A Weyl semimetal from AdS/CFT with flavour

Abstract

Abstract We construct a top-down holographic model of Weyl semimetal states using (3 + 1)-dimensional N $$ \mathcal{N} $$ = 4 supersymmetric SU(N c ) Yang-Mills theory, at large N c and strong coupling, coupled to a number N f ≪ N c of N $$ \mathcal{N} $$ = 2 hypermultiplets with mass m. A U(1) subgroup of the R-symmetry acts on the hypermultiplet fermions as an axial symmetry. In the presence of a constant external axial gauge field in a spatial direction, b, we find the defining characteristic of a Weyl semi-metal: a quantum phase transition as m/b increases, from a topological state with non-zero anomalous Hall conductivity to a trivial insulator. The transition is first order. Remarkably, the anomalous Hall conductivity is independent of the hypermultiplet mass, taking the value dictated by the axial anomaly. At non-zero temperature the transition remains first order, and the anomalous Hall conductivity acquires non-trivial dependence on the hypermultiplet mass and temperature.

Keywords

• AdS-CFT Correspondence
• Gauge-gravity correspondence
• Holography and condensed matter physics (AdS/CMT)
• Topological States of Matter