2019/07/02 by Simon Etter, Etter, Simon, Daniel Massatt +5
Computer Science · Materials Science · Mathematics · Physics and Astronomy · #Algorithm #Computation #Condensed matter physics #Conductivity #FOS: Mathematics #FOS: Physical sciences #Graphene research and applications #Kubo formula #Materials Science (cond-mat.mtrl-sci) #Materials science #Mathematics #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Numerical Analysis (math.NA) #Optimization and Search Problems #Physics #Quantum mechanics #Statistical physics #Stochastic Gradient Optimization Techniques #cond-mat.mes-hall #cond-mat.mtrl-sci #cs.NA #math.NA
paper · pdf · doi:10.48550/arxiv.1907.01314
40 pages, 10 figures
openalex publication_date 2019/07/02 · arxiv created 2020/09/23 · arxiv updated 2020/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper presents a unified approach to the modeling and computation of the Kubo conductivity of incommensurate bilayer heterostructures at finite temperature. Firstly, we derive an expression for the large-body limit of Kubo-Greenwood conductivity in terms of an integral of the conductivity function with respect to a current-current correlation measure. We then observe that the incommensurate structure can be exploited to decompose the current-current correlation measure into local contribution and deduce an approximation scheme which is exponentially convergent in terms of domain size. Secondly, we analyze the cost of computing local conductivities via Chebyshev approximation. Our main finding is that if the inverse temperature β is sufficiently small compared to the inverse relaxation time η, namely β\lesssim η-1/2, then the dominant computational cost is O(η-3/2) inner products for a suitably truncated Chebyshev series, which significantly improves on the O(η-2) inner products required by a naive Chebyshev approximation. Thirdly, we propose a rational approximation scheme for the low temperature regime η-1/2 \lesssim β, where the cost of the polynomial method increases up to O(β2), but the rational scheme scales much more mildly with respect to β.