We present a scattering theory of transport through noncollinear disordered magnetic insulators. For concreteness, we study and compare the random field model (RFM) and the random anisotropy model (RAM). The RFM and RAM are used to model random spin disorder systems and amorphous materials, respectively. We utilize the Landauer-Buttiker formalism to compute the transmission probability and spin conductance of one-dimensional disordered spin chains. The RFM and the RAM both exhibit Anderson localization, which means that the transmission probability and spin conductance decay exponentially with the system length. We define two localization lengths based on the transmission probability and the spin conductance, respectively. Next, we numerically determine the relationship between the localization lengths and the strength of the disorder. In the limit of weak disorder, we find that the localization lengths obey power laws and determine the critical exponents. Our results are expressed via the universal exchange length and are therefore expected to be general.
Our study of the evolution of transmission eigenvalues, due to changes in various physical parameters in a disordered region of arbitrary dimensions, results in a generalization of the celebrated DMPK equation. The evolution is shown to be governed by a single complexity parameter which implies a deep level of universality of transport phenomena through a wide range of disordered regions. We also find that the interaction among eigenvalues is of many body type that has important consequences for the statistical behavior of transport properties.
We continue to develop a new approach to description of charge kinetics in disordered semiconductors. It is based on fractional diffusion equations. This article is devoted to transient processes in structures under dispersive transport conditions. We demonstrate that this approach allows us (i) to take into account energetic and topological types of disorder in common, (ii) to consider transport in samples with spatial distributions of localized states, and (iii) to describe transport in non-homogeneous materials with distributed dispersion parameter. Using fractional approach provides some s…
Phononless plasmon assisted thermally activated transport through a long disordered array of finite length quantum wires is investigated analytically. Generically strong electron plasmon interaction in quantum wires results in a qualitative change of the temperature dependence of thermally activated resistance in comparison to phonon assisted transport. At high temperatures, the thermally activated resistance is determined by the Luttinger liquid interaction parameter of the wires.
For disordered quantum wires which belong to all ten universality classes, the universal quantities of transport properties are obtained through DMPK approach. Calculated are the universal parts of one- and two-point correlation functions for probability distribution functions of transmission eigenvalues. In this analysis, the asymptotic solution of DMPK equation is used. Transport properties for new universality classes(chiral and Bogoliubov-de Gennes classes) are discussed comparing with those for standard class.
We present a diagrammatic theory for coherent backscattering from disordered dilute media in the nonlinear regime. The approach is non-perturbative in the strength of the nonlinearity. We show that the coherent backscattering enhancement factor is strongly affected by the nonlinearity, and corroborate these results by numerical simulations. Our theory can be applied to several physical scenarios like scattering of light in nonlinear Kerr media, or propagation of matter waves in disordered potentials.
Using the transfer matrix technique, we investigate the propagation of electron through a two dimensional disordered sample. We find that the spatial distribution of electrons is homogeneous only in the limit of weak disorder (diffusive transport regime). In the limit of very strong disorder, we identify a narrow channel through which the electron propagates from one side of the sample to the opposite side. Even in this limit, we prove the wave character of the electron propagation.
Electron transport phenomena in disordered electron systems with spin-orbit coupling in two dimensions and below are studied numerically. The scaling hypothesis is checked by analyzing the scaling of the quasi-1D localization length. A logarithmic increase of the mean conductance is also confirmed. These support the theoretical prediction that the two dimensional metal in systems with spin-orbit coupling has a perfect conductivity. Transport through a Sierpinski carpet is also reported.
