Real-space calculation of the conductivity tensor for disordered topological matter

Abstract

We describe an efficient numerical approach to calculate the longitudinal and transverse Kubo conductivities of large systems using Bastin's formulation. We expand the Green's functions in terms of Chebyshev polynomials and compute the conductivity tensor for any temperature and chemical potential in a single step. To illustrate the power and generality of the approach, we calculate the conductivity tensor for the quantum Hall effect in disordered graphene and analyze the effect of the disorder in a Chern insulator in Haldane's model on a honeycomb lattice.

5 pages, 3 figures and a supplementary material (3 pages)

References in corpus (30)

• The electronic properties of graphene
• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Topological Insulators
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Anomalous Hall effect
• Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator
• Electronic transport in two dimensional graphene
• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• The Kernel Polynomial Method
• Nearly-flat bands with nontrivial topology
• Topological Anderson Insulator
• Modeling electronic structure and transport properties of graphene with resonant scattering centers
• Unified description of the dc conductivity of monolayer and bilayer graphene at finite densities based on resonant scatterers
• Quantum Hall Effect of Dirac Fermions in Graphene: Disorder Effect and Phase Diagram
• Chebyshev-BdG: an efficient numerical approach to inhomogeneous superconductivity
• Investigation of quantum transport by means of O(N) real-space methods
• The dependence of topological Anderson insulator on the type of disorder
• Chebyshev Matrix Product State Impurity Solver for the Dynamical Mean-Field Theory
• Random phase vector for calculating the trace of a large matrix
• Chebyshev expansion for Impurity Models using Matrix Product States
• Numerical approaches to time evolution of complex quantum systems
• Splitting of the Zero-Energy Landau Level and Universal Dissipative Conductivity at Critical Points in Disordered Graphene
• Efficient linear-scaling quantum transport calculations on graphics processing units and applications on electron transport in graphene
• Chebyshev expansion approach to the AC conductivity of the Anderson model
• Relativistic corrections in magnetic systems
• Quantum Hall criticality and localization in graphene with short-range impurities at the Dirac point
• The noncommutative Kubo Formula: Applications to Transport in Disordered Topological Insulators with and without Magnetic Fields
• Dynamical spin Hall conductivity in a magnetic disordered system
• Optical response of electrons in a random potential

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• Quantum Hall effect and semiconductor to semimetal transition in biased black phosphorus
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• Origin of nonlocal resistance in multiterminal graphene on hexagonal-boron-nitride: Fermi surface edge currents rather than Fermi sea topological valley currents
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• Non-linear Hall Effects: Mechanisms and Materials
• Anderson localization and topological transition in Chern insulators
• A magnetic Weyl semimetallic phase in thin films of Eu${}_2$Ir${}_2$O${}_7$
• Semiclassical dynamics of spin density waves
• Unconventional Features in the Quantum Hall Regime of Disordered Graphene: Percolating Impurity States and Hall Conductance Quantization
• Kubo-Bastin approach for the spin Hall conductivity of decorated graphene
• Berry phase manipulation in ultrathin SrRuO${}_3$ films
• Flat Topological Bands and Eigenstate Criticality in a Quasiperiodic Insulator
• Quantum Hall Effect in Graphene with Interface-Induced Spin-Orbit Coupling
• Valley Hall Effect and Non-Local Resistance in Locally Gapped Graphene
• Janus Monolayers of Magnetic Transition Metal Dichalcogenides as an All-in-One Platform for Spin-Orbit Torque
• Structural and electronic properties of realistic two-dimensional amorphous topological insulators
• Anderson-Kitaev spin liquid
• Numerical calculation of the Casimir-Polder interaction between a graphene sheet with vacancies and an atom
• Spin and Charge Transport of Multi-Orbital Quantum Spin Hall Insulators
• Systematic Quantum Cluster Typical Medium Method For the Study of Localization in Strongly Disordered Electronic Systems
• Quantum Hall studies of a Semi-Dirac Nanoribbon
• Efficient Linear Scaling Approach for Computing the Kubo Hall Conductivity
• Quantum transport in flat bands and super-metallicity
• Fast Fourier-Chebyshev approach to real-space simulations of the Kubo formula
• Anisotropic three-dimensional quantum Hall effect and magnetotransport in mesoscopic Weyl semimetals
• Quantum transport in graphene Hall bars: Effects of vacancy disorder
• Disorder-induced topological quantum phase transitions in multi-gap Euler semimetals
• Nonlinear Hall effect on a disordered lattice
• Anatomy of topological Anderson transitions
• Orbital Hall Responses in Disordered Topological Materials
• Strain field in graphene induced by nanopillar mesh
• Charge and Spin Transport Anisotropy in Nanopatterned Graphene
• GPUQT: An efficient linear-scaling quantum transport code fully implemented on graphics processing units
• From topological phase to Anderson localization in a two-dimensional quasiperiodic system
• Scaling of the Integrated Quantum Metric in Disordered Topological Phases
• Cloaking Resonant Scatterers and Tuning Electron Flow in Graphene
• Efficient Time-Domain Approach for Linear Response Functions
• The Calculation of Two-Particle Quantities in the Typical Medium Dynamical Cluster Approximation
• Absence of quantization in the circular photogalvanic effect in disordered chiral Weyl semimetals
• Quantum Hall effect and Landau levels without spatial long-range correlations
• Scattering from spin-polarized charged impurities in graphene
• Decoding the DC and optical conductivities of disordered MoS${}_2$ films: an inverse problem
• Chebyshev Polynomial Method to Landauer-Büttiker Formula of Quantum Transport in Nanostructures
• Optical Hall response of bilayer graphene: the manifestation of chiral hybridised states in broken mirror symmetry lattices
• Orbital Hall effect and topology on a two-dimensional triangular lattice: from bulk to edge
• A spectrum adaptive kernel polynomial method
• Unambiguous Simulation of Diffusive Charge Transport in Disordered Nanoribbons
• Large scale calculations of thermoelectric transport coefficients: a case study of γ-graphyne with point defects
• Shubnikov-de Haas oscillations in the anomalous Hall conductivity of Chern insulators
• Instability of QBC systems to Topological Anderson Insulating phases
• Direct topological insulator transitions in three dimensions are destabilized by non-perturbative effects of disorder
• Review of the tight-binding method applicable to the properties of moiré superlattices
• Sudden quench of harmonically trapped mass-imbalanced fermions
• Fate of Quadratic Band Crossing under quasiperiodic modulation
• Evaluation of real-space second Chern number using the kernel polynomial method
• Real-space spectral simulation of quantum spin models: Application to generalized Kitaev models
• Quantum Hall Effect without Chern Bands
• Fragile magnetic order in metallic quasicrystals
• Disorder, Low-Energy Excitations, and Topology in the Kitaev Spin Liquid