Name
Title | ||
|---|---|---|
Modeling And Computation Of Kubo Conductivity For Two-Dimensional Incommensurate Bilayers |
Abstract | ||
|---|---|---|
This paper presents a unified approach to the modeling and computation of the Kubo conductivity of incommensurate bilayer heterostructures at finite temperature. First, 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 contributions and deduce an approximation scheme which is exponentially convergent in terms of domain size. Second, we analyze the cost of computing local conductivities via Chebyshev approximation. Our main finding is that if the inverse temperature beta is sufficiently small compared to the inverse relaxation time eta, namely beta less than or similar to eta(-1/2), then the dominant computational cost is O(eta(-3/2)) inner products for a suitably truncated Chebyshev series, which significantly improves on the O(eta(-2)) inner products required by a naive Chebyshev approximation. Third, we propose a rational approximation scheme for the low temperature regime eta(-1/2 )less than or similar to beta, where the cost of the polynomial method increases up to O(beta(2)), but the rational scheme scales much more mildly with respect to beta. |
Year | DOI | Venue |
|---|---|---|
2020 | 10.1137/19M1273499 | MULTISCALE MODELING & SIMULATION |
Keywords | DocType | Volume |
two-dimensional materials, Kubo, Chebyshev | Journal | 18 |
Issue | ISSN | Citations |
4 | 1540-3459 | 0 |
PageRank | References | Authors |
0.34 | 0 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Simon Etter | 1 | 0 | 0.34 |
| Daniel Massatt | 2 | 0 | 0.34 |
| Mitchell Luskin | 3 | 124 | 23.89 |
| Christoph Ortner | 4 | 3 | 0.77 |