Quantum transport properties of disordered graphene with structural defects (Stone-Wales and divacancies) are investigated using a realistic π-π* tight-binding model elaborated from ab initio calculations. Mean free paths and semiclassical conductivities are then computed as a function of the nature and density of defects (using an order-N real-space Kubo-Greenwood method). By increasing of the defect density, the decay of the semiclassical conductivities is predicted to saturate to a minimum value of 4e^2/πh over a large range (plateau) of carrier density (> 0.5 10^{14}cm^{-2}). Additionally, strong contributions of quantum interferences suggest that the Anderson localization regime could be experimentally measurable for a defect density as low as 1%.
An efficient computational methodology is used to explore charge transport properties in chemically-modified (and randomly disordered) graphene-based materials. The Hamiltonians of various complex forms of graphene are constructed using tight-binding models enriched by first-principles calculations. These atomistic models are further implemented into a real-space order-N Kubo-Greenwood approach, giving access to the main transport length scales (mean free paths, localization lengths) as a function of defect density and charge carrier energy. An extensive investigation is performed for epoxide …
A recently proposed statistical model for the effects of decoherence on electron transport manifests a decoherence-driven transition from quantum-coherent localized to ohmic behavior when applied to the one-dimensional Anderson model. Here we derive the resistivity in the ohmic case and show that the transition to localized behavior occurs when the coherence length surpasses a value which only depends on the second-order generalized Lyapunov exponent $ξ^{-1}$. We determine the exact value of $ξ^{-1}$ of an infinite system for arbitrary uncorrelated disorder and electron energy. Likewise all hi…
We study Anderson localization in graphene with short-range disorder using the real-space Kubo-Greenwood method implemented on graphics processing units. Two models of short-range disorder, namely, the Anderson on-site disorder model and the vacancy defect model, are considered. For graphene with Anderson disorder, localization lengths of quasi-one-dimensional systems with various disorder strengths, edge symmetries, and boundary conditions are calculated using the real-space Kubo-Greenwood formalism, showing excellent agreement with independent transfer matrix calculations and superior comput…
We analyze numerically the thermal conductivity of carbon nanoribbons with ideal and rough edges. We demonstrate that edge disorder can lead to a suppression of thermal conductivity by several orders of magnitude. This effect is associated with the edge-induced Anderson localization and suppression of the phonon transport, and it becomes more pronounced for longer nanoribbons and low temperatures.
We report observations of the Coulomb drag effect between two effectively 2-d insulating a-Si_{1-x}Nb_{x} films. We find that there only exist a limited range of experimental parameters over which we can measure a sizable linear-response transresistivity (ρ_{d}). The temperature dependence of ρ_{d} is consistent with the layers being Efros-Shklovskii Anderson insulators provided that a 3-d density of states and a localization length smaller than that obtained from the DC layer-conductivity are assumed.
A field theory of the Anderson transition in two dimensional disordered systems with spin-orbit interactions and time-reversal symmetry is developed, in which the proliferation of vortex-like topological defects is essential for localization. The sign of vortex fugacity determines the $Z_2$ topological class of the localized phase. There are two distinct, but equivalent transitions between the metallic phase and the two insulating phases. The critical conductivity and correlation length exponent of these transitions are computed in a $N=1-ε$ expansion in the number of replicas, where for small…
After exactly half a century of Anderson localization, the subject is more alive than ever. Direct observation of Anderson localization of electrons was always hampered by interactions and finite temperatures. Yet, many theoretical breakthroughs were made, highlighted by finite-size scaling, the self-consistent theory and the numerical solution of the Anderson tight-binding model. Theoretical understanding is based on simplified models or approximations and comparison with experiment is crucial. Despite a wealth of new experimental data, with microwaves, light, ultrasound and cold atoms, many …
Presented here is a nanowire model, consisting of coupled elastic membranes with the purpose of investigating thermal transport in quasi-one-dimensional quantum systems. The vibrations of each elastic membrane are quantized and the flow of the vibrational energy between adjacent membranes is allowed. The ends of the nanowire are attached to thermal baths held at different temperatures. We derived quantum master equation for energy flow across the nanowire and obtained thermal currents and other key observables. We study the effects of a disordered boundary on the thermal current by randomizing…
