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Register a new userNovel Spin-texture on the warped Dirac-cone surface states in topological insulators
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We have investigated the nature of surface states in the Bi2Te3 family of three-dimensional topological insulators using first-principles calculations as well as model Hamiltonians. When the surface Dirac cone is warped due to Dresselhaus spin-orbit coupling in rhombohedral structures, the spin acquires a finite out-of-plane component. We predict a novel in-plane spin-texture of the warped surface Dirac cone with spins not perpendicular to the electron momentum. Our k.p model calculation reveals that this novel in-plane spin-texture requires high order Dresselhaus spin-orbit coupling terms.
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We study the properties of a family of anti-pervoskite materials, which are topological crystalline insulators with an insulating bulk but a conducting surface. Using ab-initio DFT calculations, we investigate the bulk and surface topology and show that these materials exhibit type-I as well as type-II Dirac surface states protected by reflection symmetry. While type-I Dirac states give rise to closed circular Fermi surfaces, type-II Dirac surface states are characterized by open electron and hole pockets that touch each other. We find that the type-II Dirac states exhibit characteristic van-Hove singularities in their dispersion, which can serve as an experimental fingerprint. In addition, we study the response of the surface states to magnetic fields.
Interactions between the surface and the bulk in a strong topological insulator (TI) cause a finite lifetime of the topological surface states (TSS) as shown by the recent experiments. On the other hand, interactions also induce unitary processes, which, in the presence of anisotropy and the spin-orbit coupling (SOC), can induce non-trivial effects on the spin texture. Recently, such effects were observed experimentally in the $Bi_2X_3$ family, raising the question that the hexagonal warping (HW) may be linked with new spin-related anomalies. The most remarkable among which is the 6-fold periodic canting of the in-plane spin vector. Here, we show that, this anomaly is the result of a {it triple cooperation between the interactions, the SOC and the HW}. To demonstrate it, we formulate the spin-off-diagonal self energy. A unitary phase with an even symmetry develops in the latter and modulates the spin-1/2 vortex when the Fermi surface is anisotropic. When the anisotropy is provided by the HW, a 6-fold in-plane spin-canting is observed. Our theory suggests that the spin-canting anomaly in $Bi_2X_3$ is a strong evidence of the interactions. High precision analysis of the spin-texture is a promising support for further understanding of the interactions in TIs.
The unoccupied states in topological insulators Bi_2Se_3, PbSb_2Te_4, and Pb_2Bi_2Te_2S_3 are studied by the density functional theory methods. It is shown that a surface state with linear dispersion emerges in the inverted conduction band energy gap at the center of the surface Brillouin zone on the (0001) surface of these insulators. The alternative expression of Z_2 invariant allowed us to show that a necessary condition for the existence of the second Gamma Dirac cone is the presence of local gaps at the time reversal invariant momentum points of the bulk spectrum and change of parity in one of these points.
We investigate the spin and charge densities of surface states of the three-dimensional topological insulator $Bi_2Se_3$, starting from the continuum description of the material [Zhang {em et al.}, Nat. Phys. 5, 438 (2009)]. The spin structure on surfaces other than the 111 surface has additional complexity because of a misalignment of the contributions coming from the two sublattices of the crystal. For these surfaces we expect new features to be seen in the spin-resolved ARPES experiments, caused by a non-helical spin-polarization of electrons at the individual sublattices as well as by the interference of the electron waves emitted coherently from two sublattices. We also show that the position of the Dirac crossing in spectrum of surface states depends on the orientation of the interface. This leads to contact potentials and surface charge redistribution at edges between different facets of the crystal.
Existence of a protected surface state described by a massless Dirac equation is a defining property of the topological insulator. Though this statement can be explicitly verified on an idealized flat surface, it remains to be addressed to what extent it could be general. On a curved surface, the surface Dirac equation is modified by the spin connection terms. Here, in the light of the differential geometry, we give a general framework for constructing the surface Dirac equation starting from the Hamiltonian for bulk topological insulators. The obtained unified description clarifies the physical meaning of the spin connection.
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