Query: Electronic wave functions in semiconductors cluster: Experiment and theory

Candidate papers:

author_names: Louis E Brus
title: Electronic wave functions in semiconductor clusters: experiment and theory
year: 1986

author_names: Louis E Brus
title: Electronic Wave Functions in semiconductor Clusters: Experiment and Theory
year: 1986

abstract: TiO2 is an active semiconductor used in photocatalysis, solar cells devices and energy storage applications. For this reason, recent efforts are aimed to design and modify the properties of this semiconductor. In the present work we calculate theoretically the lowest energy structures of TiO2, and The Density of States (DOS using Molecular Dynamics and DFT respectively. Such geometries were compared with those reported experimentally, and their atomic structures were constructed with planes (1 0 1) of anatase symmetry. The nanoparticles considered were (TiO2)n with n=18, 28, and 38. The aim of this work is to correlate the size dependence of TiO2 nanoparticles with temperature effects on anatasa simmetry. A quenching process was used in order to reproduce the temperature conditions found at experiment. Also, The RDFs (Radial Distribution Function) of these materials were obtained. The DOS were determined using Density Functional Theory (DFT) calculations, it was implemented with FHI AIMS software package [1,2] and Molecular Dynamics using DL POLY[3] and REAXFF software packages [4,5] The DFT calculations were performed using a plane wave basis set, and the generalized gradient approximation (GGA) of Perdew Burke Ernzerhof for the exchange correlation energy [6] The core electrons were described with Projector Augmented Wave (PWA) method. Moreover, relativistic scalars effects (ZORA)[7] and Van Der Waals interactions were considered using Tkatchenko Scheffler methodology[8]
author_names: Tania G Diaz Rodriguez

G Gonzalez

H Santiesteban Juarez

Mauricio Pacio

Jesus Muniz
title: Theoretical study of the electronic structure and stability of titanium dioxide clusters (TiO2) n with n 18, 28 and 38
year: 2018

abstract: Sakoharaet al. "Visible Luminescence and Surface Proper ties of Nanosized ZnO Colloids Prepared by Hydrolyzing Zinc Acetate" J. Phys. Chem B. vol. 102, No. 50, Dec. 1998, pp. 1016910175. Hilgendorff et al. "From ZnO Colloids to Nanocrystalline Highly Conductive Films" J. Electrochem. Soc. vol. 145, No. 10, Oct. 1998, pp. 3632 3637. Spanhel et al. "Semiconductor Clusters in the Sol Gel Process: Quantized Aggregation, Gelation, and Crystal Growth in Concentrated ZnO Colloids' J. Am. Chem. Soc. 1991 (month unavailable) 113, pp. 2826 2833. Patent Abstracts of Japan, vol. 199, No. 605, corresponding to Jp 08 026823 A (Toshio Tsuchiya) Jan. 30, 1996. J. Phys. Chem. 92 (month unavailable) 1988, Month unknown pp. 482 487, "Photochemistry and Radiation Chemistry of Colloidal Semiconductors. 23. Electron Stor age on ZnO Particles and Size Quantization" Markus Haase, Horst Weller and Arnim Henglein. J. Phys. Chem. 90 (month unavailable) 1986, Month unknown pp. 2555 2560, "Electronic Wave Functions in Semiconductor Clusters: Experiment and Theory" Louis Brus. Gmelins Handbuch, Vol 32, 8" ed. Supplementary vol. (month unavailable) 1956, Month unknown pp. 722 773 "Zinkoxyd"
author_names: Markus Haase

