Coupled Spin and Pseudo-magnetic Field in Graphene Nanoribbons

TL;DR

This paper explores how pseudo-magnetic fields in strained graphene nanoribbons influence spin states via spin-orbit coupling, revealing potential for edge state manipulation and valley-dependent transport.

Contribution

It demonstrates the coupling between pseudo-magnetic fields and spin in graphene nanoribbons through spin-orbit interactions, affecting edge state degeneracy and propagation.

Findings

Pseudo-magnetic fields lift degeneracy of edge states with opposite spins.

Edge states can propagate only at one edge due to valley-dependent pseudo-magnetic fields.

Group velocities of charge carriers differ at opposite edges, enabling edge-specific conduction.

Abstract

Pseudo-magnetic field becomes an experimental reality after the observation of zero-field Landau level-like quantization in strained graphene, but it is not expected that the time-reversal symmetric pseudo-magnetic fields will have any effect on the spin degree of freedom of the charge carriers. Here, we demonstrate that spin-orbit coupling (SOC) could act as a bridge between pseudo-magnetic field and spin. In quantum spin Hall (QSH) states, the direction of the spin of edge states is tied to their direction of motion because of the SOC. The pseudo-magnetic field affects the clockwise and counter-clock-wise edge currents of the QSH states, and consequently lifts the degenerate edge states of opposite spin orientation. Because of opposite signs of the pseudo-magnetic field in two valleys of graphene, the one-dimensional charge carriers at the two opposite edges have different group velocities, and in some special cases the edge states can only propagate at one edge of the nanoribbon and the group velocity at the other edge becomes zero.