Giovanna Marcelli, A new approach to transport coefficients in the quantum spin Hall effect
Channel: Scrambled Maths
Date: 2021-09-08

Giovanna Marcelli, A new approach to transport coefficients in the quantum spin Hall effect

Abstract:
We investigate some foundational issues in the quantum theory of spin transport, in the general case when the unperturbed Hamiltonian operator does not commute with the spin operator in view of Rashba interactions. A gapped periodic one-particle Hamiltonian is perturbed by adding a constant electric field of small intensity and the linear response, with respect to the strength of the electric field, in terms of a spin current is computed. We derive a general formula for the spin conductivity that covers both the choice of the conventional and of the proper spin current operator. We study the independence of the spin conductivity from the choice of the fundamental cell, and we isolate a subclass of discrete periodic models (including the Kane-Mele model) where the conventional and the proper spin conductivity agree. As a consequence of the general theory, we obtain that whenever the spin is (almost) conserved, the spin conductivity is (approximately) equal to the spin-Chern number. The method relies on the characterization of a non-equilibrium almost-stationary state, which well approximates the physical state of the system. This seminar is based on joint work with G. Panati and S. Teufel.

Slides: https://unishare.nl/index.php/s/k8XeDYpWkxntB6k

Recording of the workshop "Learning from Insulators: New Trends in the Study of Conductivity of Metals". For additional material and information, please consult the workshop page
https://www.lorentzcenter.nl/learning-from-insulators-new-trends-in-the-study-of-conductivity-of-metals.html