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We study some of the transport processes which are specific to an ideal gas of relativistic Weyl fermions and relate the corresponding transport coefficients to various anomaly coefficients of the system. We propose that these transport processes can be thought of as arising from the continuous injection of chiral states and their subsequent adiabatic flow driven by vorticity. This in turn leads to an elegant expression relating the anomaly induced transport coefficients to the anomaly polynomial of the Ideal Weyl gas.
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Using the anomaly inflow mechanism, we compute the flavor/Lorentz non-invariant contribution to the partition function in a background with a U(1) isometry. This contribution is a local functional of the background fields. By identifying the U(1) isometry with Euclidean time we obtain a contribution of the anomaly to the thermodynamic partition function from which hydrostatic correlators can be efficiently computed. Our result is in line with, and an extension of, previous studies on the role of anomalies in a hydrodynamic setting. Along the way we find simplified expressions for Bardeen-Zumino polynomials and various transgression formulae
Magnetic Weyl fermions, which occur in magnets, have novel transport phenomena related to pairs of Weyl nodes, and they are, of both, scientific and technological interest, with the potential for use in high-performance electronics, spintronics and quantum computing. Although magnetic Weyl fermions have been predicted to exist in various oxides, evidence for their existence in oxide materials remains elusive. SrRuO3, a 4d ferromagnetic metal often used as an epitaxial conducting layer in oxide heterostructures, provides a promising opportunity to seek for the existence of magnetic Weyl fermions. Advanced oxide thin film preparation techniques, driven by machine learning technologies, may allow access to such topological matter. Here we show direct quantum transport evidence of magnetic Weyl fermions in an epitaxial ferromagnetic oxide SrRuO3: unsaturated linear positive magnetoresistance (MR), chiral-anomaly-induced negative MR, Pi Berry phase accumulated along cyclotron orbits, light cyclotron masses and high quantum mobility of about 10000 cm2/Vs. We employed machine-learning-assisted molecular beam epitaxy (MBE) to synthesize SrRuO3 films whose quality is sufficiently high to probe their intrinsic quantum transport properties. We also clarified the disorder dependence of the transport of the magnetic Weyl fermions, and provided a brand-new diagram for the Weyl transport, which gives a clear guideline for accessing the topologically nontrivial transport phenomena. Our results establish SrRuO3 as a magnetic Weyl semimetal and topological oxide electronics as a new research field.
Chiral anomalies give rise to dissipationless transport phenomena such as the chiral magnetic and vortical effects. In these notes I review the theory from a quantum field theoretic, hydrodynamic and holographic perspective. A physical interpretation of the otherwise somewhat obscure concepts of consistent and covariant anomalies will be given. Vanishing of the CME in strict equilibrium will be connected to the boundary conditions in momentum space imposed by the regularization. The role of the gravitational anomaly will be explained. That it contributes to transport in an unexpectedly low order in the derivative expansion can be easiest understood via holography. Anomalous transport is supposed to play also a key role in understanding the electronics of advanced materials, the Dirac- and Weyl (semi)metals. Anomaly related phenomena such as negative magnetoresistivity, anomalous Hall effect, thermal anomalous Hall effect and Fermi arcs can be understood via anomalous transport. Finally I briefly review a holographic model of Weyl semimetal which allows to infer a new phenomenon related to the gravitational anomaly: the presence of odd viscosity.
Momentum transport is anomalous in chiral $p+ip$ superfluids and superconductors in the presence of textures and superflow. Using the gradient expansion of the semi-classical approximation, we show how gauge and Galilean symmetries induce an emergent curved spacetime with torsion and curvature for the quasirelativistic low-energy Majorana-Weyl quasiparticles. We explicitly show the emergence of the spin-connection and curvature, in addition to torsion, using the superfluid hydrodynamics. The background constitutes an emergent quasirelativistic Riemann-Cartan spacetime for the Weyl quasiparticles and they satisfy the conservation laws associated with local Lorentz symmetry, restricted to the plane of uniaxial anisotropy of the superfluid (or -conductor). Moreover, we show that the anomalous Galilean momentum conservation is a consequence of the gravitational Nieh-Yan (NY) chiral anomaly the Weyl fermions experience on the background geometry. Notably, the NY anomaly coefficient features a non-universal ultraviolet cut-off scale $Lambda$, with canonical dimensions of momentum. Comparison of the anomaly equation and the hydrodynamic equations suggests that the value of the cut-off parameter $Lambda$ is determined by the normal state Fermi liquid and non-relativistic uniaxial symmetry of the $p$-wave superfluid or superconductor.
We study the effects of momentum relaxation on the holographic Weyl semimetal which exhibits a topological quantum phase transition between the Weyl semimetal phase and a topological trivial phase. The conservation of momentum in the field theory is broken by the axion fields in holography. The topological Weyl semimetal phase is characterized by a nontrivial anomalous Hall conductivity. We find that the critical value of the phase transition decreases when we increase the momentum relaxation strength up to a special value, above which it goes to zero. This indicates that the Weyl semimetal phase shrinks and finally disappears as the momentum relaxation strength is increased, which is consistent with the weakly coupled field theory predictions. We also study the behavior of transverse/longitudinal conductivities and low temperature dependence of the d.c.resistivities with respect to momentum relaxation strength.
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