Symmetries of electron interactions in Hubbard models of unconventional superconductors

TL;DR

This paper uses symmetry principles to analyze how electron interactions in lattice models of unconventional superconductors reach extrema near high-symmetry points, influencing pairing mechanisms and guiding superconductor discovery.

Contribution

It demonstrates that electron-electron interaction matrix elements are maximized near high-symmetry points in the Brillouin zone, offering a symmetry-based framework for understanding pairing in unconventional superconductors.

Findings

Interaction matrix elements peak near high-symmetry points

Wavevector-dependent orbital composition influences interactions

Results suggest pathways for finite-momentum pairing

Abstract

We use symmetry arguments to show that the matrix elements of electron-electron interaction on a lattice reach extrema in states composed of wavevectors near high-symmetry points of the Brillouin zone. The mechanism is illustrated by minimal models of cuprates and Fe-based superconductors, where this dependence originates from the wavevector-dependent orbital composition of wavefunctions. We discuss how these dependences can facilitate finite-momentum pairing. Our results provide symmetry-based guidance for the search for new high-temperature superconductors.