Fast Fourier-Chebyshev approach to real-space simulations of the Kubo formula

Abstract

The Kubo formula is a cornerstone in our understanding of near-equilibrium transport phenomena. While conceptually elegant, the application of Kubo's linear-response theory to interesting problems is hindered by the need for algorithms that are accurate and scalable to large lattice sizes beyond one spatial dimension. Here, we propose a general framework to numerically study large systems, which combines the spectral accuracy of Chebyshev expansions with the efficiency of divide-and-conquer methods. We use the hybrid algorithm to calculate the two-terminal conductance and the bulk conductivity tensor of 2D lattice models with over $10^7$ sites. By efficiently sampling the microscopic information contained in billions of Chebyshev moments, the algorithm is able to accurately resolve the linear-response properties of complex systems in the presence of quenched disorder. Our results lay the groundwork for future studies of transport phenomena in previously inaccessible regimes.

9 pages, 3 figures

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• Unambiguous Simulation of Diffusive Charge Transport in Disordered Nanoribbons
• Review of the tight-binding method applicable to the properties of moiré superlattices
• Layer-Resolved Quantum Transport in Twisted Bilayer Graphene: Counterflow and Machine Learning Predictions
• Genuine topological Anderson insulator from impurity induced chirality reversal
• General method for calculating transport properties of disordered mesoscopic systems based on the nonequilibrium Green's function formalism
• Reconciling Kubo and Keldysh Approaches to Fermi-Sea-Dependent Nonequilibrium Observables: Application to Spin Hall Current and Spin-Orbit Torque in Spintronics
• Markov Inequality as a Tool for Linear-Scaling Estimation of Local Observables
• Structural dependence of quantum transport properties on topological nodal-line semimetal bilayer borophene