Arnim Henglein

Gary Matz
title: ZINC OXDE GELS
year: 2017

abstract: In this paper we report the study of the change in electrical properties of zigzag carbon nanotubes (10, 0) under uniaxial compressive and tensile deformation using Density Functional Theory (DFT) calculation. There is an energy gap of 0.972 eV between occupied and unoccupied region in the optimized structure calculation. We found that the band gap of the semi conducting zigzag (10, 0) CNTs decreases as the strain increases for both compressive and tensile deformation. Different profiles of charge density appear for tensile and compressive deformations. The charge density of compressed state is more localized in the z direction of C C bonds. Meanwhile, charge density of elongated state is localized in the diagonal C C bonds direction. At the large tensile strain, the C C bonds break at the z direction C C bonds. ICOHP analysis shows that the bond strength of CNT drastically decreases under tensile deformation. Keyword: band gap, carbon nanotubes, charge density, density functional theory. INTRODUCTION The development of science and technology has evolved into the era of nanotechnology. Among the many nanostructured materials, carbon nanotubes (CNTs) have attracted considerable attention. Compared to other nanoscale materials, single walled carbon nanotubes (SWCNT) possess particularly outstanding physical and electronic properties. Due to the extremely small size of CNTs, the evaluation of its mechanical properties, such as elastic modulus and tensile/compressive strength presents significant challenges to researchers who work in nanomechanics. Electronic states of single walled carbon nanotubes (SWNCT) such as Density of states (DOS) and band gap, could be correlated with their finite mechanical deformation behavior. The study of this effect is important in view of the ability to manipulate individual nanotubes for many applications. Recently, Obitayo and Liu [1] have been developed carbon nanotubes as strain sensor its I V characteristic behavior due to axial change has been explored. In that work, they conclude that for carbon nanotube based strain sensing applications, the small gap semiconducting single walled carbon nanotubes offer the greatest sensitivity. Even though many research have studied the change of electronics properties of nanotubes under uniaxial deformation [1 3] the theoretical approach in investigating the band gap changes has not been revealed up completely. Because of the nanoscale size of CNTs, the experiments to measure the properties of individual CNT are quite difficult. Therefore, the ab initio calculations have been regarded as a powerful tool to study properties of CNTs. In the present report, we calculate the atomic and electronic structure changes of the CNTs under tensile and compressive deformation by using Density Functional Theory (DFT) calculation. We focused on band gap and bond strength changes due to mechanical uniaxial tensile and compressive deformation. COMPUTATIONAL DETAILS We carried out the first principles calculations on the density functional theory (DFT) level, using the "Vienna ab initio simulation package" [4 6] The calculation was performed in QC Cluster at Department of Physics ITB. Generalized gradient approximation (GGA) with the Perdew Burke Ernzerhof (PBE) [7] functional is selected in our calculations. A plane wave basis set was employed within the framework of the projector augmented wave method.[8, 9] K points (1 x 1 x 17 Monkhorst Pack grid) were used in this simulations. One k point in the two perpendicular directions was enough because the distance between the individual tubes was chosen very large (16 A) so that the interaction between them was negligible. We selected zigzag type semiconducting CNTs (10,0) The axial direction (z) of these CNTs was selected as the tensile direction. Before we started the tensile test, the z dimension of the supercells and the initial atomic configuration were completely relaxed. These relaxed z dimensions of the supercells were used as a reference when calculating the applied strains in the following discussion. The electronic properties of zigzag CNT can be obtained by using electronic density of states calculations. The optimized structure data from SCF calculations can be used to reduce calculation time and neglect structural optimization process. Generally, the mesh K point sampling for DOS calculation is higher than that of SCF calculations for calculation's accuracy. To know further the nature of bonding of elongated /compressed CNT, we projected plane waves to local orbital basis functions to extract the crystal orbital Hamilton population COHP) [10] The integration of COHP for all energies up to EF gives integrated COHP (ICOHP) to render a quasiquantitative interpretation [11] of the net bonding characteristics. This ICOHP were calculated by using the program Local Orbital Basis Suite towards Electronic Structure Reconstruction (LOBSTER) [11 13] VOL. 13, NO. 7, APRIL 2018 ISSN 1819 6608 ARPN Journal of Engineering and