Laboratoire de Physique Théorique
Toulouse - UMR 5152

The recent discovery of materials whose electronic properties are described by three-dimensional relativistic fermions opened fascinating opportunities to study physical phenomena which have never been accessible before. Among these phenomena is a remarkable disorder-driven quantum transition in the simplest relativistic phases, the Weyl semimetals. This transition is fascinating : it is different from the Anderson transition, yet accessible experimentally. Despite a burst of papers, the understanding of this transition is still lacking. A standard approach relates this transition to the $U(N)$ Gross-Neveu model in the limit of $N \to 0$ [1]. However, there is little agreement between the predictions of numerical simulations and the various analytical results derived from the Gross-Neveu model. Recently we have developed a functional renormalization group amenable to include non-analytic effects [2]. We show that the previously considered fixed point is infinitely unstable, demonstrating the necessity to describe fluctuations beyond the usual Gaussian approximation. Furthermore, the disorder distribution renormalizes following the so-called porous medium equation which appears in different context in fluid mechanics, mathematical biology, boundary layer theory, and other fields. We relate self-similar solutions of the porous medium equation to a universal mechanism of generation of finite density of states responsible for the transition. We find that the transition is controlled by a non-analytic fixed point drastically different from the fixed point of the $U(N)$ Gross-Neveu model. Our findings provide a framework for extensions to problems ranging from the mass generation at the chiral symmetry breaking transitions in the high energy physics to non-linear sigma models with infinitely many relevant operators.

[1] T. Louvet, D. Carpentier, A. A. Fedorenko, Phys. Rev. B 94, 220201(R) (2016)

[2] I. Balog, D. Carpentier, A. A. Fedorenko, arXiv:1710.07932