Study of the single-particle energy spectrum of disordered systems: III. The two-band case

A previous investigation of the energy spectrum of strongly disordered systems with the help of the recursion method is generalized to the two-band case. The real atomic structure of the considered systems is taken into consideration. The presence of short-range order within the system is shown to be the reason for the existence of extended states and of mobility edges. Typical fields of application are doped crystalline and amorphous Silicon as well as Germanium. For the two-band case a number of results is obtained: Mobility edges and their physical interpretation, localized and extended states as well as the structural conditions for their coexistence, analytical representation of the local density of states and of the state vectors, resonances and the general form of the total density of states (TDS) in the complete energy region. The spectral strength as function of the energy is shown to be discontinuous at the mobility edges. The TDS has a square root behaviour on both sides of the mobility edges what leads to a pseudogap of vanishing width at these points. This edge behaviour is shown to be related with the divergency the localization length of a state has as the state energy tends to the mobility edges. Model calculations are carried out.     

Mobility edges and reentrant localization in one-dimensional dimerized non-Hermitian quasiperiodic lattice

The mobility edges and reentrant localization transitions are studied in one-dimensional dimerized lattice with nonHermitian either uniform or staggered quasiperiodic potentials.We find that the non-Hermitian uniform quasiperiodic disorder can induce an intermediate phase where the extended states coexist with the localized ones,which implies that the system has mobility edges.The localization transition is accompanied by the PT symmetry breaking transition.While if the non-Hermitian quasiperiodic disorder is staggered,we demonstrate the existence of multiple intermediate phases and multiple reentrant localization transitions based on the finite size scaling analysis.Interestingly,some already localized states will become extended states and can also be localized again for certain non-Hermitian parameters.The reentrant localization transitions are associated with the intermediate phases hosting mobility edges.Besides,we also find that the non-Hermiticity can break the reentrant localization transition where only one intermediate phase survives.More detailed information about the mobility edges and reentrant localization transitions are presented by analyzing the eigenenergy spectrum,inverse participation ratio,and normalized participation ratio.     

具有p波超流的一维非公度晶格中迁移率边研究

研究了具有p波超流的一维非公度晶格中迁移率边的性质. 发现适当的p波超流可以增加体系中的迁移率边的数目, 并且通过多分形分析确定了迁移率边所在的位置.     

Electric field dependent mobility edge and theory of the breakdown of the integer quantum Hall effect

We discuss the microscopic mechanism for the onset of dissipation in a quantum Hall system. Based on general results on the time dependence of the states in a disorder-broadened Landau band in the presence of a macroscopic electric field E, it is found that the mobility edges move from the band center towards the band tails when |E| is increased, in agreement with experiments. Since in real samples, |E| is space dependent, the mobility edges are also space dependent. Dissipation (i.e. breakdown of the quantum Hall effect) sets in at points (x, y), where |E(x, y)| has the value for which a mobility edge attains the Fermi energy. This value depends on the disorder potential and on the filling factor. Inside a sample, the conductivities depend on |E(x, y)| and hence on space. We discuss experimental applications, including dissipation in opposite corners of a Hall bar and related breakdown phenomena.     

Bloch-like oscillations in a one-dimensional lattice with long-range correlated disorder

We study the dynamics of an electron subjected to a uniform electric field within a tight-binding model with long-range-correlated diagonal disorder. The random distribution of site energies is assumed to have a power spectrum S(k) approximately 1/k(alpha) with alpha>0. de Moura and Lyra [Phys. Rev. Lett. 81, 3735 (1998)]] predicted that this model supports a phase of delocalized states at the band center, separated from localized states by two mobility edges, provided alpha>2. We find clear signatures of Bloch-like oscillations of an initial Gaussian wave packet between the two mobility edges and determine the bandwidth of extended states, in perfect agreement with the zero-field prediction.     

A derivation for the energy dependence of the density of band tail states in disordered materials

Variational arguments are employed to present the first explicit derivation of the behavior of band tail states and localization length over most of the tail region of a random alloy. Exponential tails are shown to exist near the mobility edges, in conformity with the observation in disordered systems. The character of the states forming the band tails is discussed and, for random alloys, the localization length is shown to exhibit a minimum as a function of energy between band edge and mobility edge.     

