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.
Highlights
Nodal line semimetals (NLSMs) are a recently discovered class of materials, in which two electronic bands intersect along a closed curve in momentum space at or near the Fermi energy
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
We show in appendix B that the T μν that we obtain in holography satisfies this Ward identity
Summary
Nodal line semimetals (NLSMs) are a recently discovered class of materials, in which two electronic bands intersect along a closed curve in momentum space at or near the Fermi energy As reviewed below, this intersection is protected by the non-trivial topology of the electronic band structure, combined with the discrete symmetries of the system. If the integral of A around any curve C that does not encircle a band-touching vanishes, a small perturbation to the Hamiltonian that does not break the symmetries cannot destroy the nodal line without changing the right-hand side of equation (1.4) to zero. With eigenvalues equal to the two eigenvalues in equation (1.3) that have a minus sign inside the square root These are the two eigenvalues that meet to form the nodal line, i.e. the inner two eigenvalues, so we may regard H2(k) as an effective Hamiltonian for these two bands.
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