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

TL;DR

This paper explores unconventional quantum criticality and phase transitions in zero-gap semiconductors caused by orbital currents, revealing quantum critical lines and topological phase changes beyond traditional symmetry-breaking theories.

Contribution

It introduces the concept of quantum critical lines extending at zero temperature, driven by topology changes in topological Mott transitions, beyond the Landau-Ginzburg-Wilson framework.

Findings

Quantum critical lines separate topological phases at T=0.

Unconventional critical exponents beta>1/2 and delta<3.

Topological phase diagrams for various lattice models.

Abstract

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.