Anomalous behavior of the electronic structure of (Bi${}_{1-x}$In${}_x$)${}_2$Se${}_3$ across the quantum-phase transition from topological to trivial insulator

Abstract

Using spin- and angle-resolved spectroscopy and relativistic many-body calculations, we investigate the evolution of the electronic structure of (Bi${}_{1-x}$In${}_x$)${}_2$Se${}_3$ bulk single crystals around the critical point of the trivial to topological insulator quantum-phase transition. By increasing $x$, we observe how a surface gap opens at the Dirac point of the initially gapless topological surface state of Bi${}_2$Se${}_3$, leading to the existence of massive fermions. The surface gap monotonically increases for a wide range of $x$ values across the topological and trivial sides of the quantum-phase transition. By means of photon-energy dependent measurements, we demonstrate that the gapped surface state survives the inversion of the bulk bands which occurs at a critical point near $x=0.055$. The surface state exhibits a non-zero in-plane spin polarization which decays exponentially with increasing $x$, and that persists on both the topological and trivial insulator phases. Its out-of-plane spin polarization remains zero demonstrating the absence of a hedgehog spin texture expected from broken time-reversal symmetry. Our calculations reveal qualitative agreement with the experimental results all across the quantum-phase transition upon the systematic variation of the spin-orbit coupling strength. A non-time reversal symmetry breaking mechanism of bulk-mediated scattering processes that increase with decreasing spin-orbit coupling strength is proposed as explanation.

arXiv comment9 pages, 5 figures

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• The electronic structure of Mn${}_{1-x}$Pb${}_x$Bi${}_2$Te${}_4$: experimental evidence of topological phase transition
• Surface Conductivity in Antiferromagnetic Semiconductor CrSb${}_2$
• Double band inversion in the topological phase transition of Ge1-xSnx alloys
• Terahertz electro-optic effect in Bi${}_2$Se${}_3$ crystals
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