Intrinsic spin-Hall accumulation in honeycomb lattices: Band structure effects

TL;DR

This paper investigates how the band structure of honeycomb lattices influences intrinsic spin-Hall accumulation patterns, demonstrating the effects of Fermi energy and transport direction on spin and charge transport.

Contribution

It introduces a method to incorporate realistic band structures into the Landauer-Keldysh formalism for analyzing spin-Hall effects in honeycomb lattices.

Findings

ISHA patterns are nearly isotropic near the band bottom

Fermi energy significantly affects ISHA patterns at higher energies

Band structure effects influence transport direction dependence

Abstract

Local spin and charge densities on a two-dimensional honeycomb lattice are calculated by the Landauer-Keldysh formalism (LKF). Through the empirical tight-binding method, we show how the realistic band structure can be brought into the LKF. Taking the Bi(111) surface, on which strong surface states and Rashba spin-orbit coupling are present [Phys. Rev. Lett. 93, 046403 (2004)], as a numeric example, we show typical intrinsic spin-Hall accumulation (ISHA) patterns thereon. The Fermi-energy-dependence of the spin and charge transport in two-terminal nanostructure samples is subsequently analyzed. By changing E_{F}, we show that the ISHA pattern is nearly isotropic (free-electron-like) only when E_{F} is close to the band bottom, and is sensitive/insensitive to E_{F} for the low/high bias regime with such E_{F}. With E_{F} far from the band bottom, band structure effects thus enter the ISHA patterns and the transport direction becomes significant.