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

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.

24 pages, 11 figures

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• Spin-Orbit Semimetals in the Layer Groups
• Topologically non-trivial valley states in bilayer graphene quantum point contacts
• High-Temperature Quantum Valley Hall Effect with Quantized Resistance and a Topological Switch
• Spontaneous Chiral Symmetry Breaking in Bilayer Graphene
• Epitaxially defined Luttinger liquids on MoS${}_2$ bicrystals
• Fingerprints of bosonic symmetry protected topological state in a quantum point contact
• Corrugation induced stacking solitons with topologically confined states in gapped bilayer graphene
• Decoherence of charge density waves in beam splitters for interacting quantum wires
• Twisted bilayer graphene as a terahertz plasmonic crystal