Applied Sciences (c)2006 2018 Asian Research Publishing Network (ARPN) All rights reserved. www.arpnjournals.com 2391 RESULT AND DISCUSSIONS Change in density of states during deformation From the DFT calculation using VASP software, we got the optimized structure of zigzag CNTs (10, 0) The zigzag edge (10, 0) CNT has two different carboncarbon (C C) bond length, 1.42 A and 1.43 A. The diameter of this optimize structure is 7.89 A. Our optimized CNTs model was then be compressed and elongated in uniaxial direction (z direction) There is an energy gap of 0.972 eV between occupied and unoccupied region, which indicates that the system is semiconducting. This result is in agreement with other first principle calculation studies which have been published [14 16] This result is also supported by experimental and theoretical approach results from other studies. According to the chiral vector information, the pristine zigzag edge (10,0) CNT is semiconducting material [17] This result is also in a good agreement with experimental result by using scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS) [17, 18] The electronic structures of CNTs with various structures under axial strain are evaluated by DFT calculations. To analyze the band gap dependency on uniaxial deformation, we observe the DOS of the deform structure of zigzag edge CNT (10, 0) The band gap versus strain curves for a zigzag (10, 0) CNTs during the tensile tests are shown in Figure 1. Negative value means that the final deformed structure is shorter than the optimize bulk structure (compressed) Vice versa, the positive value shows that the final deformed structure is longer than the optimize bulk structure (elongated) Previous work on semiconducting CNTs shows the same result with this work. The band gap for the semiconducting zigzag (10, 0) CNTs displays some variation upon deformation, but most of it decreases as the strain increases [16] This calculation result also shows that there is semiconductor metallic transition of the CNTs. The (10,0) zigzag tube has zero band gap like graphene at the strain of 8.3% which means that it possesses metallic electronic properties at this state and returns to the semiconducting state as the strain increases. Since another work suggests that the small gap semiconducting single walled carbon nanotubes offer the greatest sensitivity for the sensor application, we can conclude that CNT (10, 0) can be a good candidate for CNT based strain sensors. Figure 1. The band gap versus strain for semi conducting zigzag (10,0) CNTs. Deformation electron density VOL. 13, NO. 7, APRIL 2018 ISSN 1819 6608 ARPN Journal of Engineering and Applied Sciences (c)2006 2018 Asian Research Publishing Network (ARPN) All rights reserved. www.arpnjournals.com 2392 Figure 2. (a) Focused area for charge density analyzing; Charge density of the (10,0) zigzag CNT under: (b) 2% (c) 10% compressive and (e) 1% (f) 10% tensile strain. Figure 2 shows change in the charge density of the (10,0) zigzag CNT under compressive and tensile strain. We analyze the two dimensional charge density slice of the semiconducting zigzag (10, 0) CNTs focusing on the red circle area shown in the Figure 2(a) Charge density of the CNT before imposed by uniform stretching or compressed of the initial atomic configuration in the z direction is shown in Figure 2(b) Charge density during the compressive deformation is shown in Figure 2(c) and (d) it can be seen that the charge density becomes more localized in the z direction C C bonds and the angle of the hexagonal carbon formation decreases. The amount of localized charge density also increases as the compressive strain increase. The different profile appears during tensile deformation. The charge density, as shown in Figure 2(e) and (f) decreases as the tensile strain increase. The Charge density is localized in the diagonal C C bonds. At large strain, i.e. 7% for tensile and 5% for compression, the C C bonds break at the z direction C C bonds. This indicates that for more than 7% tensile and 5% compressive strain, CNT starts to break and no longer efficient to be used as a sensor. Because when some C C bonds are broken, the CNT is in plastic region, so when it is strained, it will not return to its original shape. For the strain sensor application, CNT should be able to return to its original shape, it means that the CNT should be in the elastic region. From our charge density analysis, the elastic region of CNT (10, 0) might be below 7% tensile and 5% compressive strain. From this figure also we can conclude that the bond strength of the CNT under compressive deformation is higher compared to that of tensile deformation. It is indicated by the higher value of the electron density in compressive deformation compared to tensile deformation at the same strain. To study further about this bond strength, we perform the ICOHP calculation. Bond strength Integratin
author_names: Irfan Dwi Aditya
title: ELECTRONIC PROPERTIES OF SEMICONDUCTING ZIGZAG 10 0 CARBON NANOTUBES DUE TO UNIAXIAL STRAIN
year: 2018

