Gravitational anomaly in the ferrimagnetic topological Weyl semimetal NdAlSi

Quantum anomalies are the breakdowns of classical conservation laws that occur in quantum-field theory description of a physical system. They appear in relativistic field theories of chiral fermions and are expected to lead to anomalous transport properties in Weyl semimetals. This includes a chiral anomaly, which is a violation of the chiral current conservation that takes place when a Weyl semimetal is subjected to parallel electric and magnetic fields. A charge pumping between Weyl points of opposite chirality causes the chiral magnetic effect that has been extensively studied with electrical transport. On the other hand, if the thermal gradient, instead of the electrical field, is applied along the magnetic field, then as a consequence of the gravitational (also called the thermal chiral) anomaly an energy pumping occurs within a pair of Weyl cones. As a result, this is expected to generate anomalous heat current contributing to the thermal conductivity. We report an increase of both the magneto-electric and magneto-thermal conductivities in quasi-classical regime of the magnetic Weyl semimetal NdAlSi. Our work also shows that the anomalous electric and heat currents, which occur due to the chiral magnetic effect and gravitational anomalies respectively, are still linked by a 170 years old relation called the Wiedemann-Franz law.