In this Letter, we study an Anderson-localization-induced quantized transport in disordered Chern insulators (CIs). By investigating the disordered CIs with a step potential, we find that the chiral interface states emerge along the interfaces of the step potential, and the energy range for such quantized transport can be manipulated through the potential strength. Furthermore, numerical simulations on cases with a multi-step potential demonstrate that such chiral state can be spatially shifted by varying the Fermi energy, and the energy window for quantized transport is greatly enlarged. Expe…
We report on a numerical study of quantum transport in disordered two dimensional graphene and graphene nanoribbons. By using the Kubo and the Landauer approaches, transport length scales in the diffusive (mean free path, charge mobilities) and localized regimes (localization lengths) are computed, assuming a short range disorder (Anderson-type). In agreement with localization scaling theory, the electronic systems are found to undergo a conventional Anderson localization in the zero temperature limit. Localization lengths in weakly disordered ribbons are found to differ by two orders of magni…
We address the controversy concerning the necessary conditions for the observation of Berry phases in disordered mesoscopic conductors. For this purpose we calculate the spin-dependent conductance of disordered two-dimensional structures in the presence of inhomogeneous magnetic fields. Our numerical results show that for both, the overall conductance and quantum corrections, the relevant parameter defining adiabatic spin transport scales with the square root of the number of scattering events, in generalization of Stern's original proposal [Phys. Rev. Lett. 68, 1022 (1992)]. This could hinder…
We study charge transport in a monolayer molybdenum disulfide nanoflake over a wide range of carrier density, temperature, and electric bias. We find that the transport is best described by a percolating picture in which the disorder breaks translational invariance, breaking the system up into a series of puddles, rather than previous pictures in which the disorder is treated as homogeneous and uniform. Our work provides insight to a unified picture of charge transport in monolayer molybdenum disulfide nanoflakes and contributes to the development of next-generation molybdenum disulfide based …
We study heat conduction in quantum disordered harmonic chains connected to general heat reservoirs which are modeled as infinite collection of oscillators. Formal exact expressions for the thermal current are obtained and it is shown that, in some special cases, they reduce to Landauer-like forms. The asymptotic system size dependence of the current is analysed and is found to be similar to the classical case. It is a power law dependence and the power depends on the spectral properties of the reservoirs.
Spin transport through magnetic insulators via magnons has recently been explored for a growing variety of magnetic systems with long-range order and well-understood spin excitation spectra. Here we show dramatic effects of spin transport through an amorphous magnetic insulator, which is both magnetically and structurally disordered. We generate and detect spin flow though amorphous yttrium-iron-garnet ($a$-YIG) thin films in a non-local geometry by use of the spin Hall and inverse spin Hall effects in platinum strips separated by 10 or more microns. By comparing non-local spin transport in $a…
We study electronic transport in graphene nanoribbons with rough edges. We first consider a model of weak disorder that corresponds to an armchair ribbon whose width randomly changes by a single unit cell size. We find that in this case, the low-temperature conductivity is governed by an effective one-dimensional hopping between segments of distinct band structure. We then provide numerical evidence and qualitative arguments that similar behavior also occurs in the limit of strong uncorrelated boundary disorder.
Quantum transport in disordered magnetic fields is investigated numerically in two-dimensional systems. In particular, the case where the mean and the fluctuation of disordered magnetic fields are of the same order is considered. It is found that in the limit of weak disorder the conductivity exhibits a qualitatively different behavior from that in the conventional random magnetic fields with zero mean. The conductivity is estimated by the equation of motion method and by the two-terminal Landauer formula. It is demonstrated that the conductance stays on the order of $e^2/h$ even in the weak d…
We study the dynamics of Dirac and Weyl electrons in disordered point-node semimetals. The ballistic feature of the transport is demonstrated by simulating the wave-packet dynamics on lattice models. We show that the ballistic transport survives under a considerable strength of disorder up to the semimetal-metal transition point, which indicates the robustness of point-node semimetals against disorder. We also visualize the robustness of the nodal points and linear dispersion under broken translational symmetry. The speed of the wave packets slows down with increasing disorder strength, and va…
We study electron transport properties of a monoatomic graphite layer (graphene) with different types of disorder. We show that the transport properties of the system depend strongly on the character of disorder. Away from half filling, the concentration dependence of conductivity is linear in the case of strong scatterers, in line with recent experimental observations, and logarithmic for weak scatterers. At half filling the conductivity is of the order of e^2/h if the randomness preserves one of the chiral symmetries of the clean Hamiltonian; otherwise, the conductivity is strongly affected …
The combined influence of disorder and interactions on the transport properties of electrons in one dimension is investigated. The numerical simulations are carried out by means of the Hartree-Fock-based diagonalization (HFD), a very efficient method to determine the low-energy properties of a disordered many-particle system. We find that the conductance of a strongly localized system can become considerably enhanced by the interactions. The enhancement for long-range interactions is significantly larger than for short-range interactions. In contrast, the conductance of weakly localized system…
