Valley-isospin dependence of the quantum Hall effect in a graphenep−njunction

Abstract

We calculate the conductance $G$ of a bipolar junction in a graphene nanoribbon, in the high-magnetic-field regime where the Hall conductance in the $p$-doped and $n$-doped regions is $2e^2∕h$. In the absence of intervalley scattering, the result $G=(e^2∕h)(1-\cos \Phi )$ depends only on the angle $\Phi$ between the valley isospins ($=\text{Bloch}$ vectors representing the spinor of the valley polarization) at the two opposite edges. This plateau in the conductance versus Fermi energy is insensitive to electrostatic disorder, while it is destabilized by the dispersionless edge state which may exist at a zigzag boundary. A strain-induced vector potential shifts the conductance plateau up or down by rotating the valley isospin.