 O 7 , with 0.30 ≤ x ≤ 0.475. Although several x-ray photoemission studies on (perovskite) LSMO exist in the literature, for example Refs. [22] and [23], the majority has been conducted either on polycrystals or on single crystals cleaved in air or poor vacuum, disqualifying a comparison between surface and bulk electronic properties. This study is conducted on properly in vacuum cleaved single crystals and carried out using excitation radiation in the hard and soft xray regime on a wide range of doping levels across the metallic part of the phase diagram. Making use of the increased bulk sensitivity with higher excitation energies (several nanometers for 6 keV radiation, instead of a typical ≈ 1 nm for VUV excited ARPES experiments and Al Kα x-ray photoemission studies), owing to the increased mean free path length of escaping photoelectrons with higher kinetic energy, we show that the surface electronic structure of bilayered LSMO is identical to that of the bulk. Furthermore, evaluating the core level shift per element as a function of doping, we show that the chemical potential of bilayered LSMO is not pinned upon approaching half doping, putting strong constraints on the temperature range and length scales at which phase separation could occur for these samples. | cond-mat.str-el |
2 with the analytical predictions given in Eqs. ( 8) and ( 9), one should focus on the B/B f ocus ≥ 1 regime, where the edge states are the current carrying modes. One can see that the peak positions for the armchair nanoribbon are in very good agreement with the prediction of the semiclassical theory. Up to B/B f ocus 5 the focusing peaks are also clearly discernible in the focusing spectra of zigzag nanoribbons but for stronger magnetic fields a more complex interference pattern emerges. The peak at B/B f ocus = 7 for example can clearly be seen for the armchair case. In contrast, for the zigzag edge a number of oscillations with similar amplitudes can only be observed. | cond-mat.mes-hall |
We now show that this is indeed the case. Let a steady current with the drift velocity v 0 flow across the boundary (x = 0) of a semi-infinite sample situated at x > 0. The general boundary condition at x = 0 is defined by the impedance ζ relating the ac voltage and the ac current (compare with Eq. ( 5)):u = ζ(v 0 u + s 2 v x ). (18) The boundary condition at x = ∞ corresponds to the vanishing of the small perturbations, u = v x = v y = 0. The impedance ζ will be considered as purely imaginary: ζ = iλ/s, where λ is the dimensionless parameter proportional to the effective capacitance. | cond-mat.mes-hall |
10 presents the normalized standard deviation of the conductance, for different system sizes, as a function of the temperature. The variations of the conductance are lower than 1% from one realization to the other. This is due to the fact that the conductance is the integral of the transmission function (with the proper weighting function), and therefore the variations of the transmission function for only one realization of the mass disorder are averaged out. Fig. 11 presents the averaged normalized thermal conductance as a function of the system length (in log-log scale) for (5,5) and (10,10) CNTs. Three temperatures are considered in both cases: T = 50 K, T = 300 K, T = 1000 K. The scalings obtained for T = 50 K show that the transmission regime is quasi-ballistic since the conductance does not change much with the system size. | cond-mat.mtrl-sci |
From Figure 6 it can be seen that Ag-nano ink traces has greater losses than the Cu lines due to its thinner profile and lower electric conductivity. However, the difference between insertion losses is not so large and can be tolerated in some applications. Therefore, the results indicate that printed Ag-nano traces have relatively good potential for future RF-circuit applications. NUMERICAL SIMULATIONS Thermal and stress analysis has been done by performing thermo-mechanical Finite Element (FE) simulations. A 2D-transient axisymmetric model was made by ABAQUS. The model consisted of an ink jet printed pad on a polymeric layer under which either a polymer layer, Fig 5, or silicon layer could be place. | cond-mat.mtrl-sci |