Quantum discord and classical correlation signatures of mobility edges in one-dimensional aperiodic single-electron systems

We investigate numerically the quantum discord and the classical correlation in a one-dimensional slowly varying potential model and a one-dimensional Soukoulis–Economou ones, respectively. There are well-defined mobility edges in the slowly varying potential model, while there are discrepancies on mobility edges in the Soukoulis–Economou ones. In the slowly varying potential model, we find that extended and localized states can be distinguished by both the quantum discord and the classical correlation. There are sharp transitions in the quantum discord and the classical correlation at mobility edges. Based on these, we study “mobility edges” in the Soukoulis–Economou model using the quantum discord and the classical correlation, which gives another perspectives for these “mobility edges”. All these provide us good quantities, i.e., the quantum discord and the classical correlation, to reflect mobility edges in these one-dimensional aperiodic single-electron systems. Moreover, our studies propose a consistent interpretation of the discrepancies between previous numerical results about the Soukoulis–Economou model.     

一类一维势场中电子态的研究

研究了在一维势场Ｖ_n＝λｃｏｓ（Ｑn＋ａｎ^ｖ）（０＜ｖ＜１）中运动的电子状态，计算了本征能量和本征态的局域化指数。对Ｑ＝２π／３，系统的能带由三个子能带构成。当λ小于２时，每个子带中有两个迁移率边界。研究了扩展态、局域态以及迁移率边界随参数λ，ν，α的变化。 关键词：     

Majorana zero modes,unconventional real-complex transition,and mobility edges in a one-dimensional non-Hermitian quasi-periodic lattice

A one-dimensional non-Hermitian quasiperiodic p-wave superconductor without PT-symmetry is studied.By analyzing the spectrum,we discovered that there still exists real-complex energy transition even if the inexistence of PT-symmetry breaking.By the inverse participation ratio,we constructed such a correspondence that pure real energies correspond to the extended states and complex energies correspond to the localized states,and this correspondence is precise and effective to detect the mobility edges.After investigating the topological properties,we arrived at a fact that the Majorana zero modes in this system are immune to the non-Hermiticity.     

Faceting of a moving grain boundary and its effect on the kinetic properties of grain boundaries

The motion of an individual half-loop grain boundary in zinc is studied experimentally. A correlation is revealed between the half-loop’s mobility and the change in the shape of its structural elements (curved segments, facets, and grain boundary edges). A hysteresis is observed on the temperature dependence curve of grain boundary mobility. The results from investigating grain boundary migration accompanied by faceting inside zinc bicrystals indicate that unsteady grain boundary motion occurs upon high-temperature isothermal annealing. The unsteady motion is due to the considerable difference between the mobility of a facet and that of the curved part of a grain boundary.     

Localization and off-diagonal disorder

The question of localization is examined in the framework of a tight-binding Hamiltonian with randomness in the off-diagonal matrix elements. It is shown that the mobility edges, although they may move initially inwards into the band with increasing off-diagonal randomness, eventually move outwards leaving always a region of extended states around the middle of the band.     

Magnetic hyperfine field for zinc in nickel

Electron mobility in the narrow band solid with a cellular disorder is investigated by methods of the coherent potential theory. Numerical results for the tight-binding model with the Lorentzian distribution of site potentials are presented. The motion of the electron in the region of extended states is neither a well defined coherent band motion nor a simple Brownian diffusion. The statistical electron-hole correlation proves to be important and increases fast with the potential distribution width to band width ratio. The correlation also increases when approaching the mobility edges.     

Effect of hydrostatic pressure on the migration of tilt grain boundaries in Sn- and Al-bicrystals

Abstract

The use of hydrostatic pressure as an intensive parameter for investigation of grain boundaries (GBs) migration in bicrystals is potentially important in gaining additional information on the mechanism of GB migration. This is because an analysis of the pressure dependence of the GB mobility yields a new activation parameter of the migration process, namely the activation volume V* which quantitatively is the difference between the volumes of the system in the ground and activated states. Only a few experiments to study the pressure dependence of GB mobility are known [1,2]. These experiments were made on polycrystalline materials. They provide the average data for all GBs in polycrystal and do not permit the determination of the connection between GB structure and value of activation volume V* of GB migration. In studying the mobility of single boundaries of a given type, there is the possibility of connecting the activation volume with the GB structural peculiarities, in particular, of determining the misorientation dependence of the activation volume, that is, of determining V* for GBs having various degrees of ordering.     

