# Supermetal

## TL;DR

This paper investigates the effects of electron interactions in systems with high-order Van Hove singularities, revealing a novel non-Fermi liquid metallic state called supermetal through renormalization group analysis.

## Contribution

It introduces the concept of supermetal, a non-Fermi liquid state arising from electron interactions at high-order Van Hove singularities, supported by a controlled RG analysis.

## Key findings

- Identification of a nontrivial metallic state called supermetal.
- Discovery of noninteracting and interacting fixed points analogous to $^4$ theory.
- Establishment of an interacting supermetal as a non-Fermi liquid.

## Abstract

We study the effect of electron interaction in an electronic system with a high-order Van Hove singularity, where the density of states shows a power-law divergence. Owing to scale invariance, we perform a renormalization group (RG) analysis to find a nontrivial metallic behavior where various divergent susceptibilities coexist but no long-range order appears. We term such a metallic state as a supermetal. Our RG analysis reveals noninteracting and interacting fixed points, which draws an analogy to the $\phi^4$ theory. We further present a finite anomalous dimension at the interacting fixed point by a controlled RG analysis, thus establishing an interacting supermetal as a non-Fermi liquid.