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Quantum anomalies are the breakdowns of classical conservation laws thatoccur in quantum-field theory description of a physical system. They appear inrelativistic field theories of chiral fermions and are expected to lead toanomalous transport properties in Weyl semimetals. This includes a chiralanomaly, which is a violation of the chiral current conservation that takesplace when a Weyl semimetal is subjected to parallel electric and magneticfields. A charge pumping between Weyl points of opposite chirality causes thechiral magnetic effect that has been extensively studied with electricaltransport. On the other hand, if the thermal gradient, instead of theelectrical field, is applied along the magnetic field, then as a consequence ofthe gravitational (also called the thermal chiral) anomaly an energy pumpingoccurs within a pair of Weyl cones. As a result, this is expected to generateanomalous heat current contributing to the thermal conductivity. We report anincrease of both the magneto-electric and magneto-thermal conductivities inquasi-classical regime of the magnetic Weyl semimetal NdAlSi. Our work alsoshows that the anomalous electric and heat currents, which occur due to thechiral magnetic effect and gravitational anomalies respectively, are stilllinked by a 170 years old relation called the Wiedemann-Franz law.

Gravitational anomaly in the ferrimagnetic topological Weyl semimetal NdAlSi