Hedgehog orbital texture in p -type tellurium and the antisymmetric nonreciprocal Hall response

What are Weyl fermions? How do they arise in semiconductors? Which conditions make possible their observation and what signatures do they leave in transport? The authors thoroughly address all these questions in tellurium. Weyl fermions are hedgehogs in reciprocal space, namely, their orbital moments are parallel to their wave vectors. They arise in time reversal invariant semiconductors that feature lack of inversion symmetry. They can be observed in optically active, spatially dispersive media. They lead to two novel, antisymmetric, nonreciprocal Hall responses: the anomalous and planar Hall effects, herein fully characterized theoretically and measured experimentally via Hall transport.