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

A positive magneto-thermoelectric conductance is observed in the Weyl semimetal niobium phosphide, suggesting the presence of the elusive mixed axial–gravitational anomaly. Adding to the anomaly of Weyl semimetals A fundamental rule of our universe is that energy, charge and momentum are conserved. However, these rules can be broken at the quantum mechanical level. Such exotic physics had been exclusively explored in the realm of quantum field theory until recently when a new class of materials called Weyl semimetals was discovered. These systems harbour fundamental particles called Weyl fermions, which have been shown to exhibit a so-called chiral anomaly, meaning that under certain circumstances their spin is not conserved. Johannes Gooth et al . now provide another intriguing connection to quantum field theory. They show that a condensed-matter analogue of curved space time can add an additional, gravitational component to the chiral anomaly in Weyl semimetals. The work opens the door to further experimental exploration of previously undetected quantum field effects. 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 1 . One of the most prominent examples is the chiral anomaly 2 , 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 fields 4 ) 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 1 , 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 5 , 6 , even in flat space-time, suggesting that such types of mixed anomal