abstract: Recent theoretical studies on the origin of the pseudogap emerging in underdoped cuprate superconductors are overviewed, based on insights obtained by a cluster extension of the dynamical mean field theory (cDMFT) for the doped two dimensional (2D) Mott insulator. The pseudogap obtained in the cDMFT shows an s wave like full gap structure, distinct from the d wave superconducting gap. The zero temperature electronic structure supports that a non Fermi liquid phase exists and underlies the pseudogap. The non Fermi liquid phase is separated from the larger doped Fermi liquid by topological transitions of the Fermi surface and an emergence of zeros of Green's function. A coexisting evolution of the poles (Fermi surface) and zeros of the Green's function is a unique feature of the pseudogap phase. The spectra well reproduce the arc/pocket formation, together with basic experimental properties of the pseudogap phase in the cuprates. Furthermore, a full gap structure is supported by a comparison with the results of Raman experiments. The overall feature supports the proximity of the Mott insulator and the significance of the quantum criticality of the Mott transition. These numerical results are further favorably interpreted by extending the exciton concept, known in semiconductors, to doped Mott insulators. In this composite fermion (CF) theory, the pseudogap emerges as a gap arising from a hybridization of the quasiparticle (QP) with the CF. The pairing channel opening between a QP and a CF solves the puzzle of the dichotomy between the d wave superconductivity and the precursory insulating gap in the same antinodal region. A mechanism of superconductivity emerges from this pairing.
author_names: Masatoshi Imada