The Anderson localization of thermal phonons has been shown only in few nano-structures with strong random disorder by the exponential decay of transmission to zero and a thermal conductivity maximum when increasing system length. In this work, we present a path to demonstrate the phonon localization with distinctive features in graded superlattices with short-range order and long-range disorder. A thermal conductivity minimum with system length appears due to the exponential decay of transmission to a non-zero constant, which is a feature of partial phonon localization caused by the moderate …
Atomically thin rhenium disulphide (ReS2) is a member of the transition metal dichalcogenide (TMDC) family of materials characterized by weak interlayer coupling and a distorted 1T structure. Here, we report on the electrical transport study of mono- and multilayer ReS2 with polymer electrolyte gating. We find that the conductivity of monolayer ReS2 is completely suppressed at high carrier densities, an unusual feature unique to monolayers, making ReS2 the first example of such a material. While thicker flakes of ReS2 also exhibit a conductivity dome and an insulator-metal-insulator sequence, …
Anderson localization of electron states on graphene lattice with diagonal and off-diagonal (OD) disorder in the absence of magnetic field is investigated by using the standard finite-size scaling analysis. In the presence of diagonal disorder all states are localized as predicted by the scaling theory for two-dimensional systems. In the case of OD disorder, the states at the Dirac point (E=0) are shown to be delocalized due to the specific chiral symmetry, although other states ($E \neq 0$) are still localized. In OD disorder the conductance at E=0 in an $M\times L$ rectangular system at the …
This letter reports thermopower and conductivity measurements through the metal-insulator transition for 2-dimensional electron gases in high mobility Si-MOSFET's. At low temperatures both thermopower and conductivity show critical behavior as a function of electron density which is very similar to that expected for an Anderson transition. In particular, when approaching the critical density from the metallic side the diffusion thermopower appears to diverge and the conductivity vanishes. On the insulating side the thermopower shows an upturn with decreasing temperature.
Experimental realization of single-layer MoSi2N4 is among the latest groundbreaking advances in the field of two-dimensional (2D) materials. Inspired by this accomplishment, herein we conduct first-principles calculations to explore the stability of MC2N4 (M= Cr, Mo, W, V, Nb, Ta, Ti, Zr, Hf) monolayers. Acquired results confirm the desirable thermal, dynamical and mechanical stability of MC2N4 (M= Cr, Mo, W, V) nanosheets. Interestingly, CrC2N4, MoC2N4 and WC2N4 monolayers are found to be semiconductors with band gaps of 2.32, 2.76 and 2.86 eV, respectively, using the HSE06 functional, wherea…
Nothing is known about the thermal conductivity in twisted bilayer graphene (TBG) at small twist angles, and how it approaches its aligned value as the twist angle approaches 0 degrees. To provide insight into these questions, we perform large scale non-equilibrium molecular dynamics calculations on commensurate TBG structures with angles down to 1.87 degrees. The results show a smooth, non-monotonic behavior of the thermal conductivity with respect to the commensurate lattice constant. As the commensurate lattice constant increases, the thermal conductivity initially decreases by 50%, and the…
The anomalous behavior of electron induced phonon transport is investigated using an Anderson-Holstein based dissipative quantum dot setup under two relevant bias situations: (a) a voltage bias in the absence of an electronic temperature gradient and (b) an electronic temperature gradient at zero voltage. It is shown that the direction of phonon transport in the non-linear regime is different in the two cases since the first case facilitates the accumulation of phonons in the dot and the second case leads to the absorption of phonons in the dot. In the linear regime, both the phonon and electr…
We consider the properties of the type II Weyl semimetals at low temperatures basing on the particular tight - binding model. In the presence of electric field directed along the line connecting the Weyl points of opposite chirality the occupied states flow along this axis giving rise to the creation of electron - hole pairs. The electrons belong to a vicinity of one of the two type II Weyl points while the holes belong to the vicinity of the other. This process may be considered as the manifestation of the chiral anomaly that exists without any external magnetic field. It may be observed expe…
For the two-dimensional ideal electron gas with the Rashba spin-orbit interaction and in the presence of non-magnetic short-ranged potential impurities the spin-Hall conductivity $σ_{sH}$ is found by direct microscopic calculation. Within the semiclassical approximation $\hbar/τ\ll ε_F$ and $Δ\ll ε_F$ the value of $σ_{sH}$ is zero for arbitrary ratio of the spin-orbit splitting $Δ$ and the inverse elastic scattering time $1/τ$.
