Experimental signatures of the mixed axial-gravitational anomaly in the Weyl semimetal NbP.

The conservation laws, such as those of charge, energy and momentum, have a central role in physics. In some special cases, classical conservation laws are broken at the quantum level by quantum fluctuations, in which case the theory is said to have quantum anomalies. One of the most prominent examples is the chiral anomaly, which involves massless chiral fermions. These particles have their spin, or internal angular momentum, aligned either parallel or antiparallel with their linear momentum, labelled as left and right chirality, respectively. In three spatial dimensions, the chiral anomaly is the breakdown (as a result of externally applied parallel electric and magnetic fields) of the classical conservation law that dictates that the number of massless fermions of each chirality are separately conserved. The current that measures the difference between left- and right-handed particles is called the axial current and is not conserved at the quantum level. In addition, an underlying curved space-time provides a distinct contribution to a chiral imbalance, an effect known as the mixed axial-gravitational anomaly, but this anomaly has yet to be confirmed experimentally. However, the presence of a mixed gauge-gravitational anomaly has recently been tied to thermoelectrical transport in a magnetic field, even in flat space-time, suggesting that such types of mixed anomaly could be experimentally probed in condensed matter systems known as Weyl semimetals. Here, using a temperature gradient, we observe experimentally a positive magneto-thermoelectric conductance in the Weyl semimetal niobium phosphide (NbP) for collinear temperature gradients and magnetic fields that vanishes in the ultra-quantum limit, when only a single Landau level is occupied. This observation is consistent with the presence of a mixed axial-gravitational anomaly, providing clear evidence for a theoretical concept that has so far eluded experimental detection.

Quenching the Chiral Magnetic Effect via the Gravitational Anomaly and Holography.

In the presence of a gravitational contribution to the chiral anomaly, the chiral magnetic effect induces an energy current proportional to the square of the temperature in equilibrium. In holography the thermal state corresponds to a black hole. We numerically study holographic quenches in which a planar shell of scalar matter falls into a black hole and raises its temperature. During the process the momentum density (energy current) is conserved. The energy current has two components, a nondissipative one induced by the anomaly and a dissipative flow component. The dissipative component can be measured via the drag it asserts on an additional auxiliary color charge. Our results indicate strong suppression very far from equilibrium.

Quantum Phase Transition between a Topological and a Trivial Semimetal from Holography.

We present a holographic model of a topological Weyl semimetal. A key ingredient is a time-reversal breaking parameter and a mass deformation. Upon varying the ratio of mass to time-reversal breaking parameter the model undergoes a quantum phase transition from a topologically nontrivial semimetal to a trivial one. The topological nontrivial semimetal is characterized by the presence of an anomalous Hall effect. The results can be interpreted in terms of the holographic renormalization group (RG) flow leading to restoration of time reversal at the end point of the RG flow in the trivial phase.

Odd Viscosity in the Quantum Critical Region of a Holographic Weyl Semimetal.

We study odd viscosity in a holographic model of a Weyl semimetal. The model is characterized by a quantum phase transition from a topological semimetal to a trivial semimetal state. Since the model is axisymmetric in three spatial dimensions there are two independent odd viscosities. Both odd viscosity coefficients are nonvanishing in the quantum critical region and nonzero only due to the mixed axial gravitational anomaly. It is therefore a novel example in which the mixed axial gravitational anomaly gives rise to a transport coefficient at first order in derivatives at finite temperature. In the quantum critical region, the physics of viscosities as well as conductivities is governed by the quantum critical point.

Elastic Gauge Fields in Weyl Semimetals.

We show that, as happens in graphene, elastic deformations couple to the electronic degrees of freedom as pseudogauge fields in Weyl semimetals. We derive the form of the elastic gauge fields in a tight-binding model hosting Weyl nodes and see that this vector electron-phonon coupling is chiral, providing an example of axial gauge fields in three dimensions. As an example of the new response functions that arise associated with these elastic gauge fields, we derive a nonzero phonon Hall viscosity for the neutral system at zero temperature. The axial nature of the fields provides a test of the chiral anomaly in high energy with three axial vector couplings.

Gravitational anomaly and transport phenomena.

Quantum anomalies give rise to new transport phenomena. In particular, a magnetic field can induce an anomalous current via the chiral magnetic effect and a vortex in the relativistic fluid can also induce a current via the chiral vortical effect. The related transport coefficients can be calculated via Kubo formulas. We evaluate the Kubo formula for the anomalous vortical conductivity at weak coupling and show that it receives contributions proportional to the gravitational anomaly coefficient. The gravitational anomaly gives rise to an anomalous vortical effect even for an uncharged fluid.