Universal Fermi-surface anisotropy renormalization for interacting Dirac fermions with long-range interactions

TL;DR

This paper demonstrates a universal square-root reduction in Fermi surface anisotropy for interacting Dirac fermions with long-range Coulomb interactions, supported by quantum Monte Carlo simulations and applicable to various 2D materials.

Contribution

It reveals a universal anisotropy renormalization law for Dirac fermions with long-range interactions, supported by non-perturbative numerical methods.

Findings

Universal square-root decrease of Fermi-surface anisotropy.

Applicable to Dirac materials like graphene and topological insulators.

Supports the Dirac fermion ground state in composite Fermi liquids.

Abstract

Recent experimental and numerical evidence suggest an intriguing universal relationship between the Fermi surface anisotropy of the non-interacting parent two-dimensional electron gas and the strongly correlated composite Fermi liquid formed in a strong magnetic field close to half-filing. Inspired by these observations, we explore more generally the question of anisotropy renormalization in interacting 2D Fermi systems. Using a recently developed non-perturbative and numerically-exact projective quantum Monte Carlo simulation as well as other numerical and analytic techniques, only for Dirac fermions with long-range Coulomb interactions do we find a universal square-root decrease of the Fermi-surface anisotropy. For the half-filled composite Fermi liquid, this result is surprising since a Dirac fermion ground state was only recently proposed as an alternative to the usual HLR state. The importance of the long-range interaction, expected for Dirac systems, is also consistent with recent transport measurements. Our proposed universality can be tested in several anisotropic Dirac materials including graphene, topological insulators organic conductors, and magic-angle twisted bilayer graphene.