Local spin density in two-dimensional electron gas with hexagonal boundary

TL;DR

This paper investigates how the geometry of hexagon-shaped samples influences the intrinsic spin-Hall effect in a two-dimensional electron gas, revealing geometry-dependent spin accumulation patterns and effects of Rashba and Dresselhaus couplings.

Contribution

It introduces a triangular tight-binding model for hexagonal samples and analyzes the geometry-dependent spin-Hall accumulation patterns using non-equilibrium Green functions.

Findings

Spin accumulation patterns depend on sample size, spin-orbit coupling, bias, and lead configuration.

Hexagonal geometry leads to different accumulation patterns compared to rectangular samples.

Reversing Rashba and Dresselhaus couplings reverses the spin accumulation pattern.

Abstract

The intrinsic spin-Hall effect in hexagon-shaped samples is investigated. To take into account the spin-orbit couplings and to fit the hexagon edges, we derive the triangular version of the tight-binding model for the linear Rashba [Sov. Phys. Solid State 2, 1109 (1960)] and Dresselhaus [Phys. Rev. 100, 580 (1955)] [001] Hamiltonians, which allow direct application of the Landauer-Keldysh non-equilibrium Green function formalism to calculating the local spin density within the hexagonal sample. Focusing on the out-of-plane component of spin, we obtain the geometry-dependent spin-Hall accumulation patterns, which are sensitive to not only the sample size, the spin-orbit coupling strength, the bias strength, but also the lead configurations. Contrary to the rectangular samples, the accumulation pattern can be very different in our hexagonal samples. Our present work provides a fundamental description of the geometry effect on the intrinsic spin-Hall effect, taking the hexagon as the specific case. Moreover, broken spin-Hall symmetry due to the coexistence of the Rashba and Dresselhaus couplings is also discussed. Upon exchanging the two coupling strengths, the accumulation pattern is reversed, confirming the earlier predicted sign change in spin-Hall conductivity.