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
\mbox{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 \mbox{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 βlm2∝1/B and a narrow channel of width lm∝1/B (with
lm=ℏ/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.Comment: V4: 10 pages, 14 figures. Added figure and discussion about
"uncrossing deformations" of oriented contours, plus minor corrections.
Published in NJ