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We investigate a generalized two-dimensional Weyl Hamiltonian, which maydescribe the low-energy properties of mechanically deformed graphene and of theorganic compound alpha-(BEDT-TTF)_2I_3 under pressure. The associateddispersion has generically the form of tilted anisotropic Dirac cones. The tiltarises due to next-nearest-neighbor hopping when the Dirac points, where thevalence band touches the conduction band, do not coincide with crystallographichigh-symmetry points within the first Brillouin zone. Within a semiclassicaltreatment, we describe the formation of Landau levels in a strong magneticfield, the relativistic form of which is reminiscent to that of graphene, witha renormalized Fermi velocity due to the tilt of the Dirac cones. Theserelativistic Landau levels, experimentally accessible via spectroscopy or evena quantum Hall effect measurement, may be used as a direct experimentalverification of Dirac cones in alpha-(BEDT-TTF)_2I_3.

Tilted anisotropic Dirac cones in quinoid-type graphene and alpha-(BEDT-TTF)_2I_3