Abstract
Strong topological insulators (TIs) support topological surfaces states on any crystal surface. In contrast, a weak, time-reversal-symmetry-driven TI with at least one non-zero v1, v2, v3 ℤ2 index should host spin-locked topological surface states on the surfaces that are not parallel to the crystal plane with Miller indices (v1 v2 v3). On the other hand, mirror symmetry can protect an even number of topological states on the surfaces that are perpendicular to a mirror plane. Various symmetries in a bulk material with a band inversion can independently preordain distinct crystal planes for realization of topological states. Here we demonstrate the first instance of coexistence of both phenomena in the weak 3D TI Bi2TeI which (v1 v2 v3) surface hosts a gapless spin-split surface state protected by the crystal mirror-symmetry. The observed topological state has an even number of crossing points in the directions of the 2D Brillouin zone due to a non-TRIM bulk-band inversion. Our findings shed light on hitherto uncharted features of the electronic structure of weak topological insulators and open up new vistas for applications of these materials in spintronics.
Highlights
The gapless spin-polarized states of topological insulators (TIs) at the edge (in two-dimensional (2D) TIs) or at the surface (in three-dimensional (3D) TIs) open up exciting possibilities for applications of these materials in spintronics[1,2,3]
Weak TIs are perspective for realization of a dual topological phase where the Dirac surface state of the 2 topological phase and the topological states protected by the crystal symmetry can be manipulated separately without applying a magnetic field, owing to the fact that they appear at different crystal surfaces
The compound crystallizes in a centrosymmetric monoclinic unit cell with 16 atoms which can be represented as a Niggli-reduced cell (a = b = 4.380 Å, c = 17.741 Å, α = β = 82.9047°, γ = 60.0025°) with 8 atoms [Fig. 1(a)]
Summary
The crystal structure of Bi2TeI was elucidated from a single-crystal X-ray diffraction experiment[16]. The surface spectrum calculated without taking spin-orbit coupling into account (see Fig. 3(a)) is generally similar to the Te-terminated surface spectrum (see Fig. 2(a)) with an exception of a surface state residing at the Γ point at ≈ 0.2 eV in a local gap of the conduction band (marked by a deep pink curve). This state originates from the splitting of the upper edge of the first conduction band which is caused by positive band bending that is provided by the [I-Bi-Te] overlayer. The counterpart gapless state located in the Γ − (−M) direction has an opposite spin direction and, the net spin equals zero over the Brillouin zone
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