Spin Hall Conductivity on the Anisotropic Triangular Lattice

TL;DR

This paper investigates how anisotropy in a triangular lattice affects spin Hall conductivity, revealing significant changes in magnitude and sign, with implications for spintronics and topological properties.

Contribution

It provides a systematic analysis of anisotropic effects on spin Hall conductivity on a triangular lattice, including Berry phase insights and sign change mechanisms.

Findings

Anisotropy drastically alters spin Hall conductivity.

Sign reversal occurs at specific carrier densities.

Differences from square lattice highlight lattice-specific effects.

Abstract

We present a detailed study of the spin Hall conductivity on a two-dimensional triangular lattice in the presence of Rashba spin-orbit coupling. In particular, we focus part of our attention on the effect of the anisotropy of the nearest neighbor hopping amplitude. It is found that the presence of anisotropy has drastic effects on the spin Hall conductivity, especially in the hole doped regime where a significant increase or/and reversed sign of the spin Hall conductivity has been obtained. We also provide a systematic analysis of the numerical results in terms of Berry phases. The changes of signs observed at particular density of carriers appear to be a consequence of both Fermi surface topology and change of sign of electron velocity. In addition, in contrast to the two-dimensional square lattice, it is shown that the tight binding spin-orbit Hamiltonian should be derived carefully from the continuous model on the triangular lattice.