General method for calculating transport properties of disordered mesoscopic systems based on the nonequilibrium Green's function formalism

Abstract

Disorder scattering plays important roles in quantum transport as well as various Hall effects, including the second-order nonlinear Hall effect induced by Berry curvature dipole. Calculation of disorder-averaged transport properties usually requires substantial computational resources, especially for higher-order effects. Existing methods are either limited by approximation conditions or constrained by numerical stability, making it difficult to conveniently obtain average physical quantities over a wide range of disorder strength. In this work, we develop a general method for noninteracting system to obtain analytical expressions of disorder averages in finite orders of disorder strength. This method utilizes the Dyson equation to expand physical quantities expressed in terms of the Green's functions into series of disorder-averaged matrices, and the only approximation involved is the truncation of the Dyson equation. Therefore, this method not only avoids the brute force calculation of disorder samples, but also widely applies to different model systems, types of disorder, and the number of Green's functions in the expressions. We demonstrate the applicability of this general method by calculating averages of the linear conductance of a two-terminal system, the spin Hall conductance and the second-order nonlinear conductance of four-terminal Hall setups. It is found that truncation at the fourth order of disorder strength provides a reasonable accuracy and a convenient Padé treatment effectively extends its applicable range. Numerical results also confirms disorder enhancement of the second-order nonlinear Hall current in four-terminal systems. Moreover, more accurate predictions for a broader range of disorder strength can be achieved by including higher-order terms in a similar manner.

References in corpus (26)

• Detection of Individual Gas Molecules Absorbed on Graphene
• Anomalous Hall effect
• Quantum nonlinear Hall effect induced by Berry curvature dipole in time-reversal invariant materials
• Experimental realization of a topological crystalline insulator in SnTe
• Topological Anderson Insulator
• Theory of the topological Anderson insulator
• Disorder-induced nonlinear Hall effect with time-reversal symmetry
• Topological Anderson Insulator in Three Dimensions
• Quantum theory of the nonlinear Hall effect
• Spin-Hall Effect in Two-Dimensional Electron Systems with Rashba Spin-Orbit Coupling and Disorder
• A knitting algorithm for calculating Green functions in quantum systems
• Topological Anderson insulator phenomena
• Spin Hall Current Driven by Quantum Interferences in Mesoscopic Rashba Rings
• Universal spin-Hall conductance fluctuations in two dimensions
• Magnus Hall Effect
• Nonlinear I-V Characteristics of a Mesoscopic Conductor
• Quantum Transport Theory with the Nonequilibrium Coherent Potentials
• Parallel implementation of the recursive Green's function method
• Universal quantized spin-Hall conductance fluctuation in graphene
• Generalized non-equilibrium vertex correction method in coherent medium theory for quantum transport simulation of disordered nanoelectronics
• Fast Fourier-Chebyshev approach to real-space simulations of the Kubo formula
• Nonlinear Hall effect induced by internal Coulomb interaction and phase relaxation process in a four-terminal system with time-reversal symmetry
• Quantum third-order nonlinear Hall effect of a four-terminal device with time-reversal symmetry
• Efficient Chebyshev polynomial approach to quantum conductance calculations: Application to twisted bilayer graphene
• Low field phase diagram of spin-Hall effect in the mesoscopic regime
• Full Counting Statistics of Phonon Transport in Disordered Systems