Reentrant superconductivity through a quantum Lifshitz transition in twisted trilayer graphene

A series of recent experiments has demonstrated robust superconductivity in magic-angle twisted trilayer graphene (TTG). In particular, a recent work by Cao et al. [Nature (London) 595, 526 (2021)] studies the behavior of the superconductor in an in-plane magnetic field and an out-of-plane displacement field, finding that the superconductor is unlikely to have purely spin-singlet pairing. This work also finds that at high magnetic fields and a smaller range of dopings and displacement fields, the superconductor undergoes a transition to a distinct field-induced superconducting state. Inspired by these results, we develop an understanding of the superconductivity in TTG using a combination of phenomenological reasoning and microscopic theory. We describe the role that an in-plane field plays in TTG, and we use this understanding to argue that the reentrant transition may be associated with a quantum Lifshitz phase transition, with the high-field phase possessing finite-momentum pairing. We argue that the superconductor is likely to involve a superposition of singlet and triplet pairing, and we describe the structure of the normal state. We also draw lessons for twisted bilayer graphene (TBG), and we explain the differences in the phenomenology with TTG despite their close microscopic relationship. We propose that a singlet-triplet superposition is realized in the TBG superconductor as well, and that the nu = -2 correlated insulator may be a time-reversal protected Z(2) topological insulator obtained through spontaneous spin symmetry breaking.

Automated summary

Recent experiments have shown robust superconductivity in magic-angle twisted trilayer graphene (TTG). The superconductor in TTG exhibits different behaviors in various magnetic and displacement fields, potentially involving a combination of singlet and triplet pairing. The research provides insights into the superconductivity and normal state structure in TTG, as well as implications for twisted bilayer graphene (TBG).