Valley-selection rule in the equilibration of quantum Hall edge states in bilayer graphene

The Landau levels (LLs) in Bernal-stacked bilayer graphene (BLG) support an electric field and magnetic field-tuned LL diagram in the parameter space of spin, valley, and orbital indices (Li et al., PRL 120, 047701 (2018)). In this work, we study the scattering between the quantum Hall edge states of BLG using a three-zone (ν_s / ν_m / ν_s) line junction structure and examine the role of valley-selection rules. We observe quantized plateaus in the longitudinal resistance R_xx as ν_s and ν_m are varied over a large range. In the scenario of ν_s > ν_m, our results can be well explained by the Landauer-Büttiker formalism without considering any spin/valley index of the edge states. In the scenario of ν_s < ν_m, selective edge state equilibration occurs, and this process obeys the valley-selection rule, similar to the spin-selection rule found in monolayer graphene (Amet et al., PRL 112, 196601 (2014)). Deviations from a perfect valley-selection rule are observed in certain filling factor regions, and we discuss possible reasons. Our work indicates that the valley isospin is a good quantum number for both the bulk LLs and the edge states in BLG and provides useful information for edge state experiments in this material.