Critical Behavior of Four-Terminal Conductance of Bilayer Graphene Domain Walls

TL;DR

This paper investigates the critical behavior of four-terminal conductance in bilayer graphene domain wall junctions, revealing quantum phase transitions and unique conductance phases influenced by electron interactions.

Contribution

It provides a theoretical analysis of quantum critical points and phase transitions in bilayer graphene domain wall junctions, including universal scaling functions and conductance behavior.

Findings

Identification of two classes of quantum critical points.

Calculation of universal scaling functions for conductance.

Discovery of phases with unique charge and valley conductances.

Abstract

Bilayer graphene in a perpendicular electric field can host domain walls between regions of reversed field direction or interlayer stacking. The gapless modes propagating along these domain walls, while not strictly topological, nevertheless have interesting physical properties, including valley-momentum locking. A junction where two domain walls intersect forms the analogue of a quantum point contact. We study theoretically the critical behavior of this junction near the pinch-off transition, which is controlled by two separate classes of non-trivial quantum critical points. For strong interactions, the junction can host phases of unique charge and valley conductances. For weaker interactions, the low-temperature charge conductance can undergo one of two possible quantum phase transitions, each characterized by a specific critical exponent and a collapse to a universal scaling function, which we compute.