Dynamic surface electronic reconstruction as symmetry-protected topological orders in topological insulator Bi2Se3

Abstract

The layered narrow-band-gap semiconductor ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ is composed of heavy elements with strong spin-orbital coupling, which has been identified both as a good candidate for a thermoelectric material with high thermoelectric figure of merit $(ZT)$ and as a topological insulator of the ${Z}_{2}$ type with a gapless surface band in a Dirac-cone shape. The existence of a conjugated $\ensuremath{\pi}$-bond system on the surface of each ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ quintuple layer is proposed based on an extended valence bond model with valence electrons distributed in the hybridized orbitals. Supporting experimental evidence of a two-dimensional (2D) conjugated $\ensuremath{\pi}$-bond system on each quintuple layer of ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ is provided using electron energy-loss spectroscopy and electron density mapping through inverse Fourier transform of x-ray diffraction data. Quantum chemistry calculations support the $\ensuremath{\pi}$-bond existence between partially filled $4{p}_{z}$ orbitals of Se via side-to-side orbital overlap positively. The conjugated $\ensuremath{\pi}$-bond system on the surface of each quintuple ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ layer is proposed to be similar to that found in graphite (graphene) and responsible for the unique 2D conduction mechanism. The van der Waals (vdW) attractive force between quintuple layers is interpreted to be coming from the antiferroelectrically ordered effective electric dipoles, which are constructed with $\ensuremath{\pi}$-bond trimer pairs on Se layers across the vdW gap of minimized Coulomb repulsion.