For the Fano factor f we find similarly f = N (2πh) 2 g ds α du ′ α ds γ du ′ γ × α,β,γδ A α A β A γ A δ e i(Sα-S β +Sγ -S δ )/h , (13) where the trajectories α and β connect contacts 1 and 2, the trajectories γ and δ connect contact 2 to itself, and the coordinates of the trajectories β and δ satisfy s β = s γ , s δ = s α , u ′ β = u ′ α , and u ′ δ = u ′ γ . These expressions will be the basis of the calculations of the next sections. III. SHOT NOISE In order to establish our methods and relevant approximations we first calculate the Fano factor f . A. Encounter in sample interior Technically, the simplest avenue to a semiclassical calculation of the Fano factor f is to use the unitarity of the scattering matrix to write f as f = - 1 g tr S 21 S † 22 S 12 S † 11 . | cond-mat.mes-hall |
In the first, the current is measured as a time-dependent function It, for example, with a normal ammeter, and then the spectral density So is calculated numerically using a Fourier transformation. The classical equation of motion for an ammeter coincides with the equation for an oscillator with friction and external forceG It f ÀO 2 f À g f lIt X1 Making the Fourier transformation, we express the angleangle correlator as: hf o f Ào i l 2 I o I Ào O 2 À o 2 2 o 2 g 2 X 2 To eliminate proper oscillations, it is usually assumed thatg 4 O 1 O 2 À g 2 a4 1a2 . The method is appropriate for recording ultra-low frequency noise, for instance, flicker noise, but, for various reasons, it cannot be used at high frequencies. For example, as in the case of voltage measurements with a discrete voltmeter there is a `dead' time during which the device cannot record changes in current (below we consider the measurement of a time-dependent current±current correlator with an ammeter). In recording high frequencies it is more suitable to use a resonance circuit (RC) as a detector coupled by inductance with the investigated conductor so that the RC is not affected by dc. In this case the detector can still be described by Eqn (1), but now the external force is proportional to the derivative of the measured current l It, and the circuit quality should be high, so g 5 O. | cond-mat.mes-hall |
The convergence of this series cannot be determined within geometrical theory alone, and needs an additional physical input. By including the interfacial energy cost for creating twin variants, the series of interfaces may be made to converge in the mean to a limiting interface over the Young measure. A parallel approach to the study of martensitic structures was initiated by Barsch and Krumhansl [12]. In this framework, the martensitic structure results from the minimization of a non-linear, elastic free-energy functional where the components of elastic strain are used as order parameter (OP) distinguishing parent and product. Unlike geometrical theories however, this programme can be developed to study the dynamical evolution of microstructure [13,14,15,16]. The driving force for the nucleation dynamics of martensite from the austenite is derived from the same free-energy functional, written in terms of a dynamical elastic strain tensor. | cond-mat.mtrl-sci |
Moreover, B Lz2 is determined by the competition between the Luttinger term and the Zeeman splitting, and B Lz2 decreases as κ increases when κ < √ 6γ 2 . From Eq. ( 5) and ( 6), it is useful to find that the required magnetic field for the resonance may be effectively reduced by enlarging the effective width of the quantum well. Secondly, let us discuss the effect of SIA on this resonant spin phenomenon. The relatively large 5 meV measured spitting [12,23] of the heavy hole band implies that the effect of Rashba spin-orbit coupling arising from the SIA term is important. Energy levels as functions as 1/B with α=10 5 m/s [12,23] are shown in Fig. | cond-mat.mes-hall |
3), it is more appropriate to calculate a continuous C(T ) curve from the time derivative of the relaxation curve directly (solid lines in Fig. 3). The relaxation curve across the transition is shown in the inset of Fig. 3. One immediately notices the shoulder in the heating part which is a direct evidence for a thermal arrest and thus for a first-order transition [13]. Preliminary magnetic field dependent data are also shown in Fig. | cond-mat.str-el |
Although the FQH states are a manifestation of strong electron correlations, the quasiparticles are only weakly interacting. Thus, the zero frequency spectral density of the shot noise (introduced via partitioning) can be well accounted for by an analytic expression that is strictly valid for non-interacting particles [8,9,10]. Transport is more complicated if there are one or more counter-propagating edge channels, as is the case of the so called hole conjugate quantum hall states, ν =2/3, 3/5, etc. In the case of ν =2/3, which is the subject of our present work, a clean sample devoid of any impurities is expected to support two charged modes: one with conductance of e 2 /h -carrying electrons, and a counterpropagating one with conductance (1/3)e 2 /h, carrying e/3 fractional charges [11,12,13]. Inclusion of interaction between the channels leads to a non-universal Hall conductance (in contrast to experimental observations), which depends on the interaction strength [14]. For a smooth edge potential, the two counter-propagating modes will have different momenta (the difference being proportional to the enclosed flux), and hence unlikely to equilibrate. | cond-mat.mes-hall |
