Unconventional Self-Similar Hofstadter Superconductivity from Repulsive Interactions

TL;DR

This paper reveals how repulsive interactions and tunable Van Hove singularities in Hofstadter bands can induce unconventional and topological superconductivity, with self-similar properties, in moiré superlattice systems.

Contribution

It introduces a renormalization group analysis showing a new mechanism for Hofstadter superconductivity driven by Van Hove singularities and repulsive interactions, including self-similar RG flow trajectories.

Findings

Control of Van Hove singularities via flux and filling affects superconducting instabilities.

Identification of nodal and chiral topological superconductivity with Chern number ±6.

Discovery of self-similar RG flow and order parameter symmetry in Hofstadter bands.

Abstract

Fractal Hofstadter bands have become widely accessible with the advent of moir\'e superlattices, opening the door to studies of the effect of interactions in these systems. In this work we employ a renormalization group (RG) analysis to demonstrate that the combination of repulsive interactions with the presence of a tunable manifold of Van Hove singularities provides a new mechanism for driving unconventional superconductivity in Hofstadter bands. Specifically, the number of Van Hove singularities at the Fermi energy can be controlled by varying the flux per unit cell and the electronic filling, leading to instabilities toward nodal superconductivity and chiral topological superconductivity with Chern number $\mathcal{C} = \pm 6$. The latter is characterized by a self-similar fixed trajectory of the RG flow and an emerging self-similarity symmetry of the order parameter. Our results establish Hofstadter quantum materials such as moir\'e heterostructures as promising platforms for realizing novel reentrant Hofstadter superconductors.