# Stability of Topological character of Weyl Semi-metal, and Topological Dipole in Holography

## TL;DR

This paper demonstrates that the topological invariant of strongly interacting Weyl semi-metals remains stable at finite temperature within a holographic framework, even when the Fermi surface becomes fuzzy, and explores the creation of topological dipoles.

## Contribution

It provides a holographic analysis showing the robustness of topological invariants in Weyl semi-metals under interactions and temperature effects, and introduces conditions for topological dipole formation.

## Key findings

- Topological invariant remains stable despite fuzzy Fermi surface.
- Spectral function changes do not affect Berry phase singularity.
- Topological dipoles can be generated depending on fermion mass structure.

## Abstract

We discuss the stability of the topological invariant of the strongly interacting Weyl semi-metal at finite temperature. We find that if the interactions and temperature of the system are controlled by the holography, the topology is stable even in the case the Fermi surface become fuzzy. We give an argument to show that although the self energy changes the spectral function significantly to make the Fermi surface fuzzy, it cannot change the singularity structure of the Berry phase, which leads to the stability of the topology. We also find that depending on the mass term structure of the fermion Lagrangian, topological dipoles can be created.