Gap closing and universal phase diagrams in topological insulators

Abstract

We study a general problem how the gap in a nonmagnetic band insulator closes by tuning a parameter. We review our recent results on the classification of all the possible gap closing in two and three dimensions. We show that they accompany the change of Z_2 topological numbers, and that the gap closings correspond to phase transitions between the quantum spin Hall and the insulator phases. Interestingly, in inversion-asymmetric three-dimensional systems there appears a gapless phase between the quantum spin Hall and insulator phases. This gapless phase is due to a topological nature of gap-closing points in three dimensions, but not in two dimensions.

7 pages, 5 figures, proceedings for nanoPHYS'09 in Tokyo

References in corpus (14)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Topological Insulators with Inversion Symmetry
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• Dissipationless Quantum Spin Current at Room Temperature
• Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• The Helical Liquid and the Edge of Quantum Spin Hall Systems
• Quantum Spin Hall Effect and Enhanced Magnetic Response by Spin-Orbit Coupling
• Well-localized edge states in two-dimensional topological insulators: ultrathin Bi films
• Tuning phase transition between quantum spin Hall and ordinary insulating phases
• Universal phase diagrams for the quantum spin Hall systems
• Disorder effect on 3-dimensional $Z_2$ quantum spin Hall systems

Cited by in corpus (13)

• Experimental discovery of Weyl semimetal TaAs
• Topological Semimetals Predicted from First-principles Calculations
• Anomalous Hall Effect in ZrTe5
• Correlation Length, Universality Classes, and Scaling Laws Associated with Topological Phase Transitions
• Scaling Theory of Topological Phase Transitions
• Strain-induced topological insulator phase transition in HgSe
• Evolutions of helical edge states in disordered HgTe/CdTe quantum wells
• Invariants of disordered semimetals via the spectral localizer
• Topological Phase Transition in Quantum Heat Engine Cycles
• Topological phase transition between non-high symmetry critical phases and curvature function renormalization group
• Magnetic field-induced type-II Weylsemimetallic state in geometrically frustrated Shastry-Sutherland lattice GdB4
• The evolution of Weyl nodes in Ni doped thallium niobate pyrochlore Tl${}_{2-x}$Ni${}_x$Nb${}_2$O${}_7$
• Generating Weyl semimetals from alkali metals