Gauge Theories for the Thermal Hall Effect

Abstract

We consider the thermal Hall effect of fermionic matter coupled to emergent gauge fields in 2+1 dimensions. While the low-temperature thermal Hall conductivity of bulk topological phases can be connected to chiral edge states and a gravitational anomaly, there is no such interpretation at nonzero temperatures above 2+1 dimensional quantum critical points. In the limit of a large number of matter flavors, the leading contribution to the thermal Hall conductivity is that from the fermionic matter. The next-to-leading contribution is from the gauge fluctuations, and this has a sign which is opposite to that of the matter contribution. We illustrate this by computations on a Dirac Chern-Simons theory of the quantum phase transition in a square-lattice antiferromagnet involving the onset of semion topological order. We find similar results for a model of the pseudogap metal with Fermi pockets coupled to an emergent U(1) gauge field. We note connections to recent observations on the hole-doped cuprates: our theory captures the main trends, but the overall magnitude of the effect is smaller than that observed.

arXiv comment21 pages, 10 figures

References in corpus (36)

• Theory of Thermal Hall Effect in Quantum Magnets
• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Theoretical prediction of rotating magnon wavepacket in ferromagnets
• Non-zero temperature transport near quantum critical points
• Electromagnetic and gravitational responses and anomalies in topological insulators and superconductors
• Thermoelectric Response of an Interacting Two-Dimensional Electron Gas in Quantizing Magnetic Field
• Contact Terms, Unitarity, and F-Maximization in Three-Dimensional Superconformal Theories
• Comments on Chern-Simons Contact Terms in Three Dimensions
• Energy Magnetization and Thermal Hall Effect
• Topological order, emergent gauge fields, and Fermi surface reconstruction
• Unusual thermal Hall effect in a Kitaev spin liquid candidate $\alpha$-RuCl${}_3$
• Thermal Transport in Chiral Conformal Theories and Hierarchical Quantum Hall States
• Giant thermal Hall conductivity from neutral excitations in the pseudogap phase of cuprates
• Gravitational Anomalies and Thermal Hall effect in Topological Insulators
• Quantum criticality of U(1) gauge theories with fermionic and bosonic matter in two spatial dimensions
• Topological order in the pseudogap metal
• Pseudogap and Fermi surface topology in the two-dimensional Hubbard model
• Thermal Transport for Many Body Tight-Binding Models
• Fluctuating spin density waves in metals
• Nonzero temperature transport near fractional quantum Hall critical points
• Enhanced thermal Hall effect in nearly ferroelectric insulators
• From spinon band topology to the symmetry quantum numbers of monopoles in Dirac spin liquids
• Fermi surface reconstruction in electron-doped cuprates without antiferromagnetic long-range order
• Thermal Hall conductance and a relative topological invariant of gapped two-dimensional systems
• Enhanced thermal Hall effect in the square-lattice Néel state
• Thermal Hall effect in square-lattice spin liquids: A Schwinger boson mean-field study
• Quantum kinetic approach for studying thermal transport in the presence of electron-electron interactions and disorder
• Consideration of Thermal Hall Effect in Undoped Cuprates
• Orbital currents in insulating and doped antiferromagnets
• Dual vortex theory of doped Mott insulators
• Phonon Hall effect in ionic crystals in the presence of static magnetic field
• Universalty and Ultraviolet Regularizations of Chern-Simons Theory
• Absence of singular superconducting fluctuation corrections to thermal conductivity
• Noether currents of locally equivalent symmetries
• Physical stress, mass, and energy for non-relativistic matter
• Not all doped Mott insulators have a pseudogap: key role of van Hove singularities

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