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.

arXiv comment1 figure, 38 pages

References in corpus (25)

• Weyl and Dirac Semimetals in Three Dimensional Solids
• Physical Aspects of the Space-Time Torsion
• Viscosity of Quantum Hall Fluids
• Measuring Hall Viscosity of Graphene's Electron Fluid
• Interacting fermionic topological insulators/superconductors in three dimensions
• Consequences of a condensed matter realization of Lorentz violating QED in Weyl semi-metals
• Topological Invariants, Instantons and Chiral Anomaly on Spaces with Torsion
• Non-relativistic conformal symmetries and Newton-Cartan structures
• Torsional Anomalies, Hall Viscosity, and Bulk-boundary Correspondence in Topological States
• Torsional Response and Dissipationless Viscosity in Topological Insulators
• Low-energy effective theory in the bulk for transport in a topological phase
• On Euclidean spinors and Wick rotations
• On the coupling of Galilean-invariant field theories to curved spacetime
• Anomalous transport coefficients from Kubo formulas in Holography
• Quantum Criticality of Topological Phase Transitions in 3D Interacting Electronic Systems
• Hall viscosity, topological states and effective theories
• Lifshitz Hydrodynamics
• Out-of-bounds hydrodynamics in anisotropic Dirac fluids
• Investigating anisotropic quantum Hall states with bi-metric geometry
• Odd viscosity in the quantum critical region of a holographic Weyl semimetal
• Lifshitz Field Theories at Non-Zero Temperature, Hydrodynamics and Gravity
• Parity violating gravitational response and anomalous constitutive relations
• Viscoelastic response of quantum Hall fluids in a tilted field
• Berry curvature and Hall viscosities in an anisotropic Dirac semi-metal
• Existence and Construction of Galilean invariant $z\ne 2$ Theories

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• Cubic Hall viscosity in three-dimensional topological semimetals
• Chiral vortical conductivity across a topological phase transition from holography
• Shear viscosity as a probe of nodal topology
• Functional dependence of the Hall viscosity-induced transverse voltage in two-dimensional Fermi liquids
• Anomalous chiral transport with vorticity and torsion: Cancellation of two mixed gravitational anomaly currents in rotating chiral $p+ip$ Weyl condensates
• Torsion and anomalies in the warped limit of Lifschitz theories
• Non-equilibrium dynamics in Holography
• Quantum Hall effective action for anisotropic Dirac semi-metal
• Global phase diagram of Coulomb-interacting anisotropic Weyl semimetals with disorder
• Minimal Hamiltonian deformations as bulk probes of effective non-Hermiticity in Dirac materials
• Viscoelastic response and anisotropic hydrodynamics in Weyl semimetals
• Nonequilibrium steady states in driven holographic Weyl semi-metals
• Holographic Topological Semimetals