paper

Axionic quantum criticality of generalized Weyl semimetals

arXiv:2412.09609 · doi:10.1103/PhysRevB.111.L121115

Abstract

We formulate a field-theoretic description for $d$ -dimensional interacting nodal semimetals, featuring dispersion that scales with the linear and $n$ th power of momentum along $d_{L}$ and $d_{M}$ mutually orthogonal directions around a few isolated points in the reciprocal space, respectively, with $d_{L} + d_{M} = d$ , and residing at the brink of isotropic insulation, described by $N_{b}$ -component bosonic order parameter fields. The resulting renormalization group (RG) procedure, tailored to capture the associated quantum critical phenomena, is controlled by a ``small" parameter $I^µ = 2 - d_{M}$ and $1/ N_{f}$ , where $N_{f}$ is the number of identical fermion copies (flavor number) when in conjunction $d_{L} = 1$ . When applied to three-dimensional interacting general Weyl semimetals ( $d_{L} = 1$ and $d_{M} = 2$ ), characterized by the Abelian monopole charge $n > 1$ , living at the shore of the axionic insulation ( $N_{b} = 2$ ), a leading-order RG analysis suggests the Gaussian nature of the underlying quantum phase transition, around which the critical exponents assume mean-field values. A traditional field-theoretic RG analysis yields the same outcomes for simple Weyl semimetals ( $n = 1$ , $d_{L} = 3$ , and $d_{M} = 0$ ). Consequently, emergent marginal Fermi liquids showcase only logarithmic corrections to physical observables at intermediate scales of measurements.

Published version in PRB as a Letter: 7 Pages, 1 Figure (Supplemental Material as Ancillary file)