# Vestigial singlet pairing in a fluctuating magnetic triplet superconductor and its implications for graphene superlattices

## TL;DR

Researchers explore a new type of superconducting state in graphene systems that could explain recent experimental observations.

## Contribution

They identify a unique superconducting state with three electrons and one hole, which may explain properties seen in graphene moiré systems.

## Key findings

- The model exhibits vestigial phases like charge-4e superconductivity and broken time-reversal symmetry.
- A phase with finite d ⋅ N shows BCS-like symmetries and metastable supercurrents but different spectral properties.
- The electronic density of states suppression resembles both fully gapped and nodal superconductors.

## Abstract

Stacking and twisting graphene layers allows to create and control a two-dimensional electron liquid with strong correlations. Experiments indicate that these systems exhibit strong tendencies towards both magnetism and triplet superconductivity. Motivated by this phenomenology, we study a 2D model of fluctuating triplet pairing and spin magnetism. Individually, their respective order parameters, d and N, cannot order at finite temperature. Nonetheless, the model exhibits a variety of vestigial phases, including charge-4e superconductivity and broken time-reversal symmetry. Our main focus is on a phase characterized by finite d ⋅ N, which has the same symmetries as the BCS state, a Meissner effect, and metastable supercurrents, yet rather different spectral properties: most notably, the suppression of the electronic density of states at the Fermi level can resemble that of either a fully gapped or nodal superconductor, depending on parameters. This provides a possible explanation for recent tunneling experiments in the superconducting phase of graphene moiré systems.

P. Poduval et al. theoretically study the nonzero-temperature vestigial phases of a 2D model exhibiting both triplet superconductivity and magnetism. They show that this model allows for a unique superconducting state in which the condensate consists of entities with three electrons and one hole, with properties similar to those seen in experiments on moiré systems.