Low-velocity anisotropic Dirac fermions on the side surface of topological insulators

Abstract

We report anisotropic Dirac-cone surface bands on a side-surface geometry of the topological insulator Bi2Se3 revealed by first-principles density-functional calculations. We find that the electron velocity in the side-surface Dirac cone is anisotropically reduced from that in the (111)-surface Dirac cone, and the velocity is not in parallel with the wave vector k except for k in high-symmetry directions. The size of the electron spin depends on the direction of k due to anisotropic variation of the noncollinearity of the electron state. Low-energy effective Hamiltonian is proposed for sidesurface Dirac fermions, and its implications are presented including refractive transport phenomena occurring at the edges of tological insulators where different surfaces meet.PACS numbers: 71.15. Mb, 73.61.Ng, 75.70.Tj Topological insulators (TIs) are characterized by odd number of Dirac-cone-like surface bands which guarantees robust metallicity against arbitrary perturbations preserving time-reversal symmetry [1,2], and by the helical spin texture of the surface states which leads to remarkable transport properties such as the absence of backscattering by non-magnetic defects as confirmed by experiments [3][4][5]. The latter feature reminds us of graphene where charge carriers are also described as massless Dirac fermions, as demonstrated intriguingly by the Klein tunneling [6] where normal incident wave exhibits perfect transmission through any finite potential barrier. A crucial difference is that TI involves real spins whereas graphene does pseudo-spins, so that, for example, one-dimensional wires of TI have maximum magnetoconductance at half integral flux quanta due to π Berry phase acquired when circling around the wires [7,8].Promising TI materials [9, 10] include series of rhombohedral materials Bi 2 Se 3 , Bi 2 Te 3 , and Sb 2 Te 3 proposed by a recent first-principles calculation [9], with the existence of single Dirac cone on their (111) surfaces indeed confirmed by angle-resolved photoemission spectroscopies [11,12]. Among them, Bi 2 Se 3 is considered most promising in the application point of view due to its relatively large bulk band gap of ∼300 meV that can evade bulk conduction of thermally excited charge carriers at room temperature. This material has a layered structure where the Bi 2 Se 3 quintuple layers (QLs) are stacked along the rhombohedral (111) direction [13] combined by van der Waals type interaction. Thus, a natural cleaving face is the (111) surface between two QLs, and it has been the only surface considered theoretically or experimentally so far [14].Surfaces other than the (111) surface, and interfaces between different surfaces, appear inevitably as step edges on cleaved (111) surfaces [4,5,15] and as side surfaces in nanowires or nanoribbons [16][17][18][19]. According to the topological band theory [1, 2], a strong TI like Bi 2 Se 3 [9] should have odd number of Dirac cones on any arbitrary surface. However, existence of Dirac cones on (b) Top view of the topmost atomic layer, with sur...

Strain in epitaxial high-index Bi2Se3(221) films grown by molecular-beam epitaxy

“…Firstly, the pure Bi2Se3(221) slab model was calculated and the resulted band structure reproduced the result of Ref. 18 , revealing the anisotropic Dirac cone.…”

Enhanced optical conductance in graphene superlattice due to anisotropic band dispersion

“…In topological insulator (TI), the quasiparticle residing in its surface state is also in the massless Dirac form with Fermi velocity approximately half of the graphene [15]. Interestingly, the anisotropic massless Dirac fermion can also be found in the (2, 2, 1) side-surface state of Bi 2 Se 3 TI with a rather strong anisotropy of v x = 3.1 × 10 5 m s −1 and v y = 1.4 × 10 5 m s −1 [16]. In a Bi square net of SrMnBi 2 TI, highly anisotropic Fermi velocity differs by a factor of 8 and was experimentally observed [17].…”

Spin conduction in anisotropic three-dimensional topological insulators

“…This is the origin of the spin orientation angle φ which parameterizes both spin profiles. Anisotropy can be realized in TIs either by choosing reduced-symmetry materials like β −Ag 2 T e 11,12 (see Figure 2b) or by cutting a high-symmetry TI in a way that reduces the surface's symmetry 13,14 . Figure 2 illustrates distortion of the Dirac cone as rotational symmetry is progressively broken.…”