Given that nm 0 ∝ Λ (1-s)m , it is feasible to meet this condition as m → ∞ so long as the bath exponent satisfies s ≥ 1. Indeed, for Ohmic and super-Ohmic bath exponents, the NRG spectrum for λ not too much greater than λ c0 is found to be numerically indistinguishable from that for λ = 0. For s < 1, by contrast, the restriction b † m b m ≤ N b leads, for λ > λ c0 and large iteration numbers, to an artificially truncated spectrum that cannot reliably access the low-energy physical properties. Nonetheless, observation of this "localized" bosonic spectrum serves as a useful indicator, both in the zero-hybridization limit and in the full charge-coupled BFA model, that the effective e-b coupling remains nonzero. Another interpretation of Eq. ( 27) is that at the energy scale E = ΩΛ -k characteristic of interval k, the e-b coupling takes an effective value λ(E) governed by the renormalization-group equationd λ d ln(Ω/E) = 1 -s 2 λ,(28) which implies that the e-b coupling is irrelevant for s > 1, marginal for s = 1, and relevant for s < 1. | cond-mat.str-el |
To treat longer-ranged correlations, the Jastrow factor includes a two-body plane-wave expansion, p(r ij ) = A,GA a A cos(G A • r ij ). Those reciprocal lattice vectors, {G A }, that are related by the point group symmetry (denoted by A) of the Bravais lattice share the same optimizable parameters, a A . To ensure accuracy we checked the stability of the VMC results when the expansion order of the u and p terms was increased. At all densities the Jastrow factor optimized cutoff lengths took the maximum allowed value (the Wigner-Seitz radius). The DMC calculations were performed with 57 different reciprocal lattice vectors and, following Ortiz and Ballone [35], Ceperley [36], and Ceperley and Alder [37], further VMC calculations were performed at other system sizes (27,33,57, and 81 reciprocal lattice vectors) to derive the parameters to extrapolate the DMC energy to infinite system size. Additionally, all the DMC results were extrapolated to have zero time-step between successive steps in the electron random walk. | cond-mat.str-el |
For illustration, we present the case of plutonium where the Slater integrals parameters are given in Table I. Figure 1 presents the atomic spectrum of eigenvalues of Pu without spin-orbit coupling, for a given occupancy of N = 5 electrons. The different approximations with increasing order of complexity are displayed: single U , density-density approximation and spin-flip terms included respectively. Figure 2 displays the same situation when spin-orbit coupling has been taken into account for occupancies of N = 5 and N = 6 electrons. The most accurate description is given when the spinflip terms are not neglected. In this case, the spectrum is much more structured than the result for the density-density approximation. | cond-mat.str-el |
The energy of the relaxed monoclinic lattice is about -4.1 eV/atom which is in a good agreement with the values extrapolated from experimental data [15]. Similarly, the energy difference between the δ and α structures used in our simulations is about 0.3 eV/atom, which agrees with the total internal energy differences estimated in [21] by accounting for the thermal expansion of the lattice within each phase. The calculated volume of the α structure is 20.8 Å3 /atom which slightly overestimates the measured experimental volumes extrapolated to 0 K. Energetics of transformation pathways In the most general situation the prominence of individual phonon modes varies along the transformation pathway, and this necessarily gives rise to the motion of atoms along curvilinear paths. Unless one performs a more sophisticated simulations, such as the nudged elastic band (NEB) method [22], which cannot be done at present due to apparent difficulties of the MEAM potential to reproduce the positions of atoms in the α structure (more on this later), the information about the prominence of individual phonon modes is not available. Hence, one is forced to assume that the superposition of a number of phonons responsible for a given transformation results in the motion of atoms along the shortest paths connecting their initial and final positions, which is a simplification that we also adopt in our simulations here. Although these calculations were carried out for pure Pu, our conclusions are qualitatively valid also for dilute alloys of Pu with Ga, Al, Ce or Am that stabilize the fcc δ phase down to essentially 0 K. The reason is that low concentrations of these impurities do not change significantly the lattice parameters. | cond-mat.mtrl-sci |
