Holographic Fermi surfaces in charge density wave from D2-D8

Subir Mukhopadhyay,Nishal Rai

doi:10.1007/jhep09(2021)160

Subir Mukhopadhyay, Nishal Rai

Open Access

https://doi.org/10.1007/jhep09(2021)160

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Abstract

D2-D8 model admits a numerical solution that corresponds to a charge density wave and a spin density wave. Considering that as the background, we numerically solve the Dirac equation for probe fermions. From the solution, we obtain the Green’s function and study the behaviour of the spectral density. We begin with generic fermions and have studied the formation of the Fermi surface and where it develops a gap. In addition, we have incorporated an ionic lattice and study its effect on the Fermi surface. Then we analysed the worldvolume fermions. In this particular model we do not find Fermi surface for the dual operators.

Highlights

Intersecting D2-D8 brane system develops instability and for a particular region of the parameter space leads to a solution which consists of a charge density wave and a spin density wave
In order to study the Fermi surfaces we look for appropriate peak of spectral density function
Due to spontaneous breaking of the translational symmetry, the background solutions are characterised with a periodicity determined by the minimum of the free energy, which in turn depsends on the chemical potential

Summary

Introduction

Fermi surfaces have been studied for striped solution obtained in a bottom-up approach with co-existing charge density wave and superconducting phases [57] They introduced a lattice by periodic modulation of the chemical potential and studied the Fermi surface. They find when the Fermi surface is large enough and cross the Brillouin zone boundary, it develops a gap, which increases as the strength of the lattice increases. We have manually introduced a generic probe fermion in this background coupled to the gauge field in the fundamental This spatially modulated solution exhibits spontaneous breaking of the translational symmetry. In the presence of an ionic lattice, the gap widens and study of the spectral density function at the inner part indicates that a sufficiently large value of the strength of the ionic lattice will lead to disappearance of Fermi pockets (inner part of the Fermi surface)

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