Thermodynamics and transport of holographic nodal line semimetals

TL;DR

This paper investigates the thermodynamic and transport properties of a holographic model of nodal line semimetals, revealing temperature-dependent behavior of nodal lines and detailed transport coefficients, with implications for real materials.

Contribution

It introduces a holographic model capturing multiple nodal lines, their temperature evolution, and controls low-frequency conductivity, advancing understanding of NLSMs in strongly coupled regimes.

Findings

Multiple nodal lines at zero temperature broaden and vanish with increasing temperature.

Transport coefficients such as conductivities and viscosities are computed as functions of temperature.

A new non-linear coupling allows tuning of low-frequency electrical conductivity.

Abstract

We study various thermodynamic and transport properties of a holographic model of a nodal line semimetal (NLSM) at finite temperature, including the quantum phase transition to a topologically trivial phase, with Dirac semimetal-like conductivity. At zero temperature, composite fermion spectral functions obtained from holography are known to exhibit multiple Fermi surfaces. Similarly, for the holographic NLSM we observe multiple nodal lines instead of just one. We show, however, that as the temperature is raised these nodal lines broaden and disappear into the continuum one by one, so there is a finite range of temperatures for which there is only a single nodal line visible in the spectrum. We compute several transport coefficients in the holographic NLSM as a function of temperature, namely the charge and thermal conductivities, and the shear viscosities. By adding a new non-linear coupling to the model we are able to control the low frequency limit of the electrical conductivity in the direction orthogonal to the plane of the nodal line, allowing us to better match the conductivity of real NLSMs. The boundary quantum field theory is anisotropic and therefore has explicitly broken Lorentz invariance, which leads to a stress tensor that is not symmetric. This has important consequences for the energy and momentum transport: the thermal conductivity at vanishing charge density is not simply fixed by a Ward identity, and there are a much larger number of independent shear viscosities than in a Lorentz-invariant system.