Spintronics is aimed at actively controlling and manipulating the spin degrees of freedom in semiconductor devices. A promising way to achieve this goal is to make use of the tunable Rashba effect that relies on the spin-orbit interaction in a two-dimensional electron system immersed in an inversion-asymmetric environment. The spin-orbit-induced spin splitting of the two-dimensional electron state provides a basis for many theoretically proposed spintronic devices. However, the lack of semiconductors with large Rashba effect hinders realization of these devices in actual practice. Here we report on a giant Rashba-type spin splitting in two-dimensional electron systems that reside at tellurium-terminated surfaces of bismuth tellurohalides. Among these semiconductors, BiTeCl stands out for its isotropic metallic surface-state band with the Γ-point energy lying deep inside the bulk band gap. The giant spin splitting of this band ensures a substantial spin asymmetry of the inelastic mean free path of quasiparticles with different spin orientations.

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...

We present a method to microscopically derive a small-size k·p Hamiltonian in a Hilbert space spanned by physically chosen ab initio spinor wave functions. Without imposing any complementary symmetry constraints, our formalism equally treats three-and two-dimensional systems and simultaneously yields the Hamiltonian parameters and the true Z2 topological invariant. We consider bulk crystals and thin films of Bi2Se3, Bi2Te3, and Sb2Te3. It turns out that the effective continuous k·p models with open boundary conditions often incorrectly predict the topological character of thin films.PACS numbers: 71.18.+y, 71.70.Ej, Electronic structure of topological insulators (TIs) has been in focus of theoretical research regarding linear response, transport properties, Hall conductance, and motion of Dirac fermions in external fields [1,2]. These problems call for a physically justified model Hamiltonian of small dimension. As in semiconductors, it is thought sufficient that the model accurately reproduces the TI band structure near the inverted band gap [3]. The desired Hamiltonian is derived either from the theory of invariants [4] or within the k·p perturbation theory using the symmetry properties of the basis states [5].In Ref.[3], along with the pioneering prediction of the topological nature of Bi 2 Se 3 , Bi 2 Te 3 , and Sb 2 Te 3 , a 4-band Hamiltonian was first constructed from the theory of invariants, which is presently widely used to analyze the properties of bulk TIs as well as their surfaces and thin films [6][7][8][9][10][11][12][13][14]. The Hamiltonian parameters in Ref. [3] were obtained by fitting ab initio band dispersion curves. Later, an attempt was made [15] to recover the Hamiltonian of Ref.[3] by a k·p perturbation theory with symmetry arguments and to derive its parameters from the ab initio wave functions of the bulk crystals. Furthermore, in Ref. To analyze how the properties of thin films are inherited from the bulk TI features, effective continuous models have been developed: they are based on the substitution k z → −i∂ z (originally introduced for slowly varying perturbations [16]) in the Hamiltonian of Ref.[3] and on the imposition of the open boundary conditions [15,[17][18][19]. These models predict a variety of intriguing phenomena at surfaces, interfaces, and thin films of TIs [20][21][22][23]. A fundamental issue here is the topological phase transition between an ordinary 2D insulator and a quantum spin Hall insulator (QSHI). Apart from the theoretical prediction, the model parameters are fitted to the measured band dispersion to deduce the topological phase from the experiment [24,25]. By analyzing the signs and relative values of the parameters of the empirically obtained effective model a judgement is made on whether the edge states would exist in a given TI film, the logic being similar to that of Ref. [26]: The valence band should have a positive and conduction band a negative effective mass.In order to avoid any ambiguity in deriving the model Hamiltonian and to treat 3D and 2D s...