Shiro Sakai

Youhei Yamaji

Yukitoshi Motome
title: Theory of pseudogap in underdoped cuprates
year: 2013

abstract: A chromophore is a molecule that appears colorful to the human eye in sunlight. The recognized color is related to the wavelength of light, or in face of particle wave dualism, to the energy of photons absorbed by the molecule. Light absorption, also called photo excitation, corresponds to a transition of the molecule from its ground state to an electronically excited state. The energy gained during excitation allows the molecule to undergo manifold chemical and physical processes, giving rise to the presents of a plethora of chromophores in nature and technology. In order to rationalize these light induced processes, the involved electronic ground and excited states of a molecule can be investigated by means of quantum chemical methods. These allow to determine the energy and properties of the molecule in its different electronic states. An important step in the interpretation of the results of such calculations is to determine the character of an excited state, which is directly connected with many properties, such as the interaction with an environment, reaction pathways and deexcitation processes. The aim of this work is to develop new tools for the investigation of excited states, their characters, and quantum chemical methods for their description. The central idea is to rationalize excited states in terms of correlated electron hole quasiparticles, i.e. excitons, a concept from solid state physics. The working hypothesis is to identify the one particle transition density matrix (1TDM) as an effective electron hole (i.e. exciton) wave function. The character of an excited state can in turn be determined from the calculated exciton properties. These properties are computed by evaluating expectation values of the exciton wave function with respect to operators of interest. In practice, several protocols have been developed, which characterize spatial and statistical properties of the electron hole quasiparticle. These excited state descriptors are directly comparable to results from solid state physics as well as from experiments, emphasizing their physical significance. In contrast to standard approaches, deriving excited state characters from exciton properties has some immediate advantages. Different types of excited states such as charge transfer, Rydberg or local, can be directly determined according to a few exciton descriptors. The use of quantitative descriptors is comparably unbiased, since it does not rely on an ambiguous visual interpretation of molecular orbitals (MOs) involved in the electronic transition. Moreover, exciton descriptors allow to investigate excited states that are poorly represented in the MO picture. Since exciton analysis is based on the 1TDM, which is a method independent quantity, the descriptors allow to investigate quantitative differences between the descriptions of excited states at various levels of theory. The presented approach is particularly relevant for molecules featuring excited states with exciton character. A particularly important substance class are large p conjugated organic molecules. Here, delocalized p electrons play a decisive role and require precise description of correlation effects, posing a challenge for quantum chemical methods. The scientific interest in large p conjugated organic molecules is triggered by their special electronic properties, which are applied in organic electronics. In the course of this work, a variety of excited states of extended p conjugated organic molecules is calculated by means of correlated ab initio methods as well as by time dependent density functional theory (TDDFT) and subjected to exciton analysis. In Chapter 3, exciton sizes are investigated for excited states of poly(para phenylene vinylene) (PPV) oligomers and polyacenes. Excited states are found to differ in exciton sizes depending on irreducible representations and multiplicities. In Chapter 4, PPV is thoroughly investigated as a prototypical organic semiconductor to rationalize its exciton properties from a quantum chemical perspective. The emergence of excitonic states is examined for a series of PPV oligomers with different chain length. It is found that exciton formation takes place for oligomers with four or more building blocks. To gain insight into the spectroscopic properties of the PPV polymer, the largest still computationally feasible representative, the octamer (PV)7P is studied intensely. A systematic analysis of forty excited states allows to examine their exciton characters in detail. The investigated excitons are found to have well defined structures that can be rationalized in terms of Frenkel and Wannier exciton models. The results are in good agreement with experimental findings and band structure calculations of PPV. To investigate the effects of exciton formation for a more chemically diverse set of molecules, a variety of aromats as well as heteroaromats are investigated in Chapter 6. It is found that the first excited state of these p systems has a uniform exciton character with an exciton size converging towards 7 A very similar to the trends in PPV. The explicit chemical structures and presence of heteroatoms have surprisingly little influence on this character. Shifting the focus to methodological aspects, Chapter 6 reveals the influence of exchange correlation (xc) functionals on the description of exciton properties in TDDFT. By comparing exciton sizes and electron hole correlation coefficients, it is found that there are major differences in the excited state description for the tested xc functionals. The trends amongst different xc functionals suggest that these deviations are mostly governed by the amount of nonlocal orbital exchange (NLX) in the xc functionals. This finding is of great significance showing that a single parameter can induce a complete change in the electron hole interaction from repelling (anti correlated) to strongly attractive (correlated) A more general investigation of the same effect is presented for Tozer's benchmark set in Chapter 5. This set is composed of a broad selection of molecules featuring different types of excited states and designed to develop diagnostic tools for TDDFT. It is well known that excited states which involve nonlocal electron transitions, such as charge transfer, Rydberg or p p* states of extended p systems, show systematic errors in excitation energy for different types of xc functionals. Here, exciton descriptors reveal that these errors are related to substantial differences in the description of the respective excited states by the xc functionals. Since exciton descriptors are able to identify all problematic cases, they are suggested as diagnostic tools for TDDFT. Ultimately, Chapter 7 focuses on the evaluation of excited state methods. For this purpose, the selection of methods is extended to include also equation of motion coupled cluster singles doubles (EOM CCSD) and a diverse set of applications is investigated. Exciton properties calculated with correlated ab initio methods (ADC(2) ADC(3) and EOM CCSD) as well as TDDFT are compared, revealing strengths and weaknesses of the methods in different applications. The most important outcome of investigating exciton properties is that accuracy in terms of excitation energies is not necessary a measure for the quality of description of the underlying wave function and properties of a system. In fact, the best agreement in terms of exciton properties with respect to high level ab initio data is obtained with an xc functional that is the least accurate in terms of excitation energies for several examples. The presented approach is publically available as open source code package libwfa and integrated in the Q Chem program package.
author_names: Stefanie A Mewes
title: Exciton analysis tools for quantum chemical investigation of molecular photochemistry
year: 2018

