Valley detection using a graphene gradual pn junction with spin-orbit coupling: an analytical conductance calculation

TL;DR

This paper derives an analytical formula for the conductance of graphene gradual pn junctions considering spin-orbit coupling and stagger potential, revealing features useful for valley polarization detection.

Contribution

It provides the first analytical conductance expression for graphene pn junctions with spin-orbit coupling and stagger potential, highlighting valley-specific conductance features.

Findings

Conductance drops to a constant value due to the energy gap.

Conductance versus stagger potential shows two Gaussian peaks, each corresponding to a valley.

The results enable valley polarization detection without double-interface devices.

Abstract

Graphene pn junction is the brick to build up variety of graphene nano-structures. The analytical formula of the conductance of graphene gradual pn junctions in the whole bipolar region has been absent up to now. In this paper, we analytically calculated that pn conductance with the spin-orbit coupling and stagger potential taken into account. Our analytical expression indicates that the energy gap causes the conductance to drop a constant value with respect to that without gap in a certain parameter region, and manifests that the curve of the conductance versus the stagger potential consists of two Gaussian peaks -- one valley contributes one peak. The latter feature allows one to detect the valley polarization without using double-interface resonant devices.