Gate-defined wires in twisted bilayer graphene: Electrical detection of inter-valley coherence

Twisted bilayer graphene (TBG) realises a highly tunable, strongly interacting system featuring superconductivity and various correlated insulating states whose precise nature remains largely unknown. I introduce gate-defined wires in TBG with proximity-induced spin-orbit coupling as a tool for revealing the nature of correlated insulators. In particular, a class of phases possessing 'inter-valley coherent' order has been widely championed, not only as characterising the correlated insulators, but also as mediating the proximate superconductivity. Nevertheless, the symmetry breaking order in these states occurs at the level of the microscopic graphene lattice, making their experimental verification challenging - particularly in fully encapsulated samples. I demonstrate that the band structure of a gate-defined wire immersed in an inter-valley coherent correlated insulator inherits electrically detectable fingerprints of inter-valley coherence, thus promoting ultra-short-scale symmetry breaking order to a large-scale conductance signature.