Geometrical spin manipulation in Dirac flakes

TL;DR

This paper demonstrates that in Dirac material flakes with strong spin-orbit coupling, edge states become helically spin-polarized, enabling geometry-controlled spin-resolved transport, supported by numerical and analytical models.

Contribution

It introduces a numerical and analytical study of geometrical spin manipulation in Dirac flakes with intrinsic spin-orbit coupling, revealing helical edge states and spin-resolved transport mechanisms.

Findings

Edge states become helically spin-polarized with strong SOC.

Spin splitting occurs on opposite sides of the flakes.

Transport can be controlled by the flake's geometry.

Abstract

We investigate numerically the spin properties of electrons in flakes made of materials described by the Dirac equation, at the presence of intrinsic spin-orbit-coupling(SOC). We show that electrons flowing along the borders of flakes via edge states, become helically spin-polarized for strong SOC, for materials with and without a gap at the Fermi energy, corresponding to the massive and massless Dirac equation respectively. The helically spin-polarized electrons cause geometrical spin splitting on opposite sides of the flakes, leading to spin-resolved transport controlled by the flake's geometry in a multi-terminal device setup. A simple analytical model containing the basic ingredients of the problem is introduced to get an insight of the helical mechanism, along with our numerical results which are based on an effective tight-binding model.