Quantum oscillations in the type-II Weyl fermion metal PtSe$_2$

Relativistic massless fermions described by the Weyl equation have not been observed as elementary particles so far, yet analogous quasiparticles have been identified in solids. While the band structure topology protects the existence of un-gapped linear band crossings, the presence of the crystal lattice as a distinguishable rest frame breaks the Lorentz-invariance. Therefore in solids an additional class of type-II Weyl fermions is allowed that is described by a tilted dispersion cone which is forbidden in elementary particles obeying Lorentz-invariance. It physically corresponds to a sign change of the Fermi velocity along the tilting direction, and their electronic structures are characterized by a topologically protected touching point of an electron-like and a hole-like Fermi surface. PtSe$_2$ has been proposed as a candidate material hosting type-II Weyl fermions. We have performed quantum oscillation measurements in pulsed fields up to 65T on Focused Ion Beam microstructured crystallites that agree well with the Fermi surfaces of current band structure calculations. The present results support a band structure that hosts type-II Weyl fermions in the valence band.