Non-necessity of band inversion process in 2D topological insulators for bulk gapless states and topological phase transitions

Abstract

In commonly employed models for 2D topological insulators, bulk gapless states are well known to form at the band inversion points where the degeneracy of the states is protected by symmetries. It is thus sometimes quite tempting to consider this feature, the occurrence of gapless states, a result of the band inversion process under protection of the symmetries. Similarly, the band inversion process might even be perceived as necessary to induce 2D topological phase transitions. To clarify these misleading perspectives, we propose a simple model with a flexible Chern number to demonstrate that the bulk gapless states emerge at the phase boundary of topological phase transitions, despite the absence of band inversion process. Furthermore, the bulk gapless states do not need to occur at the special $k$-points protected by symmetries. Given the significance of these fundamental \textit{conceptual} issues and their wide-spread influence, our clarification should generate strong general interests and significant impacts. Furthermore, the simplicity and flexibility of our general model with an arbitrary Chern number should prove useful in a wide range of future studies of topological states of matter.

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
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Topological Insulators with Inversion Symmetry
• Discovery (theoretical prediction and experimental observation) of a large-gap topological-insulator class with spin-polarized single-Dirac-cone on the surface
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Quantized Anomalous Hall Effect in Magnetic Topological Insulators
• Weyl semimetal phase in non-centrosymmetric transition metal monophosphides
• Edge states in Graphene: from gapped flat band to gapless chiral modes
• Topological insulators in ordered double transition metals M${}_2^{\prime }$M$"$C${}_2$ (M${}^{\prime }$= Mo, W; M$"$= Ti, Zr, Hf) MXenes
• Spin-Valley Optical Selection Rule and Strong Circular Dichroism in Silicene
• Superconductors as ideal spin sources for spintronics
• Strain tuning of topological band order in cubic semiconductors
• Chern insulators without band inversion in MoS2 monolayers with 3d adatoms