Thermoelectric Relations in the Conformal Limit in Dirac and Weyl Semimetals

Dirac and Weyl semimetals are three-dimensional electronic systems with the Fermi level at or near a band crossing. Their low energy quasi-particles are described by a relativistic Dirac Hamiltonian with zero effective mass, challenging the standard Fermi liquid (FL) description of metals. In FL systems, electrical and thermo-electric transport coefficient are linked by very robust relations. The Mott relation links the thermoelectric and conductivity transport coefficients. In a previous publication, the thermoelectric coefficient was found to have an anomalous behavior originating in the quantum breakdown of the conformal anomaly by electromagnetic interactions. We analyze the fate of the Mott relation in the system. We compute the Hall conductivity of a Dirac metal as a function of the temperature and chemical potential and show that the Mott relation is not fulfilled in the conformal limit.