| Summary: | 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 $\beta {l}_{m}^{2}\propto 1/B$ and a narrow channel of width ${l}_{m}\propto 1/\sqrt{B}$ (with ${l}_{m}=\sqrt{{\hslash }/{eB}}$ the magnetic length and β the momentum separation of the Weyl points). Only one of the two is transmitted into a metallic contact, providing unique magnetotransport signatures.
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