The Anderson localization transition is considered at finite temperatures. This includes the electrical conductivity as well as the electronic thermal conductivity and the thermoelectric coefficients. An interesting critical behavior of the latter is found. A method for characterizing the conductivity critical exponent, an important signature of the transition, using the conductivity and thermopower measurements, is outlined.
We report on robust features of the longitudinal conductivity ($σ_{xx}$) of the graphene zero-energy Landau level in presence of disorder and varying magnetic fields. By mixing an Anderson disorder potential with a low density of sublattice impurities, the transition from metallic to insulating states is theoretically explored as a function of Landau-level splitting, using highly efficient real-space methods to compute the Kubo conductivities (both $σ_{xx}$ and Hall $σ_{xy}$). As long as valley-degeneracy is maintained, the obtained critical conductivity $σ_{xx}\simeq 1.4 e^{2}/h$ is robust up…
We numerically analyze the energy level statistics of the Anderson model with Gaussian site disorder and constant hopping. The model is realized on different two-dimensional lattices, namely, the honeycomb, the kagomé, the square, and the triangular lattice. By calculating the well-known statistical measures viz., nearest neighbor spacing distribution, number variance, the partition number and the dc electrical conductivity from Kubo-Greenwood formula, we show that there is clearly a delocalization to localization transition with increasing disorder. Though the statistics in different lattice …
We have surveyed the in-plane transport properties of the graphene twist bilayer using (i) a low-energy effective Hamiltonian for the underlying electronic structure, (ii) an isotropic elastic phonon model, and (iii) the linear Boltzmann equation for elastic electron-phonon scattering. We find that transport in the twist bilayer is profoundly sensitive to the rotation angle of the constituent layers. Similar to the electronic structure of the twist bilayer the transport is qualitatively different in three distinct angle regimes. At large angles ($θ> \,\approx\!\!10^\circ$) and at temperatures …
The hallmark property of two-dimensional topological materials is the incredible robustness of the quantized Hall conductivity to disorder. That robustness arises from the fact that in the topological band gap, transport can occur only along the edges modes, which are immune to scattering. However, for sufficiently strong disorder, the band gap closes and the system becomes topologically trivial as all states become localized, such that all transport vanishes -- in accordance with Anderson localization. It therefore came as a surprise when it was suggested that, for a two-dimensional quantum s…
For an isotropic single-band system, it is well known that the semiclassical Boltzmann transport theory within the relaxation time approximation and the Kubo formula with the vertex corrections provide the same result with the $(1-\cosθ)$ factor in the inverse transport relaxation time. In anisotropic multiband systems, the semiclassical Boltzmann transport equation is generalized to coupled integral equations relating transport relaxation times at different angles in different bands. Using the Kubo formula, we study the vertex corrections to the dc conductivity in anisotropic multiband system…
Percolation from Quantum Metric in Flat-Band Delocalization
Beijing National Laboratory for Condensed Matter Physics, and Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）
The electronic thermoelectric coefficients are analyzed in the vicinity of one and two Anderson localization thresholds in three dimensions. For a single mobility edge, we correct and extend previous studies, and find universal approximants which allow to deduce the critical exponent for the zero-temperature conductivity from thermoelectric measurements. In particular, we find that at non-zero low temperatures the Seebeck coefficient and the thermoelectric efficiency can be very large on the "insulating" side, for chemical potentials below the (zero-temperature) localization threshold. Correct…
We explore the longitudinal conductivity of graphene at the Dirac point in a strong magnetic field with two types of short-range scatterers: adatoms that mix the valleys and "scalar" impurities that do not mix them. A scattering theory for the Dirac equation is employed to express the conductance of a graphene sample as a function of impurity coordinates; an averaging over impurity positions is then performed numerically. The conductivity $σ$ is equal to the ballistic value $4e^2/πh$ for each disorder realization provided the number of flux quanta considerably exceeds the number of impurities.…
The electric conductance of a strip of undoped graphene increases in the presence of a disorder potential, which is smooth on atomic scales. The phenomenon is attributed to impurity-assisted resonant tunneling of massless Dirac fermions. Employing the transfer matrix approach we demonstrate the resonant character of the conductivity enhancement in the presence of a single impurity. We also calculate the two-terminal conductivity for the model with one-dimensional fluctuations of disorder potential by a mapping onto a problem of Anderson localization.
