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.

Applying a temperature gradient in a magnetic material generates a voltage that is perpendicular to both the heat flow and the magnetization. 1,2 This is the anomalous Nernst effect (ANE), 3,4 which was thought to be proportional to the value of the magnetization for a long time. However, more generally, the ANE has been predicted to originate from a net Berry curvature of all bands near the Fermi level (EF. 5,6 Subsequently, a large anomalous Nernst thermopower ( ) has recently been observed in topological materials with no net magnetization but large net Berry curvature [n(k)] around EF. 7-9 These experiments clearly fall outside the scope of the conventional magnetization-model of the ANE, but a significant question remains: Can the value of the ANE in topological ferromagnets exceed the highest values observed in conventional ferromagnets? Here, we report a remarkably high -value of ~6.0 µV K −1 at 1 T in the ferromagnetic topological Heusler compound Co2MnGa at room temperature, which is around 7-times larger than any anomalous Nernst thermopower value ever reported for a conventional ferromagnet. Combined electrical, thermoelectric and first-principles calculations reveal that this high value of the ANE arises from a large net Berry curvature near the Fermi level associated with nodal lines and Weyl points.

In stark contrast to ordinary metals, in materials in which electrons strongly interact with each other or with phonons, electron transport is thought to resemble the flow of viscous fluids. Despite their differences, it is predicted that transport in both conventional and correlated materials is fundamentally limited by the uncertainty principle applied to energy dissipation. Here we report the observation of experimental signatures of hydrodynamic electron flow in the Weyl semimetal tungsten diphosphide. Using thermal and magneto-electric transport experiments, we find indications of the transition from a conventional metallic state at higher temperatures to a hydrodynamic electron fluid below 20 K. The hydrodynamic regime is characterized by a viscosity-induced dependence of the electrical resistivity on the sample width and by a strong violation of the Wiedemann–Franz law. Following the uncertainty principle, both electrical and thermal transport are bound by the quantum indeterminacy, independent of the underlying transport regime.

An axion insulator is a correlated topological phase, predicted to arise from the formation of a charge density wave in a Weyl semimetal. The accompanying sliding mode in the charge density wave phase, the phason, is an axion. It is expected to cause anomalous magneto-electric transport effects. However, this axionic charge density wave has so far eluded experimental detection. In this paper, we report the observation of a large, positive contribution to the magneto-conductance in the sliding mode of the charge density wave Weyl semimetal (TaSe4)2I for collinear electric and magnetic fields (E||B).The positive contribution to the magneto-conductance originates from the anomalous axionic contribution of the chiral anomaly to the phason current, and is locked to the parallel alignment of E and B. By rotating B, we show that the angular dependence of the magneto-conductance is consistent with the anomalous transport of an axionic charge density wave. 3 Axions refer to elementary particles that have long been known in quantum field theory, 1,2 but have yet to be observed in nature. However, it has been recently understood that axions can emerge as collective electronic excitations in certain crystals, so-called axion insulators. 3 Despite being fully gapped to single-particle excitations in the bulk and at the surface, an axion insulator is characterized by an effective action, which includes a topological EB-term, where E and B are the electromagnetic fields inside the insulator, and  plays the role of the dynamical axion field. Physically, the average value of  is determined by the microscopic details of the band structure of the system, and gives rise to unusual magnetoelectric response properties such as quantum anomalous Hall conductivities 4-9 , the quantized circular photo-galvanic 4,10,11 effect, and the chiral magnetic effect. 4,[12][13][14] The prospect of realizing an axion insulator has inspired much theoretical and experimental work. Only very recently, signatures of a dynamic axion field have been found on the surface of magnetically doped topological insulator thin films. [15][16][17] However, the axionic quasi-particle in these systems-the axionic polariton 3 -has so far eluded experimental detection. Alternatively, axion insulators have been predicted to arise in Weyl semimetals that are unstable towards the formation of a charge density wave (CDW). [18][19][20][21][22][23] In their parent state, Weyl semimetals are materials in which the low-energy electronic quasiparticles behave as chiral relativistic fermions without rest mass, known as Weyl fermions. [24][25][26][27] The Weyl fermions exist at isolated crossing points of conductance and valence bands-so called Weyl nodes-and their energy can be approximated with a linear dispersion relation ( Fig. 1 (a)). The Weyl nodes always occur in pairs of opposite "handedness" or chirality. At low energies and in the absence of interactions the chirality is a conserved quantum number, and the two chiral populations do not mix. Parallel electric and mag...