abstract: Abstract We derive a theory of magnetization for the diluted magnetic semiconductor, p type Sn1 xGdxTe including the contributions from Gd3+ local moments, carrier local moment hybridization and lattice diamagnetism as a function of temperature and magnetic field. The local moment contribution Mlocal is a sum of three contributions: Mlocal=Ms+Mp+Mt, where Ms is the dominant single spin contribution, and Mp and Mt are the contributions from clusters of two and three spins, respectively. We have also calculated the contribution due to spin polarized holes for carrier densities of order 1020 cm 3, using a k p model, where p is the momentum operator in the presence of the spin orbit interaction and k is the hole wave vector. This contribution includes the carrier local moment hybridization. We have also included a diamagnetic lattice contribution, which comes from inter band orbital and spin orbit contributions. In this contribution, the symbol k is used for the electronic wave vector. The local moment contribution is dominant and primarily comes from the isolated spins. However, the two and three spin contributions increase with increase in the magnetic impurity concentration. The magnitude of the hole spin polarization is about two orders less than the local moment contribution even at field strength of 25 T. However, the magnetization due to carrier spin density has intrinsic importance due to its role in possible spintronics applications. The lattice diamagnetism shows considerable anisotropy. The total magnetization is calculated from all the three contributions Mlocal, Mc (due to carriers, here holes) and Mdia. We have compared our results with experiment wherever available and the agreement is fairly good.
author_names: Kalachand Dash

Gouri S Tripathi
title: Theory of magnetization of p type Sn1 xGdxTe: Contributions from local moments, lattice diamagnetism and carriers
year: 2012

abstract: Fundamental Theory. Density Functional Theory and Local Potential Approximations from Momentum Space Considerations. Aspects of Density Functional Theory. On the Calculation of Potentials from Densities. The Chemical Potential for Interacting Fermions in a Harmonic Potential. Density, Total Energy and Chemical Potential of Atomic Ions and some Molecules. Some Aspects of the Role of Single Particle Density in Chemistry. The Mechanics of and an Equation for the Electronic Charge Density. The Qualitative Theory of the Current Density in Molecules. The Constrained Search Approach, Mappings to External Potentials, and Virial Like Theorems for Electron Density and One Matrix Energy Functional Theories. Self Interaction Correction. Some Approaches to Density Functional Theory. Exchange Correlation Energy Functionals in the Density Functional Formalism. An Approach to Electron Correlation beyond the Local Spin Density Approximation. Pair Correlation Energies and Local Spin Density Functionals. On the Extension of the Statistical Energy Expression to Multi Determinantal Wave Functions. The Weizsacker Term, its Corrections and Virial Partitioning in Density Functional Theory. The Second Order Reduced Density Matrix and the Chemimal Bond. Characteristic Function Approach to Density Matrix Calculations. On the Systematic Assessment of Correlation Effects in Local Density Models. Relativistic Density Functional Theory. A Phase Space Approach to Energy Densities in Position Space. Applications. Application of the Hartree Fock Slater Method in Photoelectron Spectroscopy. SCF X? SW Cluster Molecular Orbital Models of Catalysts, Alloys, Magnetic Materials, and Superconductors. Some Applications of the Density Functional Formalism to Chemisorption. Density Functional Calculations for Atomic Clusters. Cohesive Energy, Spectroscopic, and Magnetic Properties of Small Clusters. Calculations of Hyperfine Interactions in Transition Metal Compounds in the Local Density Approximation. Local Density Approach to Surfaces and Adsorbed Layers. Electron Densities in Solid Compounds. Local Density Approximations for Relativistic Exchange Energies. Relativistic Multiple Scattering X? Calculations. Dirac Scattered Wave Calculations. Theoretical Valence Charge Densities for Graphite, Diamond and LiC6. Dependence of the Self Consistent One Electron Density of Anisotropic Semiconductors on Local Density Approximations. Ray Bragg and Compton Scattering Experiments Used as Tests of the Validity of the Local Density Approximation. Multipole Expansion as an Alternative Representation of Charge Density. Measured Electron Density Distributions in Crystals as a Basis for Band Structure Calculations. Observation of Electron Distributions on Outermost Layers of Solid Surfaces by Penning Ionization Electron Spectroscopy. Observations of Local Electron Distributions in Molecular Orbitals. Accurate Hellmann Feynman Force Method for the Study of the First and Second Derivatives of Potential Energy Hypersurface. The Calculation of Spectroscopic Data by the SCC X? Method. On Correlated One Electron Energies in the HFS and HFG Schemes. On the Atomic Wavefunctions Generated by the Hartree Fock Slater Method X?HF and the Modified Hartree Fock Slater Method ?aHF which Includes Self Interaction Explicitly. Ab Initio Calculations Incorporating Desirable Options for Large Molecules and Solids: a Competitive Completely General Alternative to Local Density Methods for Many Systems.
author_names: Jens Peder Dahl

