Re-entrant Superconductivity Through a Quantum Lifshitz Transition in Twisted Trilayer Graphene

TL;DR

This paper investigates re-entrant superconductivity in twisted trilayer graphene, proposing a quantum Lifshitz transition with finite-momentum pairing and mixed singlet-triplet states, based on phenomenological and microscopic theories.

Contribution

It introduces a novel understanding of high-field superconducting phases in TTG as a quantum Lifshitz transition with mixed pairing symmetry, extending insights to TBG.

Findings

Superconductivity in TTG is likely associated with a quantum Lifshitz transition.

High-field phase involves finite-momentum pairing.

Superposition of singlet and triplet pairing states is proposed.

Abstract

A series of recent experiments have demonstrated robust superconductivity in magic-angle twisted trilayer graphene (TTG). In particular, a recent work by Cao et al. (arxiv:2103.12083) studies the behavior of the superconductor in an in-plane magnetic field and out-of-plane displacement field, finding that the superconductor is unlikely to be spin-singlet. This work also finds that at high magnetic fields and a smaller range of dopings and displacement fields, it undergoes a transition to a distinct field-induced superconducting state. Inspired by these results, we develop an understanding of superconductivity in TTG using a combination of phenomenological reasoning and microscopic theory. We describe role that that an in-plane field plays in TTG, and use this understanding to argue that the re-entrant 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 singlet and triplet pairing, and describe the structure of the normal state. We also draw lessons for twisted bilayer graphene (TBG), and 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 $\mathbb{Z}_2$ topological insulator obtained through spontaneous spin symmetry breaking.