Non-Perturbative Theory of Charge Transport in Crystalline Solids

Our understanding of charge transport in solids predominantly relies on the Boltzmann transport equation. However, its perturbative approximations for the nuclear dynamics and for its coupling to the electrons can be inaccurate in complex materials [1]. We present an alternative, non-perturbative ab initio Green-Kubo approach based on a new formulation of the flux viz. polarization. It can be evaluated via ab initio molecular dynamics and only requires gauge-fixed properties. At variance with Berry phase approaches [2], it is thus suitable for (semi-)conductors featuring thermal electronic excitations. We demonstrate our method by calculating the electrical conductivity for 2D honeycomb lattices, for silicon, and for the perovskite SrTiO₃. We also compare to non-perturbative Kubo-Greenwood calculations and discuss why this approach has so far only been numerically applicable for materials with strong structural disorder [3].

[1] M. Zacharias, M. Scheffler, and C. Carbogno, Phys. Rev. B 102, 045126 (2020).
[2] R. D. King-Smith and D. Vanderbilt, Phys. Rev. B 47, 1651 (1993).
[3] B. Holst, M. French, and R. Redmer, Phys. Rev. B 83, 235120 (2011); C. Di Paola, et al., Phys. Rev. Research 2, 033055 (2020).