Revisiting the physical origin and nature of surface states in inverted-band semiconductors

Abstract

We revisit the problem of surface states in semiconductors with inverted band structures, such as $\alpha$-Sn and HgTe. We unravel the confusion that arose over the past decade regarding the origin of the surface states, their topological nature, and the role of strain. Within a single minimalistic description, we reconcile different solutions found in the 1980s with the results obtained from modern-day numerical simulations, allowing us to unambiguously identify all branches of surface states around the $\Gamma$-point of the Brillouin zone in different regimes. We also show that strain is a smooth "deformation" to the surface states, following the usual continuity principle of physics, and not leading to any drastic change of the physical properties in these materials, in contrast to what has recently been advanced in the literature. We consider biaxial in-plane strain that is either tensile or compressive, leading to different branches of surface states for topological insulators and Dirac semimetals, respectively. Our model can help in interpreting numerous experiments on topological surface states originating from inverted-band semiconductors.

11 pages, 7 figures; extended version. New section IV (Dirac semimetal regime), two figures and references added

References in corpus (10)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Discovery (theoretical prediction and experimental observation) of a large-gap topological-insulator class with spin-polarized single-Dirac-cone on the surface
• Quantum Spin Hall Effect in Inverted Type II Semiconductors
• Bulk Fermi surface coexistence with Dirac surface state in Bi${}_2$Se${}_3$: a comparison of photoemission and Shubnikov-de Haas measurements
• Helical edge and surface states in HgTe quantum wells and bulk insulators
• Low carrier concentration crystals of the topological insulator Bi${}_{2-x}$Sb${}_x$Te${}_{3-y}$Se${}_y$: a magnetotransport study
• Ab initio study of topological surface states of strained HgTe
• Structure of surface electronic states in strained mercury telluride
• Non-trivial topological valence bands of common diamond and zinc-blende semiconductors

Cited by in corpus (6)

• Quantum spin Hall phase in GeSn heterostructures on silicon
• 3D Topological Semimetal Phases of Strained $\alpha$-Sn on Insulating Substrate
• Subband structure of a cylindrical HgTe nanowire: transition from normal type to inverted type
• Interplay between strain and size quantization in a class of topological insulators based on inverted-band semiconductors
• Band inversion transition in HgTe nanowire grown along the [001] direction
• Electronic structure and hinge states of strained half-Heusler compounds LiSbZn and LiBiZn