[53]. Furthermore, for all three systems, a soft-core Coulombic e-e pair potential has been applied: u(|x -x |) = (x -x ) 2 + 1 -1/2 . For the 1D helium atom, we have used 11 finiteelements within an interval of x 0 = 50 a.u. length. Some smaller FEs have, thereby, been arranged around x 0 /2 to ascertain larger numerical precision in the central region. Further, the number of local DVR basis functions n g + 1 has been varied between 5 and 20 to obtain convergence of the ground-state energy E gs , and, in Eqs. | cond-mat.str-el |
, b ′ 4 ), which is a column vector of only nine (as opposed to eleven) gauge fields, Eq. 16 becomes: L = 1 4π ǫc T K∂c - e 2π ǫ(q • c)∂A + ( l ℓ ℓ • c) µ j µ V + . . . ,(34) where q = (1; O 1,5 ; O 1,3 ) T is the transformed charge vec-As for topological excitations, from the transformation between c and c, it can be seen that the correspondence between ℓ ℓ ℓ and l ℓ ℓ reads: ℓ ℓ ℓ = (0; n a1 , . . | cond-mat.str-el |
The CP simulations of metallic systems were performed with the algorithm proposed in Refs. [33] and [34]. The simulated systems are periodically repeated in all directions of space. Surface models were constructed including in the simulation cell a slab of a few layers of metal atoms separated from its periodically repeated image by a vacuum layer in the direction perpendicular to the surface. The thickness of the slab and of the vacuum layer have been chosen so as to avoid spurious effects due to truncation of the crystal or interactions with the image systems. Details of the simulation parameters and test calculations to assess the precision of the formalism can be found, in particular, in [3,35,36]. | cond-mat.mtrl-sci |
8 We characterize the films with optical transmission both in the as deposited state and after high temperature desorption. We find optical signatures (in the IR and UV regions) of the formation of NaAlH 4 , which decomposes into NaH and Al after annealing. The effect of metallic Ti doping is also explored. We observe for both the undoped and Ti-doped samples that the annealing induces a macroscopic Al segregation, which probably hinders the reverse reaction under moderate conditions. This result opens the route to the analysis of the storage properties of the sodium alanate and other light-weight complex metal hydrides, such as LiAlH 4, with combinatorial techniques. 3 A schematic view of the setup used for the deposition and optical characterization is shown in figure 1. | cond-mat.mtrl-sci |
Fig. 3(c) shows the calculated conductivity as a function of back and side gate voltages, as compared to the measured data plotted in Fig. 3(b). The white corner are in a gate voltage regime which is not accessible from the extrapolation of the data taken at V SG = 0. V BG (V) (4•4e /h) V SG (V) (4e /h) 6 14 V BG (V) V SG (V) +VSG -VSG +VSG -VSG (a)(b) (c) (d) exp. calc. | cond-mat.mes-hall |
We should keep in mind that this approximation breaks down if the fluctuations are not small with respect to the average densities. In particular, the approximation is certainly invalid if one of the average densities is zero. We therefore assume that none of the average densities n α vanishes. However, in the case of a singular charge matrix K, a redefinition of the filling factors might lift this problem, as will be discussed in more detail in Sec. IV. The Hamiltonian H aux in Fourier space is approximated by H osc = q α n α L 2 2m e 2 a • α (-q)a • α (q) + b 2 β γ P • β (-q)K βα K αγ P • γ (q) ,(3.7) where we note that a • (-q) = (a • (q)) † and P • (-q) = (P • (q)) † . | cond-mat.mes-hall |
