Single monkey-saddle singularity of a Fermi surface and its instabilities

TL;DR

This paper investigates the topological and interaction-driven instabilities of higher-order singularities, specifically monkey saddle points, in Fermi surfaces, revealing conditions under which these singularities are stable or destabilized.

Contribution

The study provides a detailed analysis of monkey saddle singularities in Fermi surfaces, including their topological properties and how interactions influence their stability.

Findings

Isolated monkey saddle singularities can be stabilized for spinless electrons with short-range repulsive interactions.

For spinful electrons, repulsive interactions lead to instabilities that destroy the singularity.

Broken symmetries allow for the existence of single monkey saddle singularities in the spectrum.

Abstract

Fermi surfaces can undergo sharp transitions under smooth changes of parameters. Such transitions can have a topological character, as is the case when a higher-order singularity, one that requires cubic or higher-order terms to describe the electronic dispersion near the singularity, develops at the transition. When time-reversal and inversion symmetries are present, odd singularities can only appear in pairs within the Brillouin zone. In this case, the combination of the enhanced density of states that accompany these singularities and the nesting between the pairs of singularities leads to interaction driven instabilities. We present examples of single $n=3$ (monkey saddle) singularities when time-reversal and inversion symmetries are broken. We then turn to the question of what instabilities are possible when the singularities are isolated. For spinful electrons, we find that the inclusion of repulsive interactions destroys any isolated monkey-saddle singularity present in the noninteracting spectrum by developing Stoner or Lifshitz instabilities. In contrast, for spinless electrons and at the mean-field level, we show that an isolated monkey-saddle singularity can be stabilized in the presence of short-range repulsive interactions.