Thermodynamics and transport of holographic nodal line semimetals

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.

Entanglement entropy as an order parameter for strongly coupled nodal line semimetals

“…Based on the properties of the dual fermionic spectral function, it has been shown that in the NLSM phase there exist multiple nodal line Fermi surfaces which are topologically stable [57]. This confirms that the holographic model describes a topological quantum phase transition between a NLSM and a trivial phase (see also [47] for a recent analysis of the thermodynamics and transport properties of a similar holographic NLSM model).…”

“…More recently, using a holographic model for strongly coupled NLSM [46], ref. [47] showed that the DC electrical conductivity at low temperature displays a structure reminiscent of a quantum critical fan, which may provide a probe for the TQPT. Finally, in CaAgAs [48], quantum oscillations have been proven to be sensitive to the topology of the Fermi surface.…”

“…Note that in the potential V B we have introduced an additional quartic term in comparison with the original model in [57]. Upon tuning λ 2 , we can control some of the IR properties related to the IR Lifshitz exponent in the NLSM phase [47], which might render the holographic model more similar to real NLSM systems. For more details about the holographic model, see [57].…”

Black hole interiors in holographic topological semimetals

“…There is no clear connection among them. The quantum Lifshitz scaling exponents near the horizon can be manifested in terms of transports at low temperature, e.g, the dependence of the conductivity on temperature or frequency in holographic WSM [12] and holographic NLSM [24], while the first two qunatities can be extracted from the correlators of heavy operators.…”

Lorentz violation in Dirac and Weyl semimetals

“…For Weyl semimetals, certain violations can be parametrized by a single axial background gauge field, and the electromagnetic response has been analyzed with field-theoretic methods [12][13][14][15][16][17][19][20][21][22][23][24][25][26][27][28]. Studies of related systems have considered some additional types of Lorentz violations [29][30][31][32]. These and other systems are described here using SME-based lattice models, which provide a starting point for understanding higher-order contributions in the energy bands at energy scales relevant in real materials and allow for nonperturbative effects in SME coefficients for Lorentz violation.…”