The transport characteristics of a disordered MoS$_2$ nanoflake in the insulator regime are studied by electrical and magnetotransport measurements. The layered MoS$_2$ nanoflake is exfoliated from a bulk MoS$_2$ crystal and the conductance $G$ and magnetoresistance are measured in a four-probe setup over a wide range of temperatures. At high temperatures, we observe that $\log_{10}G$ exhibits a $-T^{-1}$ temperature dependence and the transport in the nanoflake dominantly arises from thermal activation. At low temperatures, where the transport in the nanoflake dominantly takes place via varia…
The study explores perpendicular transport through macroscopically inhomogeneous three-dimensional disordered conductors using mesoscopic methods (real-space Green function technique in a two-probe measuring geometry). The nanoscale samples (containing $\sim1000$ atoms) are modeled by a tight-binding Hamiltonian on a simple cubic lattice where disorder is introduced in the on-site potential energy. I compute the transport properties of: disordered metallic junctions formed by concatenating two homogenous samples with different kinds of microscopic disorder, a single strongly disordered interfa…
We consider non-equilibrium transport in disordered conductors. We calculate the interaction correction to the current for a short wire connected to electron reservoirs by resistive interfaces. In the absence of charging effects we find a universal current-voltage-characteristics. The relevance of our calculation for existing experiments is discussed as well as the connection with alternative theoretical approaches.
In this communication, we numerically studied disordered quantum transport in a quantum anomalous Hall insulator-superconductor junction based on the effective edge model approach. In particular, we focus on the parameter regime with the free mean path due to elastic scattering much smaller than the sample size and discuss disordered transport behaviors in the presence of different numbers of chiral edge modes, as well as non-chiral metallic modes. Our numerical results demonstrate that the presence of multiple chiral edge modes or non-chiral metallic modes will lead to a strong Andreev conver…
We examine the charge transport through disordered arrays of metallic dots using numerical simulations. We find power law scaling in the current-voltage curves for arrays containing no voids, while for void-filled arrays charge bottlenecks form and a single scaling is absent, in agreement with recent experiments. In the void-free case we also show that the scaling exponent depends on the effective dimensionality of the system. For increasing applied drives we find a transition from 2D disordered filamentary flow near threshold to a 1D smectic flow which can be identified experimentally using c…
Charge and thermal conductivities are the most important parameters of carbon nanomaterials as candidates for future electronics. In this paper we address the effects of Anderson type disorder in long semiconductor carbon nanotubes (CNTs) to electron charge conductivity and lattice thermal conductivity using the atomistic Green function approach. The electron and phonon transmissions are analyzed as a function of the length of the disordered nanostructures. The thermal conductance as a function of temperature is calculated for different lengths. Analysis of the transmission probabilities as a …
Recent theoretical results on transport in a two-dimensional disordered electron liquid with spin and isospin degrees of freedom are reviewed. A number of experimental features in temperature dependence of resistivity at low temperatures in Si-MOSFET, n-AlAs quantum well and double quantum well heterostructures is explained. Novel behavior of low-temperature resistivity at low temperature in electron systems with isospin degrees of freedom are predicted.
The influence of plasma etched sample edges on electrical transport and doping is studied. Through electrical transport measurements the overall doping and mobility are analyzed for mono- and bilayer graphene samples. As a result the edge contributes strongly to the overall doping of the samples. Furthermore the edge disorder can be found as the main limiting source of the mobility for narrow samples.
We study conductivity of strongly disordered amorphous antimony films under high bias voltages. We observe non-linear current-voltage characteristic, where the conductivity value at zero bias is one of two distinct values, being determined by the sign of previously applied voltage. Relaxation curves demonstrate high stability of these conductivity values on a large timescale. Investigations of the antimony film structure allows to determine the percolation character of electron transport in strongly disordered films. We connect the memory effect in conductivity with modification of the percola…
We study the voltage drop along three-terminal disordered wires in all transport regimes, from the ballistic to the localized regime. This is performed by measuring the voltage drop on one side of a one-dimensional disordered wire in a three-terminal set-up as a function of disorder. Two models of disorder in the wire are considered: (i) the one-dimensional Anderson model with diagonal disorder and (ii) finite-width bulk-disordered waveguides. Based on the known $β$-dependence of the voltage drop distribution of the three-terminal chaotic case, being $β$ the Dyson symmetry index ($β=1$, 2, and…
An analytic theory of electron transport in disordered graphene in a ballistic geometry is developed. We consider a sample of a large width W and analyze the evolution of the conductance, the shot noise, and the full statistics of the charge transfer with increasing length L, both at the Dirac point and at a finite gate voltage. The transfer matrix approach combined with the disorder perturbation theory and the renormalization group is used. We also discuss the crossover to the diffusive regime and construct a ``phase diagram'' of various transport regimes in graphene.
