Novel thermoelectric and elastic responses in Dirac matter

Abstract

This thesis studies some aspects of the physics of topological semimetals, a set of novel three-dimensional matter systems whose low-energy electronic excitations are described by Dirac quasiparticles. The unconventional features of these materials, ranging from basic physics to technological applications, have generated a substantial research activity during the last years. The interest in crystalline structures hosting Dirac quasiparticles lies partially on the relativistic nature of their electronic degrees of freedom, making them an ideal laboratory to test and study fundamental physics phenomena. This thesis addresses two topics of major interest in the physics of these systems: the interplay between lattice deformations and electronic properties, and the influence of anomalies on the thermoelectric response. In the first part of this thesis, the thermoelectric response of Dirac and Weyl semimetals is studied in the presence of strong magnetic fields. The anomalous thermoelectric behaviour is addressed at the charge neutrality point, where a finite contribution to the thermoelectric coefficient is obtained in the conformal limit. The thermoelectric coefficients fulfill robust phenomenological relations based on the Landau-Fermi liquid paradigm of coherent quasiparticles. These relations may be challenged when the system has strong interactions or when it presents a poor metallic behaviour. The validity of the Mott relation, a phenomenological law that relates the thermopower and the electrical conductivity coefficients, is discussed in the regime of zero doping and zero temperature. In particular, the off-diagonal components of the electric and thermoelectric tensors are analyzed in the presence of a magnetic field. The influence of external deformations on the lattice configuration of topological semimetals is essential to understand their electronic properties. In these systems, elastic deformations couple to the low-energy electronic excitations in the form of elastic gauge fields. The possibility of controlling the dynamics of carriers by appropriate strain geometries has given rise to a prolific industry associated with straintronics. In the second part of this thesis, the coupling of lattice deformations to Dirac quasiparticles in three-dimensional materials is studied by using a symmetry approach. An interesting aspect is that, in contrast to the two-dimensional case, the antisymmetric part of the deformation tensor couple to the electronic excitations in three-dimensional Dirac materials. Finally, the interplay between electromagnetic fields and elastic deformations is also discussed, in which the collapse of Landau levels is showed in the presence of strain. The similarities of this mechanism with the case of real magnetic and electric fields are emphasized, discussing possible strain configurations giving rise to this effect.