The O 2p valence band width is 4.0 eV from about -1.8 to -5.8 eV, in qualitative agreement with the photoemission value of 5.0 eV from -3.0 to from -8.0 eV [16]. As for the unoccupied U 5f and 6d orbitals, their accurate descriptions are also indispensable to the interband transitions, since electrons are excited from the occupied valence bands to the unoccupied bands during optical excitations. The 5f and 6d bands begin at about 2.3 and 4 eV, respectively, which are consistent well with the results of 2.6 and 5 eV obtained by hybrid DFT method [17]. Note that our calculated p → d gap is 5.8 eV, which accords well with the Bremsstrahlung Isochromat Spectroscopy (BIS) value of 5.0±0.4 eV [18]. Overall, our calculated DOS agrees well the experimental spectra and other theoretical results. This supplies the safeguard for our following optical spectrum calculations. | cond-mat.str-el |
We take the associated eigenvalue, E 0 = -3N J/8, as the zero of energy. A. Excitations Excitations are formed by breaking singlets to create triplets. The spectrum of H 0 then consists of degenerate levels at energies nJ relative to the ground state, where n < N/2 is the number of triplets. These excitations are dispersionless hardcore bosons. When the perturbation H ′ is applied the degeneracies are removed and coherent single-particle excitations with dispersion relation ǫ p are formed. These magnons are not free, but interact with each other through the perturbation H ′ in addition to being subject to the hard-core constraint. | cond-mat.str-el |
3), but it changes to positive values with increasing temperature around T C ≈ 168 K, corresponding to the magnetic transition from the AFl to the Fmc state (Fig. 3). An inverse MCE has been often observed in systems displaying first-order magnetic transitions and the origin is the same for all of them. Due to the presence of mixed exchange interactions, the applied magnetic field leads to a further spin-disordered state near the transition temperature, increasing the configurational entropy 8 . As shown in Fig. 4(b), the -ΔS M max peak position moves to the low temperature side with increasing magnetic field. | cond-mat.mtrl-sci |
Then considering the tunneling process corresponding to W υ (C Λ ), we obtain the perturbative energy as δE = n | ĤI ÛI (0, -∞) | m (24) = n | ĤI ∞ j=0 Û(j) I (0, -∞) |m = n | ĤI Û(L-1) I (0, -∞) |m Now it is noted that the operator ĤI Û(L-1) I (0, -∞) is proportion to a topological string operator W υ (C Λ ). Considering all tunneling processes, we may denote the ground state energies as a four- For the first tunneling process, a virtual Z 2 vortex (or Z 2 charge) will run around the torus as long as a path with length L 0 that is equal to LxLy ξ . Here ξ is the maximum common divisor for L x and L y . For example, on a 3 × 3 lattice, we get L 0 = 3×3 3 = 3; on a 3 × 5 lattice, we get L 0 = 5×3 1 = 15. From Eq. (25), one may obtain the energy splitting ∆E of the two ground states asδE = U (L) I = ↑| ĤI (1E 0 -Ĥ0 ĤI ) L 0 -1 |↓ . | cond-mat.str-el |
This generator contains all terms which couple to the subspace without DOs. Note that this subspace is a highdimensional subspace and not a single ground state for the model under study in contrast to the situation considered by Fischer et al. 17 . But the other conceptual points, e.g., concerning the formulation in second quantization and the differences to a matrix formulation 24 are the same. The Hamiltonian and its evolution under the CUT induced by the gs-generator ( 13) is graphically represented in Fig. 7. | cond-mat.str-el |
( 4). The result is a non-self-consistent calculation which tests whether a given OF functional can reproduce T s [n KS ], or at least ∇ R T s [n KS ] if n KS is provided. There is no sense in trying to solve Eq. ( 3) with an approximate OF functional that cannot pass this test. Acknowledgments We acknowledge informative conversations with Paul Ayers, Mel Levy, Eduardo Ludeña, John Perdew, Yan Alexander Wang, and Tomasz Wesolowski. This work was supported in part by the U.S. National Science Foundation, grant DMR-0325553. | cond-mat.mtrl-sci |
(10) Remark 1. The positive-parity representation of B 4 , generated by R(2,+) j , looks different from that obtained in Ref. [25] by analytic continuation of the 4-anyon Pfaffian wave functions (with generators B (4,+) j there), however, as proven in [25], these two positive-parity representations are equivalent and the matrix establishing this equivalence is simply Z = diag(1, -1). It is worth-stressing that the two inequivalent representations S ± of the braid group B 4 , generated from the elementary braid matrices ( 9) and ( 10) respectively and their inverses coincide as sets of matrices. This is because as we saw before R(2,+) 1 = R (2,-) 1, and because R (2,+) 2 R (2,-) 2 = R (2,+) 3 R (2,-) 3 = iI 2 . Note that the matrix iI 2 does belong to both representations of the braid group B 4 , i.e., R (2,±) 1 R (2,±) 2 R (2,±) 3 2 R (2,±) 2 R (2,±) 1 = ±iI 2 . | cond-mat.mes-hall |