Dynamic representation of disordered electronic systems

A dynamic formulation of the mobility-edge problem in disordered electronic systems is presented which avoids the replica method as well as the use of Grassmann variables.     

Relativistic electronic states in disordered systems

The energy spectrum of relativistic electrons in one-dimensional disordered systems is investigated. Using an approximate solution to the one-dimensional Dirac equation as given by Steslicka and Davison and following a method reported earlier by the author for nonrelativistic cases, an equation connecting the wave functions at three consecutive atomic sites is derived. This “connection equation” is then analysed with the help of (1) Worpitzky's theorem and (2) a perturbational approach due to Phariseau. With the help of these approaches, explicit equations are derived for electronic energies in disordered systems with small deviations from periodicity. These explicit equation indicate that, in general, a band structure of electronic energies exists in each region of the system; they reveal further that there occur energies in addition to those characterising the local bands and these extra energies constitute a disturbance to the (local) band structures.     

准二维无序系统的电子结构

对形如N_t×N_l型准二维无序系统，只考虑格点之间的最近邻跳跃积分，采用特殊的格点编号方案，在单电子近似下，系统的哈密顿量可表示为简明对称矩阵，借助豪斯荷尔德变换将其约化为对称三对角矩阵，再利用负本征值理论及传输矩阵等方法,对系统态密度、局域长度及电导等电子结构特性进行数值计算. 重点研究了准一维四平行链和五平行链无序系统， 将结果与一维单链、准一维双链及三链系统进行对比，发现随维度的增加，系统的能带有所展宽，能态密度分布发生很大的变化，其峰值数量呈偶数规律增加. 并且在能带中心处存在有局域长度大于系统大小的扩展态，处于这些态下的系统具有较大电导. 从单链到多链，相当于扩大了系统的关联范围，使系统出现了类似非对角长程关联的行为. 关键词： 准二维无序系统 态密度 局域长度 电导     

Diffusion of the electronic excitation in disordered systems

The kinetic equations describing the spreading ot the electronic excitation at zero temperature as a stochastic Brownian motion have been found. In the case of a structural disorder they imply the diffusion ot the excitation into the ranges of the maximum density of atoms. The relaxation time is also density-dependent having the minimum value in the ranges of maximum density of atoms and vice versa. In the case of a substitutional disorder the master equation in the “k”-space imply the spreading of excitation as a decaying wave packet. The relaxation lifetime in the first case of disorder and the lifetime of the coherence state in the second one are much smaller than the radiation lifetimes.     

On the electronic energy spectrum of linear models for disordered systems

In this paper the basic relations for describing the electronic structure of linear models for monatomic and diatomic disordered systems are derived using a F.E.N. theoretical approach. Elegant three terms recurrence formulae between the wavefunctions at three successive atomic sites are established and their relation is discussed with recurrence formulae obtained previously by means of Green's function techniques.     

Anomalously localised electronic states in three-dimensional disordered systems

We study the Anderson model of localisation at the metal-insulator transition in the band centre of three-dimensional disordered samples. For the critical disorder we determine a large number of wave functions of the model and study the distribution of the wave function amplitudes. Deviations from scaling of multifractal correlation functions allow us to discriminate anomalously localised states from the usual critical states. The thus identified anomalously localised states lead to deviations of the critical properties and should be eliminated from the ensemble average for a characterisation of criticality.     

On spectral density of electronic states in disordered systems

In the present paper, the averaged spectral density of electronic states, 〈?(k, E)〉, has been computed for three-dimensional disordered systems with spherical well type atomic potentials. The formula for 〈?(k, E)〉 is derived by using a realistic perturbational approach that takes propagator modification into account, together with a handy approximation due toBallentine. 〈?(k, E)〉 has been computed for various sets of potential strength and concentration, and the dependence of 〈?(k, E)〉 upon these parameters has been discussed. The motivation behind the computations reported here, is to examine the circumstances under which the electron motion in disordered systems is expected to be almost free electronic. Our principal finding is that a simultaneous existence of weak electron-scatterer interaction-potential and high density of scatterers would tend to make the motion of an electron in a disordered system almost like that of a free one.     

Effects of spin interactions in disordered electronic systems: Loop expansions and exact relations among local gauge invariant models

Spindependent ensembles for disordered electronic systems are examined in the region of extended states. We derive relations between spindependent and previously studied spinless ensembles. We prove that these relations are valid in all orders of a graph theory, on the basis of which we propose them to be exact. These exact relations and supplementary two loop order calculations in 2+ dimensions are used to reveal the existence of universality classes for the critical behaviour at the mobility edges. The mobility edge behaviour of a spindependent ensemble with real (random) hopping agrees with that of the spinless phase invariant ensemble except for a crossover to the real matrix ensemble in the limit of vanishing spinflip amplitudes. Anomalous properties in the band center are also discussed. We derive a transformation which maps arbitrary correlation functions of a complex spindependent ensemble into those of the real matrix ensemble. This relation implies the absence of a mobility edge for the complex spindependent ensemble within the validity region of the theory.     

Analyticity of density of states in a gauge-invariant model for disordered electronic systems

Then-orbital gauge-invariant model of disordered electronic systems proposed by Wegner is studied in the regime of dominant diagonal disorder. Analyticity of the density of states is established in two cases: (a) when the number of orbitals is small, (b) when the number of orbitals is large and the energy is in the expected extended states region.     

Stability of the critical behavior of weakly disordered systems against replica symmetry breaking

A field-theoretical approach is used to describe the critical behavior of weakly disordered systems with a p-component order parameter. Renormalization group (RG) analysis of the effective replica Hamiltonian of a model with replica-unsymmetrical interaction potential is carried out in a two-loop approximation directly for three-dimensional systems. The Padé-Borel summation technique is used to determine fixed points of the RG equations for the case of a single-step replica symmetry breaking (RSB). Analysis of their stability showed that the type of stable critical behavior of the disordered systems against the RSB effects remains as before.     

c-Theorem for disordered systems

We find an analog of Zamolodchikov's c-theorem for disordered two-dimensional non-interacting systems in their supersymmetric field theory representation. We show that the energy momentum tensor of such field theories must be a part of a supermultiplet, and that a new parameter b can be introduced with the help of that multiplet. b flows along the renormalization group trajectories much like the central charge for unitary two-dimensional field theories. While it has not been established if this flow is irreversible, that is, if b always flows down to lower values, it does so for all the cases worked out so far. b gives a new way to label different conformal field theories for disordered systems whose central charge is always 0. b turns out to be related to the central extension of a certain algebra, a generalization of the Virasoro algebra, which we show may be present at the critical points of these theories. b is also related to the finite size corrections of the physical free energy of disordered systems. We discuss possible applications by computing b for two-dimensional Dirac fermions with random gauge potential, in other words, for U(1∣1) Kac-Moody algebra.