Boltzmann approach to spin-orbit-induced transport in effective quantum theories

TL;DR

This paper develops a Boltzmann transport framework within effective quantum theories to accurately describe spin-orbit-induced transport phenomena, revealing new effects in Rashba 2D models.

Contribution

It introduces a semiclassical Boltzmann approach directly at the effective quantum theory level, clarifying its relation to existing theories and extending the Kubo-Streda formula.

Findings

Identifies a nonzero spin Hall effect in strong Rashba coupling.

Clarifies the link between Boltzmann and quantum kinetic theories.

Extends the Kubo-Streda formula to effective quantum theories.

Abstract

In model studies of the spin/anomalous Hall effect, effective Hamiltonians often serve as the starting point. However, a complete effective quantum theory contains not only the effective Hamiltonian but also the relation linking the physical observables to the canonical ones. We construct the semiclassical Boltzmann (SB) transport framework in the weak disorder-potential regime directly in the level of the effective quantum theory, and confirm this construction by formulating a generalized Kohn-Luttinger density matrix transport theory also in this level. The link and difference between the present SB theory and previous phenomenological Boltzmann, quantum kinetic and usual Kubo-Streda theories are clarified. We also present the slightly generalized Kubo-Streda formula in the level of the effective quantum theory. In this level, it is the generalized Kubo-Streda formula rather than the usual one that leads to the same physical interpretations as the present SB theory. In the application to a Rashba 2D effective model, a nonzero spin Hall effect important in the case of strong Rashba coupling but neglected in previous theories is found.