Abstract
Based on group theoretical arguments we derive the most general Hamiltonian for the Bi2Se3-class of materials including terms to third order in the wave vector, first order in electric and magnetic fields, first order in strain and first order in both strain and wave vector. We determine analytically the effects of strain on the electronic structure of Bi2Se3. For the most experimentally relevant surface termination we analytically derive the surface state (SS) spectrum, revealing an anisotropic Dirac cone with elliptical constant energy contours giving rise to a direction-dependent group velocity. The spin-momentum locking of strained Bi2Se3 is shown to be modified. Hence, strain control can be used to manipulate the spin degree of freedom via the spin–orbit coupling. We show that for a thin film of Bi2Se3 the SS band gap induced by coupling between the opposite surfaces changes opposite to the bulk band gap under strain. Tuning the SS band gap by strain, gives new possibilities for the experimental investigation of the thickness dependent gap and optimization of optical properties relevant for, e.g., photodetector and energy harvesting applications. We finally derive analytical expressions for the effective mass tensor of the Bi2Se3 class of materials as a function of strain and electric field.
Highlights
Topological insulators have an inverted band gap which engenders topologically protected surface states (SS)
The prime examples of three-dimensional topological insulators are among Bi2Se3-class of materials[1]
For the simplest case of a (111) surface termination, where the surface is parallel to the quintuple layer, the Dirac cone is fully isotropic for small in-plane momentum, perturbed only by a hexagonal warping to third order in momentum[2]
Summary
Topological insulators have an inverted band gap which engenders topologically protected surface states (SS). The allowed third order terms in the wave vector include three terms that were neglected in a previous analysis[11] Since this model is based solely on the symmetry of the crystal, it is valid for all materials in the Bi2Se3 class. Using this model, we determine analytical expressions for the modified bulk band structure and the effective mass tensor near the Γ-point. Comparing the strain dependence of the band gap to recent density functional theory (DFT) calculations, allows us to determine some of the strain related parameters in the band structure From this bulk spectrum, we go on to investigate the effects of strain on the surface states of a semi-infinite topological insulator. This shows that the bulk, and the SS band gap can be tuned via strain
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