Non-Hermitian anomalous skin effect

A non-Hermitian topological insulator is fundamentally different from conventional topological insulators. The non-Hermitian skin effect arises in a nonreciprocal tight binding lattice with open edges. In this case, not only topological states but also bulk states are localized around the edges of the nonreciprocal system. We discuss that controllable switching from topological edge states into topological extended states in a chiral symmetric non-Hermitian system is possible. We show that the skin depth decreases with non-reciprocity for bulk states but increases with it for topological zero energy states.     

Almost mobility edges and the existence of critical regions in one-dimensional quasiperiodic lattices

We study a one-dimensional quasiperiodic system described by the Aubry–André model in the small wave vector limit and demonstrate the existence of almost mobility edges and critical regions in the system. It is well known that the eigenstates of the Aubry–André model are either extended or localized depending on the strength of incommensurate potential V being less or bigger than a critical value V _c , and thus no mobility edge exists. However, it was shown in a recent work that for the system with V < V _c and the wave vector α of the incommensurate potential is small, there exist almost mobility edges at the energy E _c±, which separate the robustly delocalized states from “almost localized” states. We find that, besides E _c±, there exist additionally another energy edges E _c′±, at which abrupt change of inverse participation ratio (IPR) occurs. By using the IPR and carrying out multifractal analyses, we identify the existence of critical regions among |E _c±|?≤?|E|?≤?|E _c′±| with the mobility edges E _c± and E _c′± separating the critical region from the extended and localized regions, respectively. We also study the system with V > V _c , for which all eigenstates are localized states, but can be divided into extended, critical and localized states in their dual space by utilizing the self-duality property of the Aubry–André model.     

Stationary states of crystal growth in three dimensions

A new Markov process describing crystal growth in three dimensions is introduced. States of the process are configurations of the crystal surface, which has a terrace-edge-kink structure. The states are continuous along edges but discrete across edges, in accordance with the very different rates for the two types of captures of particles. Stationary distributions, describing steady crystal growth, are found in general. To our knowledge, these are the first examples of stationary distributions for layered crystal growth in three dimensions. The steady growth rate and other quantities are obtained explicitly for two interacting edges. For many interacting edges, growth behavior is determined (a) in various asymptotic regimes including thermodynamic limits, (b) via simulations, and (c) using series (cluster) expansions in the slope of the surface, the first three coefficients being computed. The theoretical growth rates show a marked dependence on surface dimensions. This may contribute to the size dependence and dispersion in the observed growth rate of small crystals.     

Random Block Operators

We study fundamental spectral properties of random block operators that are common in the physical modelling of mesoscopic disordered systems such as dirty superconductors. Our results include ergodic properties, the location of the spectrum, existence and regularity of the integrated density of states, as well as Lifshits tails. Special attention is paid to the peculiarities arising from the block structure such as the occurrence of a robust gap in the middle of the spectrum. Without randomness in the off-diagonal blocks the density of states typically exhibits an inverse square-root singularity at the edges of the gap. In the presence of randomness we establish a Wegner estimate that is valid at all energies. It implies that the singularities are smeared out by randomness, and the density of states is bounded. We also show Lifshits tails at these band edges. Technically, one has to cope with a non-monotone dependence on the random couplings.     

一维准周期晶格中玻色子对的迁移率边

研究了一维非公度的准周期晶格中的玻色子对的迁移率边.通过微扰方法,解析推导出强相互作用极限下准周期晶格中玻色子对迁移率边的解析表达式,通过数值证明在系统参数b较小时,迁移率边的解析结果符合得较好,而当b→1时,解析结果将发生偏离.     

Density of states in the impurity d band and inelastic electron scattering by a system of mixed-valence iron ions in HgSe: Fe crystals

The resistivity and the Hall coefficient of HgSe: Fe crystals with various iron content are experimentally studied in the temperature range 1.3≤T≤300 K and in magnetic fields up to 60 kOe. The temperature dependences of the density and mobility of conduction electrons in these crystals are determined. The influence of spatial charge ordering in the system of mixed-valence iron ions on impurity states in HgSe: Fe crystals is considered. The density of states in the impurity d band is theoretically analyzed, and inelastic electron scattering in which bi-and trivalent iron ions are recharged is discussed. It is shown that the experimentally detected features in the dependence of the density and mobility of electrons on temperature and iron impurity content can be explained by the influence of Coulomb correlations in the mixed-valence iron ion system on the structure of the impurity d band.