Quantum interference effects for strongly localized electrons

Kardar-Parisi-Zhang Physics in the Density Fluctuations of Localized Two-Dimensional Wave Packets

We identify the key features of Kardar-Parisi-Zhang (KPZ) universality class in the fluctuations of the wave density logarithm in a two-dimensional Anderson localized wave packet. In our numerical analysis, the fluctuations are found to exhibit an algebraic scaling with distance characterized by an exponent of 1/3, and a Tracy-Widom probability distribution of the fluctuations. Additionally, within a directed polymer picture of KPZ physics, we identify the dominant contribution of a directed path to the wave packet density and find that its transverse fluctuations are characterized by a roughness exponent 2/3. Leveraging on this connection with KPZ physics, we verify that an Anderson localized wave packet in 2D exhibits a stretched exponential correction to its well-known exponential localization.

Theory and experiments for disordered elastic manifolds, depinning, avalanches, and sandpiles

Domain walls in magnets, vortex lattices in superconductors, contact lines at depinning, and many other systems can be modeled as an elastic system subject to quenched disorder. The ensuing field theory possesses a well-controlled perturbative expansion around its upper critical dimension. Contrary to standard field theory, the renormalization group (RG) flow involves a function, the disorder correlator Δ(w), and is therefore termed the functional RG. Δ(w) is a physical observable, the auto-correlation function of the center of mass of the elastic manifold. In this review, we give a pedagogical introduction into its phenomenology and techniques. This allows us to treat both equilibrium (statics), and depinning (dynamics). Building on these techniques, avalanche observables are accessible: distributions of size, duration, and velocity, as well as the spatial and temporal shape. Various equivalences between disordered elastic manifolds, and sandpile models exist: an elastic string driven at a point and the Oslo model; disordered elastic manifolds and Manna sandpiles; charge density waves and Abelian sandpiles or loop-erased random walks. Each of the mappings between these systems requires specific techniques, which we develop, including modeling of discrete stochastic systems via coarse-grained stochastic equations of motion, super-symmetry techniques, and cellular automata. Stronger than quadratic nearest-neighbor interactions lead to directed percolation, and non-linear surface growth with additional Kardar-Parisi-Zhang (KPZ) terms. On the other hand, KPZ without disorder can be mapped back to disordered elastic manifolds, either on the directed polymer for its steady state, or a single particle for its decay. Other topics covered are the relation between functional RG and replica symmetry breaking, and random-field magnets. Emphasis is given to numerical and experimental tests of the theory.

Glassy Properties of Anderson Localization: Pinning, Avalanches, and Chaos

I present the results of extensive numerical simulations, which reveal the glassy properties of Anderson localization in dimension two at zero temperature: pinning, avalanches, and chaos. I first show that strong localization confines quantum transport along paths that are pinned by disorder but can change abruptly and suddenly (avalanches) when the energy is varied. I determine the roughness exponent ζ characterizing the transverse fluctuations of these paths and find that its value ζ=2/3 is the same as for the directed polymer problem. Finally, I characterize the chaos property, namely, the fragility of the conductance with respect to small perturbations in the disorder configuration. It is linked to interference effects and universal conductance fluctuations at weak disorder and more spin-glass-like behavior at strong disorder.

Magnetotransport and conductivity mechanisms in Cu2ZnSnxGe1-xS4 single crystals

Resistivity, ρ(T), and magnetoresistance (MR) are investigated in the Cu₂ZnSn_xGe_1−xS₄ single crystals, obtained by the chemical vapor transport method, between x = 0–0.70, in the temperature range of T ~ 50–300 K in pulsed magnetic field of B up to 20 T. The Mott variable-range hopping (VRH) conductivity is observed within broad temperature intervals, lying inside that of T ~ 80–180 K for different x. The nearest-neighbor hopping conductivity and the charge transfer, connected to activation of holes into the delocalized states of the acceptor band, are identified above and below the Mott VRH conduction domain, respectively. The microscopic electronic parameters, including width of the acceptor band, the localization radius and the density of the localized states at the Fermi level, as well as the acceptor concentration and the critical concentration of the metal-insulator transition, are obtained with the analysis of the ρ(T) and MR data. All the parameters above exhibit extremums near x = 0.13, which are attributable mainly to the transition from the stannite crystal structure at x = 0 to the kesterite-like structure near x = 0.13. The detailed analysis of the activation energy in the low-temperature interval permitted estimations of contributions from different crystal phases of the border compounds into the alloy structure at different compositions.

Mechanisms of charge transfer and electronic properties of Cu2ZnGeS4 from investigations of the high-field magnetotransport

Recent development of the thin film solar cells, based on quaternary compounds, has been focused on the Ge contain compounds and their solid solutions. However, for effective utilization of Cu₂ZnGeS₄, deeper investigations of its transport properties are required. In the present manuscript, we investigate resistivity, ρ (T), magnetoresistance and Hall effect in p-type Cu₂ZnGeS₄ single crystals in pulsed magnetic fields up to 20 T. The dependence of ρ (T) in zero magnetic field is described by the Mott type of the variable-range hopping (VRH) charge transfer mechanism within a broad temperature interval of ~100-200 K. Magnetoresistance contains the positive and negative components, which are interpreted by the common reasons of doped semiconductors. On the other hand, a joint analysis of the resistivity and magnetoresistance data has yielded series of important electronic parameters and permitted specification of the Cu₂ZnGeS₄ conductivity mechanisms outside the temperature intervals of the Mott VRH conduction. The Hall coefficient is negative, exhibiting an exponential dependence on temperature, which is quite close to that of ρ(T). This is typical of the Hall effect in the domain of the VRH charge transfer.