We propose an extension to the original result derived by Simoncelli et al. (https://doi.org/10.1038/s41567-019-0520-x) to encompass the effects of a space and time dependent heat source. Via a Fourier Transfrom, we obtain closed form expressions for the dynamics of the phonon population and coherence as a function of heat source.
This paper presents an analytical study of the coexistence of different transport regimes in quasi-one-dimensional surface-disordered waveguides (or electron conductors). To elucidate main features of surface scattering, the case of two open modes (channels) is considered in great detail. Main attention is paid to the transmission in dependence on various parameters of the model with two types of rough-surface profiles (symmetric and antisymmetric). It is shown that depending on the symmetry, basic mechanisms of scattering can be either enhanced or suppressed. As a consequence, different trans…
We study the effects of disorder on the interlayer transport properties of disordered semiconductor bilayers outside of the quantum Hall regime by performing self-consistent quantum transport calculations. We find that the addition of material disorder to the system affects interlayer interactions leading to significant deviations in the interlayer transfer characteristics. In particular, we find that disorder decreases and broadens the tunneling peak, effectively reducing the interacting system to the non-interacting system, when the mean-free path for the electrons becomes shorter than the s…
We report an electron transport study of lithographically fabricated graphene nanoribbons of various widths and lengths at different temperatures. At the charge neutrality point, a length-independent transport gap forms whose size is inversely proportional to the width. In this gap, electron is localized, and charge transport exhibits a transition between simple thermally activated behavior at higher temperatures and a variable range hopping at lower temperatures. By varying the geometric capacitance through the addition of top gates, we find that charging effects constitute a significant port…
Graphene nanoribbons provide an opportunity to integrate phase-coherent transport phenomena with nanoelectromechanical systems (NEMS). Due to the strain induced by a deflection in a graphene nanoribbon resonator, coherent electron transport and mechanical deformations couple. As the electrons in graphene have a Fermi wavelength λ~ a_0 = 1.4 Å, this coupling can be used for sensitive displacement detection in both armchair and zigzag graphene nanoribbon NEMS. Here it is shown that for ordered as well as disordered ribbon systems of length L, a strain ε~ (w/L)^2 due to a deflection w leads to a …
Hyperuniform disordered photonic materials (HDPM) are spatially correlated dielectric structures with unconventional optical properties. They can be transparent to long-wavelength radiation while at the same time have isotropic band gaps in another frequency range. This phenomenon raises fundamental questions concerning photon transport through disordered media. While optical transparency is robust against recurrent multiple scattering, little is known about other transport regimes like diffusive multiple scattering or Anderson localization. Here we investigate band gaps, and we report Anderso…
We theoretically study the spin and charge generation along with the electron transport on a disordered surface of a doped three-dimensional topological insulator/magnetic insulator junction by using Green's function techniques. We find that the spin and charge current are induced by not only local but also nonlocal magnetization dynamics through nonmagnetic impurity scattering on the disordered surface of the doped topological insulator. We also clarify that the spin current as well as charge density are induced by spatially inhomogeneous magnetization dynamics, and the spin current diffusive…
We develop a temperature dependent theory for singlet exciton hopping transport in disordered semiconductors. It draws on the transport level concept within a Förster transfer model and bridges the gap in describing the transition from equilibrium to non-equilibrium time dependent spectral diffusion. We test the validity range of the developed model using kinetic Monte Carlo simulations and find agreement over a broad range of temperatures. It reproduces the scaling of the diffusion length and spectral shift with the dimensionless disorder parameter and describes in a unified manner the transi…
Transport properties of disordered carbon nanotubes are investigated with including long range Coulomb interactions. The resistivity and optical conductivity are calculated by using the memory functional method. In addition, the effect of localization is taken into account by use of the renormalization group analysis and it is shown that the backward scattering of the intra-valley and that of the inter-valley cannot coexist in the localized regime.
