Fingerprints of the conformal anomaly in the thermoelectric transport in Dirac and Weyl semimetals

Abstract

A quantum anomaly arises when a symmetry of the classical action can not survive quantization. The physical consequences of having quantum anomalies were first explored in the construction of quantum field theory to describe elementary particles and played an important role in grand unification and string theory. Nowadays, the interest on anomalies and anomaly related transport has shifted to emergent condensed matter systems which support low energy descriptions akin to their QFT partners. Dirac and Weyl semimetals are 3D crystals having band crossings near the Fermi surface. Their low energy quasiparticles are described by a massless Dirac Hamiltonian sharing all the properties of their high energy counterparts. After an intense and successful analysis of the consequences of the chiral anomaly on magneto-electric transport, the interest has shifted to gravitational effects, in particular these of the mixed axial-gravitational anomaly. These phenomena involve thermo-electric measurements in magnetic field. A less known quantum anomaly, the conformal anomaly, also related to metric deformations, has been recently shown to give rise to a special contribution to the Nernst signal which remains finite at zero temperature and chemical potential. In this work we provide distinctive signatures for the experimental confirmation of this unexpected signal.

Thermoelectric Relations in the Conformal Limit in Dirac and Weyl Semimetals

“…In a recent publication [29], it was shown that the conformal anomaly [30], related to metric deformations, gives rise to a special contribution to the Nernst signal which remains finite at zero temperature and chemical potential, a very unusual property. This result was later confirmed with a more standard Kubo calculation in [31]. In this work we analyze the validity of the phenomenological thermoelectric relations in Dirac and Weyl semimetals in the conformal limit (zero temperature and chemical potential).…”

“…A non-zero thermoelectric coefficient was predicted at zero temperature and chemical potential where the theory is scale invariant at the classical level. A Kubo formula calculation of the thermoelectric coefficient extended the calculation to finite temperature and chemical potential and gave the same result in the conformal limit [31].…”

“…We perform an explicit calculation of the Hall conductivity in the conformal limit and, combining it with the thermoelectric coefficient of ref. [31], we see that the Mott relation, an easy to measure property, is violated in the conformal limit. Since the density of states is zero at the neotrality point we cannot use a Boltzmann formalism, and the calculation is done with a Kubo formula.…”

“…In the next section we will analyze the Mott relation at the light of the results in [29,31] that we will summarize here. Close to a two bands band crossing in three spacial dimensions, the dispersion relation of an electronic system can be linearized giving rise to the effective low energy Hamiltonian [46]…”

“…In this work the Hall conductivity is computed with a Kubo formulation as the one done in [31] for the thermoelectric coefficient. In the Kubo approach, the conductivity tensor is given by the expression:…”