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magnetic field are analyzed under weak population of one-dimensional subbands that gives rise to the efficient quenching of the kinetic energy by the exchange energy of carriers. The critical linear concentration of carriers above which the quasi one-dimensional gas undergoes a complete spin depolarization is determined by the Hartree-Fock approximation. The dependence of the critical linear concentration on the carrier’s concentration is defined to reveal the interplay of the spin depolarization with the evolution of the "0.7 ? ( 2e 2 / h )" feature in the quantum conductance staircase from the e 2 / h to 3 / 2 ? (e 2 / h ) values. This dependence is used to study the effect of the hole concentration on the "0.7 ? ( 2e 2 / h )" feature in the quantum conductance staircase of the quantum wire prepared inside the p-type silicon quantum well using the split-gate technique. The 1D channel is demonstrated to be spin-polarized at the linear concentration of holes lower than the critical linear concentration, because the "0.7 ? ( 2e 2 / h )" feature is close to the value of 0.5 ? ( 2e 2 / h ) that indicates the spin degeneracy lifting for the first step of the quantum conductance staircase. The "0.7 ? ( 2e 2 / h )" feature is found to take however its normal magnitude when the linear concentration of holes attains the critical value corresponding to the spin depolarization. The variations in the height of the "0.7 ? ( 2e 2 / h )" feature observed in the hole quantum conductance staircase that is revealed by the p-type silicon quantum wire seem to be related to the evidences of the quantum conductance staircase obtained by varying the concentration of electrons in the 1D channel prepared inside the GaAs-AlGaAs heterojunction .
1D fermions. The form of H 0 depends on the dimensionality of the system under consideration.
Since the motion of charge carriers in 1D systems is quantized in two directions (x, y), the Hamiltonian for non-interacting particles has the form ? p2 ? j = ∑? + U (x j , y j )? ? ? j =1 ? 2 m ?
? n1D R ? β γ 3 C? 2? 1 ? (ρ' ' ) ? ? ln (k F ρ'?ρ' ' ) + ? ? dρ' dρ' ' ≈ ? 1D n12D + 1D n12D ln? ? ? πg ? 4 2? gs gs ? 2 ? s ?
π 2 ! 2 n13D ? ? n R ?? ? n12D ? β1D ? γ 1D ln ? 1D ?? 12m ? π ?? ?
? ? n1D R ?? ? β1D ? γ 1D ln? 2π ?? ? ?? ?
3π ! n0 ? 2n R ? = β 1D ? γ 1D ln? 0 ? 24m ? π ?
mass with increasing the values of n2 D or p2 D (see (22) and (24)). Such a gain in the exchange interaction may account for a rise in the effective mass of electrons as their concentration decreases in quantum wells , because the low density 2D gas is able to decay in the system of two-dimensional lakes connected by quantum wires or quantum point contacts, which result from specifically in the presence of disorder . The dependences of the electron effective mass in the GaAs based quantum wells on the value of n2 D that were calculated when the exchange energy has been taken into account in the relationship (24) allowed to determine the values of the critical linear concentration, n0 (see (23)), which corresponds to a complete spin depolarization of electrons in the quantum wire connecting two 2D GaAs reservoirs (Fig. 1). Here, these dependences of n0 on the value of n2 D are used in analysis of the "0.7 ? ( 2e 2 / h )" feature in the quantum conductance staircase as a function of the electron concentration in the quantum wire prepared in the GaAs based quantum well by the split-gate method, with the electron sheet density tuned controllably over one order of magnitude by biasing an overall top gate  (Fig. 1). The "0.7 ? ( 2e 2 / h )" feature is seen to attain almost the value of 0.5 ? ( 2e 2 / h ) at sufficiently small values of n2 D . Thus, spin degeneracy of the substep in the quantum conductance staircase is lifted, when the 1D channel is completely spin-polarized. However, if the electron concentration in the 2D reservoir attains the value corresponding to the critical linear concentration in the 1D channel, n0 , the "0.7 ? ( 2e 2 / h )" feature evolves towards its normal value because of partial spin depolarization. Besides, the apparent level-off of the "0.7 ? ( 2e 2 / h )" feature near the value of 0.75 ? ( 2e 2 / h ) appears to be due to its temperature dependence, which results from because of partial spin depolarization of the electron gas near the bottom of the 1D subband at finite temperatures . A most interesting result is the unexpected transformation of the "0.7 ? ( 2e 2 / h )" feature to the value of 0.5 ? ( 2e 2 / h ) with a subsequent increase in the electron sheet density (see Fig. 1).
the p-type Si based quantum well studied in this work and inside the n-type GaAs based quantum well discussed above .
Analysis of the conditions for the appearance of a spontaneous spin polarization in onedimensional systems placed in a zero magnetic field, which has been carried out within the Hartree�CFock approximation, enabled to determine the critical concentration of carriers that defines a complete spin depolarization of a quasi-1D gas. The range of the linear concentration of carriers that imposes the restrictions to use the plane waves in the studies of the ferromagnetic ordering in one-dimensional systems has been evaluated in the case of dominance of the exchange energy over the kinetic energy. The transition of a of a quasi-1D gas to the crystalline state has been demonstrated to occur at the concentration of carriers that is two to four orders of magnitude lower than those corresponding to the transition to a spontaneously spin-polarized state with extended wave functions. The spontaneous spin-polarized state with extended wave functions seems to be expected in a quantum wire at higher values of n 2 D than in a 2D gas of charge carriers because of an additional partial decay of the kinetic energy with a reduction in the system dimensionality. The dependence of the critical linear concentration that defines a complete spin depolarization in a 1D channel connecting two 2D reservoirs on the carrier’s concentration has been derived to analyze corresponding the evolution of the "0.7 ? ( 2e 2 / h )" feature from the e 2 / h to 3 / 2 ? (e 2 / h ) values in the quantum conductance staircase of the quantum wire prepared inside the p-type silicon quantum well using the split-gate technique. The 1D channel studied seems to be spin-polarized at the linear concentration of holes lower than the critical linear concentration, because the "0.7 ? ( 2e 2 / h )" feature is close to the value of 0.5 ? ( 2e 2 / h ) that indicates the spin degeneracy lifting for the first step of the quantum conductance staircase.
The "0.7 ? ( 2e 2 / h )" feature has been found, however, to tend to the value of 0.75 ? ( 2e 2 / h ) when the linear concentration of holes attains the critical value corresponding to the spin depolarization. The variations in the height of the "0.7 ? ( 2e 2 / h )" feature observed in the hole quantum conductance staircase of the p-type silicon quantum wire seem to be related to the evidences of the quantum conductance staircase obtained by varying the concentration of electrons in the 1D channel prepared inside the GaAs-AlGaAs heterojunction . ACKNOWLEDGMENTS We are grateful to V.F. Sapega and W. Gehlhoff for useful discussions of the results obtained, to V.V. Shnitov for his help in carrying out numerical calculations, and to A.M. Malyarenko for technological assistance.
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