Phase Diagram Structure of Topological Mott Transition for Zero-gap Semiconductors beyond Conventional Landau-Ginzburg-Wilson Scenario

We show that a wide class of unconventional quantum criticality emerges when orbital currents cause quantum phase transitions from zero-gap semiconductors such as Dirac fermions to topological insulator (TI) or Chern insulator (CI). Changes in Fermi surface topology concomitant with (SU(2) or time reversal) symmetry breakings generate quantum critical lines (QCL) even beyond the quantum critical point. This QCL running at temperature $T=0$ separates two distinct topological phases. This is in contrast to the simple termination of the finite temperature critical line at the quantum critical point without any extension of it at $T=0$. Topology change causes the unconventionality beyond the concept of simple spontaneous symmetry breaking assumed in the conventional Landau-Ginzburg-Wilson (LGW) scenario. The unconventional universality implied by mean-field critical exponents beta>1/2 and delta<3 is protected by the existence of the quantum critical line. It emerges for several specific lattice models including the honeycomb, kagome, diamond and pyrochlore lattices. We also clarify phase diagrams of the topological phases in these lattices at finite temperatures.