System Of Free Electrons Research Articles

Low-temperature properties of the metallic phase of the t-J model in two dimensions.

The low-temperature properties of the fluxless metallic phase of the t-J model in two dimensions are calculated using a large-N slave-boson formulation, with explicit fermion-boson decoupling of the correlated electron in the large-N limit. We find that although this metal possesses both a large Fermi-surface and Fermi-Thomas screening corresponding to a system of free electrons near half filling, both the square of the plasma frequency and the Hall conductance of this phase scale with the doping concentration. This qualitatively accounts for the observed doping dependence of the Hall constant in high-temperature superconductors. A slow zero-sound mode arising out of the bare-electron--slave-boson quasiparticle liquid is also found in the low-temperature regime of this phase. We predict that the density-density correlation function should have a pole at this resonance, and we suggest that this pole has already been observed in recent electron-energy-loss experiments on high-${\mathit{T}}_{\mathit{c}}$ materials. In addition, resonant coupling of this zero-sound mode to acoustic longitudinal phonons via the electron-phonon interaction results in an electronically driven lattice instability at a critical doping concentration. We suggest that such a mechanism is responsible for the tetragonal-to-orthorhombic crystallographic transitions generally observed in high-${\mathit{T}}_{\mathit{c}}$ materials.

Temperature Dependence of Spin Correlation Length of Half-Filled One-Dimensional Hubbard Model

We have calculated the spin correlation length of the half-filled one-dimensional Hubbard model down to the temperature of T =0.01×(transfer integral) by the Bethe-Ansatz method for the quantum transfer matrix. Its temperature dependence shows the crossover from (2 log π T ) -1 at high temperatures to a T -1 with the log corrections at low temperatures, the low- T behavior being consistent with the prediction by the conformal field theory. When the Coulomb repulsion U is small, we have found at low temperatures another crossover in the proportional constant a from the value for the free electron system to that for the antiferromagnetic Heisenberg model. This crossover is due to the disappearance of charge fluctuation. A similar crossover has been observed for the linear coefficient of specific heat, C / T .

Nuclear magnetic resonance studies of liquid metal alloys

The Knight shift K and quadrupolar relaxation rate Rq in liquid metallic systems, in which effects of bonding become increasingly prominent, are surveyed. In Rb, a theoretical calculation of Rq, including mode-coupling theory for the liquid, and the r-dependent Sternheimer factor, predicted closely the recent experimental redetermination. In Ge and in Cu-Ge and similar nearly free-electron systems, the quantitative analysis of K still poses problems, while qualitatively K(x) displays clearly a correspondence to the resistivity maximum. In metallic alloys with compound forming tendency, models based on an association (A+B from or to AB) connect K and Rq quantitatively with the heat of mixing, but the microscopic foundation of the association ansatz is uncertain.

Fermionic chemical potential

This paper gives a critical review of the physical meaning of the chemical potential, perhaps the most abstract of all thermodynamic quantities. To show its basic behavior, thereby to illustrate its physical significance, we have derived the chemical potential of a system of free electrons as a function of the density and temperature in different spatial dimensions. We have shown how to obtain the isothermal compressibility given the chemical potential. To emphasize the usefulness of the knowledge of dimensional dependence, both the compressibility and average kinetic energy are expressed as simple dimensional relationships of the density and, hence, the chemical potential. Finally, there is a certain temperature at which the chemical potential should identically vanish. Physical implications of zero chemical potential are discussed.

Simple models of phonon-drag in 3D and quasi-2D

The simple 'metallic' formulae for the phonon drag thermoelectric power (Sg) of 3D free-electron systems appears to be in conflict with the model of Herring, by predicting different dependences of Sg upon electron density and temperature (T) at low T. The authors show that both approaches can be understood physically by considering the net phonon drift velocity. A simple quasi-2D expression for Sg is then obtained which predicts the underlying dependence upon T, phonon mean free path L, and electron surface density n, as LT3/n which is the observed behaviour in heterojunctions and MOSFETs. This dependence is modified by the efficiency with which momentum is transferred between the electron and phonon systems. Boltzmann transport calculations confirm these conclusions and support the simple models by reproducing the simple formulae in appropriate limits.

