Localization and spin transport in honeycomb structures with spin-orbit coupling

TL;DR

This paper investigates electron transport and spin polarization decay in honeycomb structures with spin-orbit coupling, revealing a metal-insulator transition and how spin decay length depends on spin-orbit strength.

Contribution

It introduces a transfer-matrix approach to analyze spin transport and localization in honeycomb lattices with spin-orbit interactions, providing new insights into spin decay and phase transitions.

Findings

Identifies a metal-insulator transition with specific critical exponents.

Shows spin polarization decay length scales as the inverse square of spin-orbit coupling strength.

Provides a method to extract spin decay information from wave-function evolution.

Abstract

Transfer-matrix methods are used for a tight-binding description of electron transport in graphene-like geometries, in the presence of spin-orbit couplings. Application of finite-size scaling and phenomenological renormalization techniques shows that, for strong enough spin-orbit interactions and increasing on-site disorder, this system undergoes a metal-insulator transition characterized by the exponents $\nu=2.71(8)$, $\eta=0.174(2)$. We show how one can extract information regarding spin polarization decay with distance from an injection edge, from the evolution of wave-function amplitudes in the transfer-matrix approach. For (relatively weak) spin-orbit coupling intensity $\mu$, we obtain that the characteristic length $\Lambda_s$ for spin-polarization decay behaves as $\Lambda_s \propto \mu^{-2}$.