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 anomalies1. One of the most prominent examples is the chiral anomaly2,3, 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 fields4) 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 anomaly1, 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 field5,6, even in flat space-time, suggesting that such types of mixed anomaly could be experimentally probed in condensed matter systems known as Weyl semimetals7. 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.
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This work was supported by the research grant DFG-RSF (NI616 22/1) ‘Contribution of topological states to the thermoelectric properties of Weyl semimetals’, Severo Ochoa SEV-2012-0249, FPA 2015-65480-P and SFB 1143, by the Helmholtz association through VI-521, and by the DFG (Emmy Noether programme) via grant ME 4844/1. We thank T. Sturm and A. Pöhl, for experimental support. We also acknowledge support by W. Riess, K. Moselund and H. Riel, and thank C. Bollinger for copy-editing.
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Journal of High Energy Physics (2019)