We study, both experimentally and numerically, the Anderson localization phenomenon in torsional waves of a disordered elastic rod, which consists of a cylinder with randomly spaced notches. We find that the normal-mode wave amplitudes are exponentially localized as occurs in disordered solids. The localization length is measured using these wave amplitudes and it is shown to decrease as a function of frequency. The normal-mode spectrum is also measured as well as computed, so its level statistics can be analyzed. Fitting the nearest-neighbor spacing distribution a level repulsion parameter is…
Systems with the power-law quasiparticle dispersion $ε_{\bf k}\propto k^α$ exhibit non-Anderson disorder-driven transitions in dimensions $d>2α$, as exemplified by Weyl semimetals, 1D and 2D arrays of ultracold ions with long-range interactions, quantum kicked rotors and semiconductor models in high dimensions. We study the wavefunction structure in such systems and demonstrate that at these transitions they exhibit fractal behaviour with an infinite set of multifractal exponents. The multifractality persists even when the wavefunction localisation is forbidden by symmetry or topology and occu…
We consider d dimensional systems which are localized in the absence of interactions, but whose single particle (SP) localization length diverges near a discrete set of (single-particle) energies, with critical exponent ν. This class includes disordered systems with intrinsic- or symmetry-protected- topological bands, such as disordered integer quantum Hall insulators. In the absence of interactions, such marginally localized systems exhibit anomalous properties intermediate between localized and extended including: vanishing DC conductivity but sub-diffusive dynamics, and fractal entanglement…
We extend the microscopic Fermi-liquid theory for the Anderson impurity [Phys.\ Rev.\ B {\bf 64}, 153305 (2001)] to explore non-equilibrium transport at finite magnetic fields. Using the Ward identities in the Keldysh formalism with the analytic and anti-symmetric properties of the vertex function, the spin-dependent Fermi-liquid corrections of order $T^2$ and $(eV)^2$ are determined at low temperatures $T$ and low bias voltages $eV$. Away from half-filling, these corrections can be expressed in terms of the linear and non-linear static susceptibilities which represent the two-body and three-b…
We present a model for microwave photoconductivity in two-dimensional electron systems (2DESs) in a magnetic field at the microwave frequencies lower that the electron cyclotron frequency when the intra-Landau level (LL) transitions dominate. Using this model, we explain the effect of decrease in the 2DES dissipative conductivity (and resistivity) and smearing of its Shubnikov -- de Haas oscillations by microwave radiation observed recently \cite{1,2}. The model invokes the concept of suppression of elastic impurity scattering of electrons by the microwave electric field. We calculated the dep…
It is commonly believed that a non-interacting disordered electronic system can undergo only the Anderson metal-insulator transition. It has been suggested, however, that a broad class of systems can display disorder-driven transitions distinct from Anderson localisation that have manifestations in the disorder-averaged density of states, conductivity and other observables. Such transitions have received particular attention in the context of recently discovered 3D Weyl and Dirac materials but have also been predicted in cold-atom systems with long-range interactions, quantum kicked rotors and…
The lattice thermal conductivity and thermal transport properties of 2D $α$-selenene are investigated based on the first-principles calculations. The isotropic in-plane thermal conductivity is as low as 3.04 W m$^{-1}$ K$^{-1}$ at room temperature, even abnormally lower than $α$-tellurene which processes analogous configuration and lower Debye temperature. We find this abnormal phenomenon reasonably stems from the larger anharmonicity of the acoustic phonon branch. Moreover, the phonon spectra, elastic properties, and related thermal properties are also exhibited. Acoustic phonons contribute m…