John Scales Avery
title: Local Density Approximations in Quantum Chemistry and Solid State Physics
year: 1984

abstract: 1. Atoms as Constituents of Matter. 1.1 Introduction. 1.2 Atomic Scale. 1.3 One Electron Atoms and the Hydrogen Atom. 1.4 Central Field Approximation. 1.5 Shell Structure of Atoms and Periodicity of the Elements. 1.6 Stationary States of Atoms I. 1.7 Stationary States of Atoms II. 2. System of Protons and Electrons. 2.1 General Comments. 2.2 Electronic State of a Hydrogen Molecule. 2.3 Systems Made of Hydrogen Molecules. 2.4 Metallic State at High Density. 2.4.1 Electron Electron Interaction. 2.4.2 Interaction Between Protons and Electrons. 2.4.3 Motion of Protons. 2.5 Phase Diagram of the Proton Electron System. 3. Helium. 3.1 Characteristics of Helium. 3.2 Superfluidity. 3.3 Phonons and Rotons. 3.4 Liquid 3He Fermi Liquid. 3.4.1 Basic Ideas of the Fermi Liquid Theory. 3.4.2 The Equilibrium Properties. 4. Super fluid Helium 3. 4.1 Basic Properties. 4.1.1 Thermodynamic Properties. 4.1.2 Transport Phenomena. 4.1.3 Nuclear Magnetic Resonance (NMR) Experiments. 4.2 Spin Triplet P Wave Pairing. 4.2.1 Cooper Pair. 4.2.2 Generalization of the BCS Theory. 4.2.3 Order Parameters of the Spin Triplet P Wave Superfluid. 4.2.4 ABM State and BW State. 4.3 Physical Properties of ABM and BW States. 4.3.1 Energy Gap. 4.3.2 Normal (Super) Fluid Component ?n(?s) 4.3.3 Susceptibility. 4.4 Fermi Liquid Effects. 4.5 Nuclear Spin Dynamics. 4.5.1 Small Oscillations. 4.5.2 Ringing. 4.6 Texture and Superfluidity. 5. Metals. 5.1 Characteristics of Metals. 5.2 Band Theory of Metals. 5.3 Fermi Surface. 5.4 Pseudopotential of Simple Metals. 5.5 Structure of Simple Metals, 5.6 Transition Metals. 5.7 Alloys. 5.8 Superconductivity. 6. Nonmetals. 6.1 Molecular Crystals. 6.2 Ionic Crystals. 6.3 Covalent Crystal. 6.4 Hydrogen Bonded Crystals. 6.5 Electron Theory of Nonmetals (Semiconductors) 6.6 Semimetals. 6.7 Properties of Matter Under High Pressure. 7. Localized Electron Approximation. 7.1 A Simple Model for Tetrahedrally Bonded Semiconductors. 7.2 Bond Orbital Model (BOM) 7.2.1 Effective Charge. 7.2.2 Dielectric Constant. 7.3 Cohesive Energy and Stability of Crystal Structures. 7.4 Relationship Between the BOM and EPM. 8. Magnetism. 8.1 Magnetic Properties of Solids. 8.2 Magnetic Properties of Simple Solids. 8.3 Mechanism of Spin Polarization and the Electronic State in Solids. 8.4 Configurations of Spin Polarization in Magnetic Ordered States. 8.4.1 Magnetic Anisotropy Energy and Crystal Fields. 