Geometric Superconductivity in 3D Hofstadter Butterfly

TL;DR

This paper explores unconventional superconductivity in a 3D Hofstadter butterfly system, revealing how flat band singularities and quantum geometry enhance superconductivity, with implications for materials like UTe2.

Contribution

It demonstrates that quasi-two-dimensional materials with tilted magnetic fields can produce Hofstadter butterflies at moderate fields, introducing a new mechanism for field-enhanced superconductivity.

Findings

Van-Hove singularities elevate critical temperature.

Quantum geometry influences superconductivity distinctly.

Relevance to re-entrant superconductivity in UTe2.

Abstract

Electrons on the lattice subject to a strong magnetic field exhibit the fractal spectrum of electrons, which is known as the Hofstadter butterfly. In this work, we investigate unconventional superconductivity in a three-dimensional Hofstadter butterfly system. While it is generally difficult to achieve the Hofstadter regime, we show that the quasi-two-dimensional materials with a tilted magnetic field produce the large-scale superlattices, which generate the Hofstadter butterfly even at the moderate magnetic field strength. We first show that the van-Hove singularities of the butterfly flat bands greatly elevate the superconducting critical temperature, offering a new mechanism of field-enhanced superconductivity. Furthermore, we demonstrate that the quantum geometry of the Landau mini-bands plays a crucial role in the description of the superconductivity, which is shown to be clearly distinct from the conventional superconductors. Finally, we discuss the relevance of our results to the recently discovered re-entrant superconductivity of UTe2 in strong magnetic fields.