On thermal Nieh-Yan anomaly in Weyl superfluids

Abstract

We discuss the possibility of the torsional Nieh-Yan anomaly of the type $\mu (e{j}_5^{\mu })=\gamma T^2({\mathcal{T}}^a\wedge {\mathcal{T}}_a)$ in Weyl superfluids, where $T$ is temperature and ${\mathcal{T}}^a$ is the effective or emergent torsion from the superfluid order parameter. As distinct from the dimensionful ultraviolet (UV) parameter ${\Lambda }^2$ in the conventional torsional Nieh-Yan anomaly, the parameter $\gamma$ is dimensionless in canonical units. This suggests that such dimensionless parameter may be fundamental, being determined by the geometry, topology and number of chiral quantum fields in the system. By comparing this to a Weyl superfluid with low-temperature corrections, $T\ll {\Delta }_0$, we show that such a term does exist in the hydrodynamics of a chiral $p$-wave superfluid, such as ${}^3$He-A, or a chiral superconductor. We also discuss and show how other $T^2$ terms of similar form and of the same order in gradients, coming from e.g. Fermi-liquid corrections and the chiral chemical potential, can also be expressed in terms of dimensionless fundamental parameters with emergent low-energy relativistic fields. Lastly, we discuss our results in comparison to relativistic Weyl fermions and the connection of the torsional gravitational anomalies to thermal transport in Weyl systems.

arXiv comment10 pages, no figures, extended version

References in corpus (39)

• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Topological response in Weyl semimetals and the chiral anomaly
• Gravitational Anomaly and Transport
• Stability of Fermi Surfaces and K-Theory
• Experimental signatures of the mixed axial-gravitational anomaly in the Weyl semimetal NbP
• Notes on Anomaly Induced Transport
• Thermodynamics, gravitational anomalies and cones
• Anomaly related transport of Weyl fermions for Weyl semi-metals
• Topological Invariants, Instantons and Chiral Anomaly on Spaces with Torsion
• Triangle anomaly in Weyl semi-metals
• Thermal Hall Effect and Geometry with Torsion
• Hydrodynamic theory of thermoelectric transport and negative magnetoresistance in Weyl semimetals
• Low-energy effective theory in the bulk for transport in a topological phase
• Pseudo-electromagnetic fields in topological semimetals
• Anomaly/Transport in an Ideal Weyl gas
• Viscoelastic response of topological tight-binding models in two and three dimensions
• Torsion, Parity-odd Response and Anomalies in Topological States
• Mixed Anomalies: Chiral Vortical Effect and the Sommerfeld Expansion
• Emergent spacetime and gravitational Nieh-Yan anomaly in chiral $p+ip$ Weyl superfluids and superconductors
• Mixed axial-torsional anomaly in Weyl semimetals
• Universal temperature corrections to the free energy for the gravitational field
• On the chiral anomaly in non-Riemannian spacetimes
• Elasticity tetrads, mixed axial-gravitational anomalies, and 3+1d quantum Hall effect
• Extended Einstein-Cartan theory a la Diakonov: the field equations
• Chiral torsional effect
• Nieh-Yan Anomaly: Torsional Landau Levels, central charge and anomalous thermal Hall effect
• Supersymmetric Particle in a Spacetime with Torsion and the Index Theorem
• Tetrads in solids: from elasticity theory to topological quantum Hall systems and Weyl fermions
• Topological magnetotorsional effect in Weyl semimetals
• Chiral torsional effect with finite temperature, density and curvature
• Lattice field theory with torsion
• Negative thermal magnetoresistivity as a signature of chiral anomaly in Weyl superconductors
• Macroscopic parity violating effects and 3He-A
• On thermal Nieh-Yan anomaly in topological Weyl materials
• Hamiltonian approach to the torsional anomalies and its dimensional ladder
• Axial anomaly in 3He-A: Simulation of baryogenesis and generation of primordial magnetic field in Manchester and Helsinki
• Symmetry breaking and lattice kirigami: finite temperature effects
• Torsional Topological Invariants (and their relevance for real life)
• Torsion and anomalies in the warped limit of Lifschitz theories

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• Scalar induced gravitational waves in metric teleparallel gravity with the Nieh-Yan term
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• Chiral kinetic theory of anomalous transport induced by torsion
• Anomalous chiral transport with vorticity and torsion: Cancellation of two mixed gravitational anomaly currents in rotating chiral $p+ip$ Weyl condensates
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• Chiral Torsional Effects in Anomalous Fluids in Thermal Equilibrium
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• Phonon helicity and Nieh-Yan Anomaly in the Kramers-Weyl semimetals of Chiral Crystals
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