Correlated Hopf insulators

TL;DR

This paper explores correlation-driven phase transitions in Hopf insulators, revealing new topological states like Weyl semimetals with unique superconducting properties, thus expanding the understanding of unconventional topological matter.

Contribution

It introduces the study of correlation effects in Hopf insulators, uncovering novel phases and linking them to other topological semimetals, which was previously unexplored.

Findings

Emergence of Weyl semimetallic states at the topological transition

Support for non-reciprocal superconductivity in the Weyl phase

Connection between correlated Hopf insulators and other semimetals

Abstract

Hopf insulators represent an exceptional class of topological matter unanticipated by the periodic table of topological invariants. These systems point to the existence of previously unexplored states of matter with unconventional topology. In this work, we take a step toward exploring this direction by investigating correlation-driven instabilities of Hopf insulators. Organizing our analysis around the topological quantum critical point that separates the Hopf insulating phase from a trivial insulator, we demonstrate the emergence of unconventional Weyl semimetallic and topological insulating states. Notably, the Weyl semimetal supports non-reciprocal superconductivity and a Bogoliubov-Fermi surface, potentially providing a novel framework for realizing the superconducting diode effect. Finally, we highlight the interconnectedness of the effective descriptions of correlated Hopf insulators, two-dimensional quadratic band-touching semimetals, and Luttinger semimetals.