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

In a graphene $pn$ junction at high magnetic field, unidirectional ``snake states'' are formed at the $pn$ interface. In a clean $pn$ 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 $pn$ interface and quantum Hall edge states at the sample boundaries [Tworzyd\l{}o et al., Phys. Rev. B 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 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.