We study the electronic transport in the lowest Landau level of disordered two-dimensional semimetals placed in a homogeneous perpendicular magnetic field. The material system is modeled by the Bernevig-Hughes-Zhang Hamiltonian, which has zero energy Landau modes due to the material's intrinsic Berry curvature. These turn out to be crucially important for the density of states and the static conductivity of the disordered system. We develop an analytical approach to the diffusion and conductivity based on a self-consistent equation of motion for the mean squared displacement. The obtained valu…
We report anomalous quantum transport features in bilayer graphene in presence of a random distribution of structural vacancies. By using an efficient real-space Kubo-Greenwood transport methodology, the impact of a varying density of dimer versus non-dimer vacancies is investigated in very large scale disordered models. While non-dimer vacancies are shown to induce localization regimes, dimer vacancies result in an unexpected ballistic regime whose energy window surprisingly enlarges with increasing impurity density. Such counterintuitive phenomenon is explained by the formation of an effecti…
The coherent potential approximation (CPA) within full counting statistics (FCS) formalism is shown to be a suitable method to investigate average electric conductance, shot noise as well as higher order cumulants in disordered systems. We develop a similar FCS-CPA formalism for phonon transport through disordered systems. As a byproduct, we derive relations among coefficients of different phonon current cumulants. We apply the FCS-CPA method to investigate phonon transport properties of graphene systems in the presence of disorders. For binary disorders as well as Anderson disorders, we calcu…
The role of defect-induced zero-energy modes on charge transport in graphene is investigated using Kubo and Landauer transport calculations. By tuning the density of random distributions of monovacancies either equally populating the two sublattices or exclusively located on a single sublattice, all conduction regimes are covered from direct tunneling through evanescent modes to mesoscopic transport in bulk disordered graphene. Depending on the transport measurement geometry, defect density, and broken sublattice-symmetry, the Dirac point conductivity is either exceptionally robust against dis…
In realistic nanoelectronics, disordered impurities/defects are inevitable and play important roles in electron transport. However, due to the lack of effective quantum transport method to do disorder average, the important effects of disorders remain largely un-explored or poorly understood. Here, we report a generalized non-equilibrium vertex correction method with coherent potential approximation for the non-equilibrium quantum transport simulation of disordered nanoelectronics. In this method, the disorder average of various Green's functions are computed by a generalized coherent potentia…
We report a systematic and detailed numerical study of statistics of the reflection coefficient $(|R(L)|^2)$ and its associated phase ($θ$) for a plane wave reflected from a one-dimensional (1D) disordered medium beyond the random phase approximation (RPA) for Gaussian white-noise disorder. We solve numerically the full Fokker-Planck (FP) equation for the probability distribution in the ($|R(L)|^2,θ(L)$)-space for different lengths of the sample with different "disorder strengths". The statistical electronic transport properties of 1D disordered conductors are calculated using the Landauer fou…
We establish a general mechanism for highly efficient quantum transport through finite, disordered 3D networks. It relies on the interplay of disorder with centro-symmetry and a dominant doublet spectral structure, and can be controlled by proper tuning of only coarse-grained quantities. Photosynthetic light harvesting complexes are discussed as potential biological incarnations of this design principle.
