Graphene pn-junction in a quantizing magnetic field: Conductance at intermediate disorder strength

TL;DR

This paper investigates how conductance in a graphene pn-junction under high magnetic fields varies with disorder, providing a detailed distribution model bridging clean and strongly disordered regimes.

Contribution

It offers an exact solution for the conductance distribution in the crossover from clean to disordered graphene pn-junctions, connecting microscopic disorder to macroscopic conductance.

Findings

Conductance distribution is derived for intermediate disorder strengths.

Results interpolate between clean limit and strong disorder limit.

The model relates microscopic disorder parameters to conductance behavior.

Abstract

In a graphene {\em pn} junction at high magnetic field, unidirectional "snake states" are formed at the {\em pn} interface. In a clean {\em pn} junction, each snake state exists in one of the valleys of the graphene band structure, and the conductance of the junction as a whole is determined by microscopic details of the coupling between the snake states at the {\em pn} interface and quantum Hall edge states at the sample boundaries [Tworzydlo {\em et al.}, Phys. Rev. B {\bf 76}, 035411 (2007)]. Disorder mixes and couples the snake states. We here report a calculation of the full conductance distribution in the crossover between the clean limit and the strong disorder limit, in which the conductance distribution is given by random matrix theory [Abanin and Levitov, Science {\bf 317}, 641 (2007)]. Our calculation involves an exact solution of the relevant scaling equation for the scattering matrix, and the results are formulated in terms of parameters describing the microscopic disorder potential in bulk graphene.