Fermions on Lifshitz Background

TL;DR

This paper investigates the properties of non-relativistic fermions in Lifshitz backgrounds, revealing features like flat bands and analyzing effects at finite temperature and chemical potential using black hole solutions.

Contribution

It introduces a method to compute fermionic Green's functions in Lifshitz geometries with z=2, highlighting novel spectral features such as flat bands.

Findings

Retarded Green's function exhibits flat band features.

Finite temperature and chemical potential effects analyzed.

Lifshitz black hole solutions used for finite conditions.

Abstract

We study a non-relativistic fermionic retarded Green's function by making use of a fermion on the Lifshitz geometry with critical exponent z = 2. With a natural boundary condition, respecting the symmetries of the model, the resultant retarded Green's function exhibits a number of interesting features including a flat band. We also study the finite temperature and finite chemical potential cases where the geometry is replaced by Lifshitz black hole solutions.