We consider the corrections to the Boltzmann theory of electrical transport arising from the Coulomb interaction in disordered conductors. In this article the theory is formulated in terms of quasiclassical Green's functions. We demonstrate that the formalism is equivalent to the conventional diagrammatic technique by deriving the well-known Altshuler-Aronov corrections to the conductivity. Compared to the conventional approach, the quasiclassical theory has the advantage of being closer to the Boltzmann theory, and also allows description of interaction effects in the transport across interfa…
Weyl semimetals are paradigmatic topological gapless phases in three dimensions. We here address the effect of disorder on charge transport in Weyl semimetals. For a single Weyl node with energy at the degeneracy point and without interactions, theory predicts the existence of a critical disorder strength beyond which the density of states takes on a nonzero value. Predictions for the conductivity are divergent, however. In this work, we present a numerical study of transport properties for a disordered Weyl cone at zero energy. For weak disorder our results are consistent with a renormalizati…
We report measurements of disordered graphene probed by both a high electric field and a high magnetic field. By apply a high source-drain voltage Vsd, we are able to study the current-voltage relation I-Vsd of our device. With increasing Vsd, a crossover from the linear I-Vsd regime to the non-linear one, and eventually to activationless-hopping transport occurs. In the activationless-hopping regime, the importance of Coulomb interactions between charged carriers is demonstrated. Moreover, we show that delocalization of carriers which are strongly localized at low T and at small Vsd occurs wi…
We study numerically the effects of edge and bulk disorder on the conductance of graphene nanoribbons. We compute the conductance suppression due to localization induced by edge scattering. We find that even for weak edge roughness, conductance steps are suppressed and transport gaps appear. These gaps are approximately inversely proportional to the nanoribbon width. On/off conductance ratios grow exponentially with the nanoribbon length. Our results impose severe limitations to the use of graphene in ballistic nanowires.
We have generalized the scattering-matrix theory of multiple Andreev reflections in mesoscopic Josephson junctions to the multi-mode case, and applied it to short superconductor/normal metal/superconductor junctions with diffusive electron transport. Both the dc and ac current-voltage characteristics are analyzed for a wide range of bias voltages $V$. For voltages smaller than the supeconducting gap the dc differential conductance of the junction diverges as $1/\sqrt{V}$.
We present a magneto-transport study of graphene samples into which a mild disorder was introduced by exposure to ozone. Unlike the conductivity of pristine graphene, the conductivity of graphene samples exposed to ozone becomes very sensitive to temperature: it decreases by more than 3 orders of magnitude between 100K and 1K. By varying either an external gate voltage or temperature, we continuously tune the transport properties from the weak to the strong localization regime. We show that the transition occurs as the phase coherence length becomes comparable to the localization length. We al…
The conductance of disordered wires with symplectic symmetry is studied by the supersymmetric field theory. Special attention is focused on the case where the number of conducting channels is odd. Such a situation can be realized in metallic carbon nanotubes. The average dimensionless conductance g is obtained using Zirnbauer's super-Fourier analysis. It is shown that with increasing wire length, g approaches to 1 in the odd-channel case, while g vanishes in the ordinary even-channel case. It should be emphasized that the so-called Zirnbauer's zero mode, which has been believed to be unphysica…
We study thermal transport in the disordered Fermi liquid at low temperatures. Gravitational potentials are used as sources for finding the heat density and its correlation function. For a comprehensive study, we extend the renormalization group (RG) analysis developed for electric transport by including the gravitational potentials into the RG scheme. Our analysis reveals that the Wiedemann-Franz law remains valid even in the presence of quantum corrections caused by the interplay of diffusion modes and the electron electron interaction. In the present scheme this fundamental relation is clos…
We present a numerical study on the light transport properties which are modulated by the disorder strength in quasi-one-dimensional disordered waveguide which consists of periodically arranged scatterers with random dielectric constant. The transport mean free path is found to stay inversely proportional to the square of the relative fluctuation of the dielectric constant as in the 1D and 2D cases but with . The transport properties of light through a sample with a fixed size can be modulated from ballistic to localized regime as well, and a generalized scaling function is defined to determin…
Charge transport is well understood in both highly ordered materials (band conduction) or highly disordered ones (hopping conduction). In moderately disordered materials -- including many organic semiconductors -- the approximations valid in either extreme break down, making it difficult to accurately model the conduction. In particular, describing wavefunction delocalisation requires a quantum treatment, which is difficult in disordered materials that lack periodicity. Here, we present the first three-dimensional model of partially delocalised charge and exciton transport in materials in the …
We report on magneto-transport measurement in disordered graphene under pulsed magnetic field of up to 57T. For large electron or hole doping, the system displays the expected anomalous Integer Quantum Hall Effect (IQHE) specific to graphene up to filling factor $ν=2$. In the close vicinity of the charge neutrality point, the system breaks up into co-existing puddles of holes and electrons, leading to a vanishing Hall and finite longitudinal resistance with no hint of divergence at very high magnetic field. Large resistance fluctuations are observed near the Dirac point. They are interpreted a…
