Anomalous Hall viscosity at the Weyl semimetal/insulator transition

Abstract

We show that 3D Lifshitz fermions arising as the critical theory at the Weyl semimetal/insulator transition naturally develop an anomalous Hall viscosity at finite temperature. We discuss how to couple the system to non-relativistic background sources for stress-tensor and momentum currents via a form of Newton-Cartan geometry with torsion and derive the Kubo formulas for the Hall viscosities. While the Lifshitz system that arises most naturally has scaling exponent $z=2$ we also generalize the theory for arbitrary Lifshitz scaling $z$ and show that, in the limit $z\to 0$, it may be given a Chern-Simons interpretation by dimensionally reducing along the anisotropic direction. The Hall viscosities are expressed in terms of zeta functions and their temperature dependence is dictated by the scaling exponent.

1 figure, 38 pages

References in corpus (5)

• Consequences of a condensed matter realization of Lorentz violating QED in Weyl semi-metals
• Non-relativistic conformal symmetries and Newton-Cartan structures
• Low-energy effective theory in the bulk for transport in a topological phase
• Quantum Criticality of Topological Phase Transitions in 3D Interacting Electronic Systems
• Hall viscosity, topological states and effective theories

Cited by in corpus (4)

• Hydrodynamic approach to two-dimensional electron systems
• Non-equilibrium dynamics in Holography
• Quantum Hall effective action for anisotropic Dirac semi-metal
• Holographic Topological Semimetals