Dirac electrons in solids

Electronic band structures in solids sometimes have features similar to Dirac electrons in vacuum. Well-known examples are bismuth and graphite; 4×4 original Dirac matrix in three dimension (3d) in the former with strong spin–orbit interaction, while 2×2 massless Dirac in two dimension (2d) with weak inter-layer coupling described essentially by Weyl equation in the latter. Recently one layer of graphite, graphene, is realized and studied both extensively and intensively. Other recent examples include a molecular solid, α-(BEDT-TTF)2I3α-(BEDT-TTF)2I3, which has a layered structure with electronic states described by tilted-Weyl equation, and Fe-pnictides. There is also a theoretical proposal that one of inverse perovskites, Ca3PbO, can be a candidate in 3d with strong spin–orbit interaction similar to bismuth. The particular feature of Dirac electrons in solids is a small, or even vanishing, band gap and then thermodynamic or transport properties are affected by inter-band coupling of electronic states. Typical ones are responses to external magnetic field. Actually, it has long been known that orbital susceptibility of these Dirac electrons has very particular features resulting from inter-band effects of magnetic field. It is of interest to see such inter-band effects on Hall effects to be compared with orbital susceptibility, which will be introduced in this paper, together with possible consequences of mutual interaction between valleys triggered by tilting in molecular solids.