Complex band structure of topological insulator Bi₂Se₃

Abstract

Topological insulators are very interesting from a fundamental point of view, and their unique properties may be useful for electronic and spintronic device applications. From the point of view of applications it is important to understand the decay behavior of carriers injected in the band gap of the topological insulator, which is determined by its complex band structure (CBS). Using first-principles calculations, we investigate the dispersion and symmetry of the complex bands of Bi2Se3 family of three-dimensional topological insulators. We compare the CBS of a band insulator and a topological insulator and follow the CBS evolution in both when the spin-orbit interaction is turned on. We find significant differences in the CBS linked to the topological band structure. In particular, our results demonstrate that the evanescent states in Bi2Se3 are non-trivially complex, i.e. contain both the real and imaginary contributions. This explains quantitatively the oscillatory behavior of the band gap obtained from Bi2Se3 (0 0 0 1) slab calculations.

Optical evidence for blue shift in topological insulator bismuth selenide in the few-layer limit

“…The data agrees very well with reports on MBE samples [31]. Band structure calculations can identify multiple candidates responsible for these transitions (both direct and indirect) [23] [24]. Even though the spectral range of our ellipsometry measurement is limited, empirical band gaps can be inferred from the Tauc gaps (Eg) of the model oscillators (Table 1).…”

All-electrical generation of spin-polarized currents in quantum spin Hall insulators

“…4(d), from which the complex wave vector k x = q + iκ can be determined for spin up and down electrons. This behavior of oscillatory decay of edge/surface states was previously reported in the QSH insulator of Bernevig, Hughes, and Zhang model [43,44] and also in the 3D topological insulator Bi 2 Se 3 [45]. Note that the position of conduction band minimum (or valence band maximum) [see Fig.…”

Bulk versus surface contributions to the Rashba spin splitting of Shockley surface states

“…For a given energy ε and planar wave vector k, the embedding potential is calculated from the wave functions of generalized Bloch states (complex energy bands) with complex wave number in the normal direction, q = k z + iκ z , which decay or propagate toward the interior of the metal. The energy versus q plot of the complex energy bands is called the complex band structure [23][24][25]. In Fig.…”