A study of the relativistic electronic state of disordered systems

We have carried out a quantitative study of the relativistic density of states (DOS) of a one-dimensional system, using analytical results of a related treatment previously reported by Roy ( J. Phys. Chem. Solids 50, 111, 1989). We have examined various features of the quantitative results of the relativistic DOS of our model of a 1D disordered system, in light of (i) non-relativistic (NR) DOS of the same disordered system, (ii) relativistic and non-relativistic DOS of free electrons, and (iii) relativistic and non-relativistic band structure of 1D periodic systems relevant to our disordered systems. Among many other things, our investigation brings out clearly the circumstances under which the relativistic effects on the DOS of disordered systems can become substantially larger; in this regard, it is found that the relativistic effects on the DOS of disordered systems are very large in the simultaneous presence of low concentration of scatterers and low values of height (depth) of potential barriers (wells) which represent the potentials due to scatterers in our model of disordered systems.

Magneto-optical activity of Ag at the plasma frequency

Kerr activity is observed in pure Ag films in the vicinity of the plasma resonance (3.85 eV) when subjected to a strong external magnetic field. This inherent magneto-optical behaviour of Ag in a narrow wavelength range (0.12 eV) around the plasma resonance is explained utilizing the classical Lorentz-Drude model for the off-diagonal elements of the dielectric function. This activity is a consequence of a combined effect of the weakly damped free electron system and the sharp onset ofd-band transitions. The possibility of enhancing the Kerr activity of amorphous TbFeCo alloys by Ag overlayers is also investigated.

Electron transport in liquid metals and alloys

This paper deals with a number of selected topics from the field of electric transport properties in liquid metals and alloys. First, some nearly free electron systems are considered; it appears that some problems associated with the properties of liquid Na–Cs alloys and of amalgams are still unsolved. Then, systems exhibiting strong compound formation, particularly alkali–nonalkali alloys with a large electronegativity difference between the components, are reviewed. A qualitative interpretation in terms of chemical-valence rules, based upon our knowledge of the solid state, is given. Next, recently developed theories dealing with transport properties in disordered media are critically discussed. Some models for the interpretation of the alkali – group IV alloys are presented. The basic ideas derived from these models are used also as guidelines for a more qualitative discussion of the alkali – group III and alkali – group V alloy systems.

THE CONVOLUTION LAW AND THE DIMENSIONALITY OF THE DENSITY OF STATES

From the basic principles of statistical physics, we have obtained the more general conditions that the convolution law of the density of states of the system and its subsystems or that of the high-dimensional system and low-dimensional system is satisfiled. We also analysed the transition of densities of states from the l-dimension to the 3-dimension in the free electron and tigkt-binding periodic systems.

Fermi Liquid Theory on the Basis of the Periodic Anderson Hamiltonian

T-linear term of specific heat and magnetic susceptibility at zero temperature are derived for the heavy electron systems, and relations among these quantities are discussed on the basis of the Fermi liquid theory. Further, a rigorous expression of the T2-term of resistivity at low temperatures is also obtained on the basis of Kubo formula. It is shown that the coefficient of the T2-term arising from the electron interaction is strongly enhanced though it vanishes because of the momentum conservation for a free electron system possessing no crystal lattice.

On the optical properties of simple metals and semiconductors: equivalence of local field corrections and dynamical screening

It is shown that the generalisation of the longitudinal dielectric function of Ehrenreich and Cohen (1959) by Adler (1962) and Wiser (1963) to include local field effects and the corrections to the Wilson-Butcher (1931, 1951) transverse dielectric function by Hopfield (1965) and Overhauser (1967), known as dynamical screening and collective effects, respectively, lead to identical modifications of the optical properties of nearly free electron systems. The importance of these effects for the optical properties and for the energy loss function of simple metals and of covalent semiconductors is discussed.

Impurity bands in a magnetic field of arbitrary strength

On the basis of the self-consistentt-matrix approximation for a system of quasi free electrons interacting with randomly distributed attractiveδ-potentials, we discuss impurity bands in the presence of a magnetic field of arbitrary strength. We compare the results with existing theoretical work on the limiting cases of weak and strong magnetic fields, which are shown to be partly incompatible, and with experimental work onn-type InSb in the magnetic freeze-out regime. Satisfactory agreement is obtained between the thermal ionisation energy, evaluated from experiments, and the calculated gap energy, separating impurity band and conduction band.

