Soutenance de Baptiste Bermond

Symmetries are a cornerstone of the physical description of the world. In some exotic situations, the symmetries of the classical description are violated by quantum fluctuations. Such symmetries are denoted anomalous. Of particular interest, the gravitational anomalies describe how momentum and energy conservation laws are not satisfied by quantum fluctuations in a curved spacetime, typically of gravitational origin.

This thesis explores the consequences of these gravitational anomalies in the context of condensed matter. Historically, R. Tolman and P. Ehrenfest studied in the 30s the black body radiation at equilibrium in a curved spacetime. They realized that the curvature of spacetime induces inhomogeneities of the equilibrium temperature. Later on, J.Luttinger, while studying thermal transport in solids, built on their study to replace an inhomogeneous temperature by a curvature of spacetime or equivalently by a gravitational potential. In this thesis, I revisit these historical works. I show how anomalous quantum fluctuations, captured by the gravitational anomalies, modify the Tolman-Ehrenfest equivalence between a curved spacetime and an inhomogeneous temperature. Then I identify several condensed matter situations in which this modified Tolman and Ehrenfest equivalence leads to measurable consequences. In particular, I consider strongly out-of-equilibrium quantum dynamics induced by a thermal quench or a periodic modulation of couplings. Finally, I discuss the magnetothermal transport properties of a Weyl semimetal, ZrTe5, as part of a collaboration with an experimental group. While initially aiming at identifying signatures of the gravitational anomalies, we realized that these measurements were the signature of a new phenomenon resulting from a strong coupling between electrons and phonons in this material, leading to remarkable quantum oscillations of the magnetothermal conductivity.