Gate-defined wires in twisted bilayer graphene: From electrical detection of intervalley coherence to internally engineered Majorana modes

Twisted bilayer graphene (TBG) realizes a highly tunable, strongly interacting system featuring superconductivity and various correlated insulating states. We establish gate-defined wires in TBG with proximity-induced spin-orbit coupling as $(i)$ tool for revealing the nature of insulators $(ii)$ platform Majorana-based topological qubits. In particular, we show that band structure wire immersed an `inter-valley coherent' insulator inherits electrically detectable fingerprints symmetry breaking native to latter. Surrounding by superconducting region on one side inter-valley coherent other further enables formation Majorana zero modes--possibly even at magnetic field depending precise symmetry-breaking order present. Our proposal not only introduces gate-tunable qubit medium relying internally generated proximity effects, but can also shed light Cooper-pairing mechanism TBG.