Twisted Fermi surface of a thin-film Weyl semimetal

The Fermi surface of a conventional two- dimensional electron gas is equivalent to a circle, up to smooth deformations that preserve the orientation of the equi- energy contour. Here we show that a Weyl semimetal confined to a thin film with an in- plane magnetization and broken spatial inversion symmetry can have a topologically distinct Fermi surface that is twisted into a figure-8-opposite orientations are coupled at a crossing which is protected up to an exponentially small gap. The twisted spectral response to a perpendicular magnetic field B is distinct from that of a deformed Fermi circle, because the two lobes of a figure-8 cyclotron orbit give opposite contributions to the Aharonov- Bohm phase. The magnetic edge channels come in two counterpropagating types, a wide channel of width b mu l B 1 m 2 and a narrow channel of width lm mu 1 B ( with lm =. eB the magnetic length and ss the momentum separation of the Weyl points). Only one of the two is transmitted into a metallic contact, providing unique magnetotransport signatures.