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We show that a wide class of unconventional quantum criticality emerges whenorbital currents cause quantum phase transitions from zero-gap semiconductorssuch 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 thequantum critical point. This QCL running at temperature $T=0$ separates twodistinct topological phases. This is in contrast to the simple termination ofthe finite temperature critical line at the quantum critical point without anyextension of it at $T=0$. Topology change causes the unconventionality beyondthe concept of simple spontaneous symmetry breaking assumed in the conventionalLandau-Ginzburg-Wilson (LGW) scenario. The unconventional universality impliedby mean-field critical exponents beta>1/2 and delta<3 is protected by theexistence of the quantum critical line. It emerges for several specific latticemodels including the honeycomb, kagome, diamond and pyrochlore lattices. Wealso clarify phase diagrams of the topological phases in these lattices atfinite temperatures.

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