Interacting Weyl semimetals

In the first part of the talk, I will discuss the effects of short-range interactions in generalized Weyl semimetals with a monopole charge (n) greater than one. I will show that a strong enough short range interaction may lead to the onset of a translational symmetry breaking axion insulator or a gapless nematic state [1]. To address this problem, I will use a new renormalization group scheme in which the monopole charge is an expansion parameter. Computed critical exponents indicate non-Gaussian nature of the quantum phase transition for any n>1.
The second part of the talk is devoted to the role of the long-range Coulomb interaction in a simple (n=1) Weyl semimetal. In particular, I will show that this interaction leads to a universal enhancement of the zero-temperature optical conductivity that depends solely on the number of Weyl points at the Fermi level [2]. This scaling is a remarkable consequence of an interplay between the quantum-critical nature of an interacting Weyl liquid, marginal irrelevance of the long-range Coulomb interaction and the violation of hyperscaling in three dimensions, and can directly be measured in recently discovered Weyl and Dirac materials.
[1] B. Roy, P. Goswami, and V. Juricic, Phys. Rev. B 95, 201102 (R) (2017).
[2] B. Roy and V. Juricic, arXiv; 1707.08564 (to appear in Phys. Rev. B).