Evidence for a direct band gap in the topological insulator Bi2Se3from theory and experiment

Abstract

Using angle-resolved photoelectron spectroscopy and ab-initio GW calculations, we unambiguously show that the widely investigated three-dimensional topological insulator Bi2Se3 has a direct band gap at the Γ point. Experimentally, this is shown by a three-dimensional band mapping in large fractions of the Brillouin zone. Theoretically, we demonstrate that the valence band maximum is located at the Γ point only if many-body effects are included in the calculation. Otherwise, it is found in a high-symmetry mirror plane away from the zone center. PACS numbers: 71.15.m, 71.20.b, 71.70.Ej, Bismuth selenide has been widely studied for many years for its potential applications in optical recording systems [1], photoelectrochemical [2] and thermoelectric devices [3,4], and is nowadays commonly used in refrigeration and power generation. Recently, it has attracted increasing interest after its identification as a prototypical topological insulator (TI) [5,6]. Its surface electronic structure consists of a single Dirac cone around the surface Brillouin zone (SBZ) centreΓ, with the Dirac point (DP) placed closely above the bulk valence band states. In order to exploit the multitude of interesting phenomena associated with the topological surface states [7,8], it is necessary to access the topological transport regime, in which the chemical potential is near the DP and simultaneously in the absolute bulk band gap. Due to the close proximity of the DP and the bulk valence states at Γ, this is only possible if there are no other valence states in Bi 2 Se 3 with energies close to or higher than the DP. Therefore, it is crucial to establish if the bulk valence band maximum (VBM) in bismuth selenide is placed at Γ (and thus projected out toΓ) or at some other position within the Brillouin zone (BZ). As the bulk conduction band minimum (CBM) is undisputedly located at Γ [9,10], the question about the VBM location is identical to the question about the nature of the fundamental band gap in this TI, direct or indirect.The nature of the bulk band gap is thus of crucial importance for the possibility of exploiting the topological surface states in transport, but the position of the VBM in band structure calculations remains disputed. In a linearized muffin-tin orbital method (LMTO) calculation within the local density approximation (LDA), the VBM was found at the Γ point, implying that Bi 2 Se 3 is a direct-gap semiconductor [11]. Contrarily, by employing the full-potential linearized augmented-plane-wave method (FLAPW) within the generalized gradient approximation (GGA), the authors of Ref. 9 have found the VBM to be located on the Z − F line of the BZ, which is lying in the mirror plane. Similar results have been obtained in Ref. 12 with the plane-wave pseudopotential method (PWP) within the LDA. Various density functional theory (DFT) calculations of the surface band structure of Bi 2 Se 3 [5,7,13,14] also indicate that the VBM of bulk bismuth selenide is not located at the BZ center. The inclusion of many-body effects within the G...

Improved Electronic Structure and Optical Performance of Bi2Te3-xSex From First-principle Calculations Within TB-mBJ Exchange Potential

“…1.The structures can be detected as Bi and Te (Se) layers stacked along the c-axis and containing five atoms per unit cell (two Bi atoms and three Te or Se atoms) 10 . Increase both theoretical and experimental investigation on electronic structure and optical properties of Bi 2 Te 3-x Se x (x=0,1,2 and 3) exhibit a direct band gap 13 and The refractive index of the Bismuth Telluride is higher than any value previously reported for a semiconductor 14 . In this work the principle of our inspection is concentrated on predicting the structural, electronic and optical properties of Bi 2 Te 3-x Se x alloys with a number of concentrations (x) (x=0,1,2 and 3).…”

“…7 indicate the zero frequency limits ε 1 (0) versus Se (selenide) concentration (x) with comparable data 10 . The bowing parameter of The static dielectric constants (the zero frequency limits) ε 1 (0) is determined by fitting the non linear variation, Relation (13) show the result: (13) The imaginary part of the dielectric function of Bi 2 Te 3-x Se x alloys with different concentration (x) is illustrated by Fig. 8.…”

Bulk and surface electron dynamics in ap-type topological insulatorSnSb2Te4

“…A lifetime of 6 ps has been reported for p-type-doped Bi 2 Se 3 with a Fermi level position ≈ 70 meV below the Dirac point [8] and attributed to filling from the CB. In Bi 2 Se 3 , the top of the VB is located at 50 meV below the Dirac point [29], i.e., E VBM ≈ 20 meV. The τ ∝ E −2 VBM scaling used for SnSb 2 Te 4 would yield a lifetime for Bi 2 Se 3 of 3 ps similar to the theoretically predicted intraband decay rate [3] but significantly shorter than the dominating lifetime of the CB.…”

Interband absorption edge in the topological insulators Bi2(Te1−xSex)3

“…However, in later ARPES data with improved signal to noise ratio, there is a noticeable intensity reaching up to the Dirac point located at about 0.2 eV below the bottom of the conduction band 7,[40][41][42][43][44] . Explicitly, Chen et al concluded that the valence band in Bi 2 Se 3 extends up to the Dirac point from below 7 .…”

“…The latter scenario is confirmed by recent Shubnikov-de Haas (SdH) measurements 37 concluding that the top of the valence band is a downward oriented paraboloid with no signatures of an M shape of the top of the valence band. Note that the M-structure of the valence band seen in some LDA bandstructure calculations 45 is absent in the more realistic results of GW calculations 44,46,47 that exhibit a paraboloidal shape of the valence band. 2 (E) towards zero is used to define E min , we obtain the value 190 meV and 152 meV at 10 K and 300 K, respectively.…”