It is known that in two dimensional relativistic Dirac systems, the Landau levels can collapse in the presence of a critical in-plane electric field. We extend this mechanism to the three dimensional Weyl semimetals and analyze the physical consequences for the cases of both, real and pseudo Landau levels arising form strain-induced elastic magnetic fields.

We use a symmetry approach to derive the coupling of lattice deformations to electronic excitations in three dimensional Dirac and Weyl semimetals in the continuum low energy model. We focus on the effects of rotational strain and show that it can drive transitions from Dirac to Weyl semimetals, gives rise to new elastic gauge fields, tilts the cones, and generates new pseudo-Zeeman couplings. It also can generate a deformation potential in volume-preserving deformations. The associated pseudo-electric field contributes to the chiral anomaly.

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.

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.