Orbital Hall effect as an alternative to the valley Hall effect

Giovanni VIGNALE

In this talk, we show that the phenomenon known as "Valley Hall Effect", whereby a an electric field induces a transverse valley current, is better described as an instance of the Orbital Hall Effect (OHE), where the ambiguous ``valley'' indices are replaced by a physical quantity, the orbital magnetic moment, which can be defined uniformly over the entire Brillouin zone. This description removes ambiguities that are present in the definition of the valley Hall current, as the conductivity in the orbital Hall effect is unambiguously defined as the Brillouin zone integral of a new quantity, called the orbital Berry curvature. The reformulation in terms of OHE is illustrated in the case of gapped graphene, which has been previously proposed to be a good platform to observe the valley Hall effect. The new formulation provides a direct explanation to the orbital moments accumulated at the edges of the sample, which were observed in previous Kerr rotation measurements.