8.4.2 Magnetic Order in Insulators. 8.4.3 Magnetic Order due to the Double Exchange Interaction. 8.4.4 Magnetic Order in Metals. 8.5 Collective Motion in Ordered States and Phase Transitions. 8.6 Magnetic Properties of Dilute Alloys. 8.7 Applications of Magnetic Measurements for Condensed Matter. 9. Magnetic Properties of Dilute Alloys the Kondo Effect. 9.1 Recent Investigations of the Kondo Effect. 9.2 A Survey of Recent Experiments. 9.3 Yosida Yamada Theory. 9.4 Renormalization Group Approach. 10. Random Systems. 10.1 Periodic and Aperiodic Systems. 10.2 Point Defects. 10.3 Line Imperfections and Dislocations. 10.4 Cradle of Random Systems Melting of Crystals and Order Disorder Phase Transition in Alloys. 10.5 Noncrystalline Solids. 10.6 Liquid Metals and Electronic and Vibrational States of Random Systems. 11. Coherent Potential Approximation (CPA) 11.1 Survey. 11.2 A Few Examples of Experimental Results. 11.2.1 Optical Absorption Spectra in Mixed Ionic Crystals. 11.2.2 Photoemission of Transition Metal Alloys and Noble Metal Alloys. 11.2.3 Magnetic Moments and Electron Specific Heat of Ferromagnetic Alloys. 11.3 Computer Simulations and Exact Solutions. 11.3.1 Results of Computer Experiments. 11.3.2 Exact Results. 11.4 Model Hamiltonian. 11.5 One Particle Green's Function. 11.6 Approximations before CPA. 11.6.1 Rigid Band Model (the Lowest Order Virtual Crystal Model) 11.6.2 Virtual Crystal Model. 11.6.3 Dilute Limit. 11.6.4 The Average t Matrix Approximation (ATA) 11.7 Derivation and the Characteristic Features of the CPA. 11.7.1 Rigid Band Limit. 11.7.2 Virtual Crystal Limit. 11.7.3 Dilute Limit. 11.7.4 Split Band Limit. 11.8 Applications of the CPA. 11.8.1 A One Dimensional AB Alloy. 11.8.2 Phonon Density of States of an Isotopically Disordered Model System. 11.8.3 Density of States of a Three Dimensional Alloy. 11.8.4 Optical Absorption Spectra of Mixed Crystals. 11.8.5 Density of States of Transition and Noble Metal Alloys. 11.8.6 Ferromagnetic Alloys. 11.9 Universality of the CPA. 11.9.1 Cluster Effects (Multi Site Approximations) 11.9.2 Extension to Systems with Off Diagonal Disorder. 11.9.3 Extension to Systems with Both Diagonal and Off Diagonal Disorder. 11.9.4 Extension to Structurally Disordered Systems Composed of Single Species. 11.9.5 Extension to the Multi Band Hamiltonian. 11.9.6 Extension of CPA to the Calculations of Other Physical Quantities. References.
author_names: Song Yuan Wu Sheng
title: The Structure and Properties of Matter
venue: Nature
year: 1928