Green functions of interacting systems in the strongly localized regime

We have developed an approach to calculate the single-particle Green function of a one-dimensional many-body system in the strongly localized limit at zero temperature. Our approach sums the contributions of all possible forward scattering paths in configuration space. We demonstrate that for fermions and nearest neighbors interactions the Green function factorizes at every link connecting two sites with the same occupation. As a consequence, the conductance distribution function for interacting systems is log-normal, in the same universality class as non-interacting systems. We have developed a numerical procedure to calculate the ground state and the Green function, generating all possible paths in configuration space. Our results agree with results obtained by exact diagonalization of small systems in the limit of large disorder.

Many-body mobility edge in a mean-field quantum spin glass

The quantum random energy model provides a mean-field description of the equilibrium spin glass transition. We show that it further exhibits a many-body localization-delocalization (MBLD) transition when viewed as a closed quantum system. The mean-field structure of the model allows an analytically tractable description of the MBLD transition using the forward-scattering approximation and replica techniques. The predictions are in good agreement with the numerics. The MBLD transition lies at energy density significantly above the equilibrium spin glass transition, indicating that the closed system dynamics freezes well outside of the traditional glass phase. We also observe that the structure of the eigenstates at the MBLD critical point changes continuously with the energy density, raising the possibility of a family of critical theories for the MBLD transition.

Anderson localization on the Bethe lattice: nonergodicity of extended States

Statistical analysis of the eigenfunctions of the Anderson tight-binding model with on-site disorder on regular random graphs strongly suggests that the extended states are multifractal at any finite disorder. The spectrum of fractal dimensions f(α) defined in Eq. (3) remains positive for α noticeably far from 1 even when the disorder is several times weaker than the one which leads to the Anderson localization; i.e., the ergodicity can be reached only in the absence of disorder. The one-particle multifractality on the Bethe lattice signals on a possible inapplicability of the equipartition law to a generic many-body quantum system as long as it remains isolated.

Magnetoresistance of an Anderson insulator of bosons

We study the magnetoresistance of two-dimensional bosonic Anderson insulators. We describe the change in spatial decay of localized excitations in response to a magnetic field, which is given by an interference sum over alternative tunneling trajectories. The excitations become more localized with increasing field (in sharp contrast to generic fermionic excitations which get weakly delocalized): the localization length ξ(B) is found to change as ξ(-1)(B)-ξ(-1)(0)~B(4/5). The quantum interference problem maps onto the classical statistical mechanics of directed polymers in random media (DPRM). We explain the observed scaling using a simplified droplet model which incorporates the nontrivial DPRM exponents. Our results have implications for a variety of experiments on magnetic-field-tuned superconductor-to-insulator transitions observed in disordered films, granular superconductors, and Josephson junction arrays, as well as for cold atoms in artificial gauge fields.

STUDY OF STRUCTURAL AND TRANSPORT PROPERTIES OF IODINATED AMORPHOUS CONDUCTING CARBON FILMS

Iodine intercalated amorphous conducting carbon (a-C:I) films are prepared by vapor phase pyrolysis of maleic anhydride and iodine. Transmission electron microscopy (TEM), Selected area electron diffraction (SAED) and X-ray photoelectron spectroscopy (XPS) studies reveal the structural changes in the iodinated amorphous conducting carbon (a-C) films. TEM micrographs accounts for a average cluster size of the order of ~900 nm in a-C:I film. SAED study depicts a polycrystalline phase of the intercalated sample. Electrical resistivity of a-C:I samples are found to decrease with the iodine incorporation. Metal–insulator transition is observed as a function of magnetic field.

Interference in disordered systems: a particle in a complex random landscape

We consider a particle in one dimension submitted to amplitude and phase disorder. It can be mapped onto the complex Burgers equation, and provides a toy model for problems with interplay of interferences and disorder, such as the Nguyen-Spivak-Shklovskii model of hopping conductivity in disordered insulators and the Chalker-Coddington model for the (spin) quantum Hall effect. We also propose a direct realization in an experiment with cold atoms. The model has three distinct phases: (I) a high-temperature or weak disorder phase, (II) a pinned phase for strong amplitude disorder, and (III) a diffusive phase for strong phase disorder, but weak amplitude disorder. We compute analytically the renormalized disorder correlator, equivalent to the Burgers velocity-velocity correlator at long times. In phase III, it assumes a universal form. For strong phase disorder, interference leads to a logarithmic singularity, related to zeros of the partition sum, or poles of the complex Burgers velocity field. These results are valuable in the search for the adequate field theory for higher-dimensional systems.

Universal distribution functions in two-dimensional localized systems

We find the conductance distribution function of the two-dimensional Anderson model in the strongly localized limit. The fluctuations of lng grow with lateral size as L1/3 and follow a universal distribution that depends on the type of leads. For narrow leads, it is the Tracy-Widom distribution, which appears in the problem of the largest eigenvalue of random matrices from the Gaussian unitary ensemble and in many other problems like the longest increasing subsequence of a permutation, directed polymers, or polynuclear growth. We also show that for wide leads the conductance follows a related, but different, distribution.

Replica model for an unusual directed polymer in 1+1 dimensions and prediction of the extremal parameter of gapped sequence alignment statistics

Sequence alignment is one of the most important bioinformatics tools for modern molecular biology. The statistical characterization of gapped alignment scores has been a long-standing problem in sequence alignment research. In this paper, we provide a self-contained exposition of sequence alignment, a short review about how this problem is related to the directed polymer problem in statistical physics, and some analytical results that can be used for predicting alignment score statistics. Basically, we present two classes of solutions for the gapped alignment statistics by explicitly calculating the evolution of the few-replica partition function in 1+1 dimensions. We have obtained the conditions under which the more important extremal parameter lambda, characterizing the alignment score statistics, becomes predictable.