A new Time-Domain Approach for Linear Responses and Charge Transport

Linear-response theory is a powerful theoretical framework to investigate, e.g., electrical and magnetic transport and to compare

theory with experiments. Many intriguing quantum-transport phenomena such as quantum Hall effects, spin Hall effects, and quantum spin Hall effects have

been derived within this framework.  Beyond the general theory, strong efforts have been spent in the last decade to develop efficient and accurate computational methods to calculate charge transport in condensed matter. [1]

In our recent work, we present a new time-domain approach to calculate arbitrary linear responses, which is based on a decomposition of the general Kubo formula into time-symmetric and time-antisymmetric parts. [2] The new algorithm is at least 1000 times faster compared to former time evolution schemes. [3] As a showcase, we have investigated the quantum anomalous Hall effect of the disordered Haldane model, where the quantum dynamics of the topological state have been analyzed. The proposed theory and computational method provide a promising route to access transport phemomena in complex and topological systems.

[1] Z. Fan et al., Physics Reports, 903, 1-69 (2021)

[2] M. Panhans and F. Ortmann, Phys. Rev. Lett. 127, 016601 (2021)

[3] F. Ortmann, N. Leconte, and Stephan Roche. Phys. Rev. B 91, 165117 (2015)