A Model Dielectric Function for Semiconductors

The microscopic dielectric function is calculated for a simple model of a semiconductor, originally proposed by Penn, in which the energy bands and wave functions are those of a one-dimensional, nearly free electron system, isotropically extended to three dimensions. The dielectric function is evaluated numerically so that all unnecessary approximations are avoided. The relationship between the static dielectric constant and the energy gap is found to be[Formula: see text]where S0 is about 0.6. The results for finite wave vectors, for a range of energy gaps, have been fitted to an interpolation formula to facilitate their use.

Exact formulae for the electrical resistivity

Abstract The theory of exact formulae for the electrical resistivity is reviewed. The derivation of an exact formula for the resistivity and the proof of the equivalence of this formula with the linear response formula for the electrical conductivity are presented. One form of the resistivity formula is evaluated in the limit of weak scattering. The model for this calculation is a system of non-interacting free electrons scattered by random fixed impurities. It is shown that the evidence which suggested that the resistivity formula is simpler to evaluate than the conductivity formula is misleading.

The electrical conductivity for imperfect crystals at finite temperature

With a method based on Kubo's formula for the electrical conductivity, developed in a previous paper, a generalized Boltzmann equation is derived. This transport equation applies for a system of free electrons, interacting with both phonons and imperfections. An application to monovalent metals shows that no important deviations from Matthiessen's rule can be expected due to coherent scattering by a phonon and an impurity, except for very low temperatures. For semiconductors the transport equation gives a new expression for the mobility. When the range of the potential is comparable with the mean free path, this mobility differs significantly from the mobility calculated previously. Approximate calculations have been done for two kinds of imperfections: ionized impurities and parallel dislocations.

Crossed diagram contribution to the electron self-energy due to impurity scattering in a magnetic field

We consider the contribution of crossed diagrams to the self-energy for a system of free electrons and fixed point impurities in the presence of a strong magnetic field. At the peaks of the Shubnikov-de Haas (S.d.H.) oscillations the dependence on the impurity concentration of the crossed diagram is the same as in the generalized Born approximation (n 2/3 ). Nevertheless, for the S.d.H. regime the contribution of the crossed diagrams is shown to be unimportant.

Note on the Hall effect of an electron gas with random impurity scattering

A formula for the Hall conductivity of a system of free electrons interacting with randomly distributed point impurities is presented and evaluated numerically. The deviation of the Hall coefficient from its classical value shows Shubnikov-de Haas type oscillations and becomes positive as well as negative. The results are in qualitative agreement with experiments on n-InSb. However, they disagree essentially with calculations presented recently by Bastin et al.

Magnetic Corrections to the Boltzmann Distribution Function

By means of an expansion in powers of the magnetic field, where classical statistics are assumed, an expression is found for the gauge-independent equilibrium distribution properly corresponding to the ordinary Boltzmann transport equation. The validity of the new distribution is demonstrated by determining the current density induced in a simple system of free electrons simultaneously accelerated by crossed electric and magnetic fields and comparing the current with that obtained using the gauge-dependent density matrix formalism. To terms of second order in the magnetic field, the results are shown to be in exact agreement.

Magnetoconductivity for a system with two scattering mechanisms

An expression is given for the magnetoconductivity of a system of free electrons in interaction with phonons and imperfections by applying the proper connected- diagram expansion method to Kubo's formula. The formulation makes it possible to give a careful analysis of the validity of Matthiessen's rule. The theory is applied for two cases. For the case of spherical imperfections in metals the limitations of Matthiessen's rule are indicated. For the case of cylindrical imperfections it is found, that correction terms have to be added to the usual expression for the relaxation time due to the mixing of electron states by the electron-phonon coupling. As an example of the latter case the mobility of germanium with an array of parallel dislocations is calculated and compared with experiment.

On the high field hall resistivity

The high field Hall resistivity for a system of free electrons and point impurities is calculated. The results are in qualitative agreement, collision broadening must be taken into account.