Hiroki Isobe, Naoto Nagaosa
We theoretically study Dirac systems with N nodes by using the renormalization group (RG), motivated by quantum critical phenomena of topological phase transition and Weyl semimetals. In such materials, the effective energy dispersion is described by Dirac fermions with N species coupled to the electromagnetic field. The RG equations for the coupling constant \alpha, the speed of light c, and electron v are obtained to reveal that (i) c and v coincide in the low-energy limit with $c^2 v^N$ being almost unrenormalized, and (ii) there are two momentum/energy scales characterizing nonrelativistic and relativistic scaling regions. The conditions on the materials to observe these scaling behaviors are determined. As for physical quantities, the dielectric constant, magnetic susceptibility, spectral function, DC conductivity, and mass gap are discussed.
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http://arxiv.org/abs/1303.2822
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