Peierls instability for systems with several Fermi surfaces: an example from the chiral Gross-Neveu model

TL;DR

This paper demonstrates a multiple Peierls instability in a generalized chiral Gross-Neveu model with multiple Fermi surfaces, showing how the Hartree-Fock ground state can be analytically determined with multiple gaps.

Contribution

It introduces an explicit example of a multiple Peierls instability in a fermionic system with several Fermi surfaces using an extended mean-field approach.

Findings

The spectrum has two gaps aligned with two Fermi energies.

The inhomogeneous ground state is energetically favored over the homogeneous one.

Analytical solutions are obtained for the Hartree-Fock ground state with multiple Fermi surfaces.

Abstract

As is well known, the chiral Gross-Neveu model at finite density can be solved semi-classically with the help of the chiral spiral mean field. The fermion spectrum has a single gap right at the Fermi energy, a reflection of the Peierls instability. Here, we divide the N fermion flavors up into two subsets to which we attribute two different densities. The Hartree-Fock ground state of such a system can again be found analytically, using as mean field the ``twisted kink crystal" of Basar and Dunne. Its spectrum displays two gaps with lower edges coinciding with the two Fermi energies. This solution is favored over the homogeneous one, providing us with an explicit example of a multiple Peierls instability.