The spin-helical surface states in three-dimensional topological insulator (TI), such as Bi2Se3, are predicted to have superior efficiency in converting charge current into spin polarization. This property is said to be responsible for the giant spin-orbit torques observed in ferromagnetic metal/TI structures. In this work, using first-principles and model tight-binding calculations, we investigate the interface between the topological insulator Bi2Se3 and 3d-transition ferromagnetic metals Ni and Co. We find that the difference in the work functions of the topological insulator and the ferromagnetic metals shift the topological surface states down about 0.5 eV below the Fermi energy where the hybridization of these surface states with the metal bands destroys their helical spin structure. The band alignment of Bi2Se3 and Ni (Co) places the Fermi energy far in the conduction band of bulk Bi2Se3, where the spin of the carriers is aligned with the magnetization in the metal. Our results indicate that the topological surface states are unlikely to be responsible for the huge spin-orbit torque effect observed experimentally in these systems.

One of the great successes of modern condensed matter physics is the discovery of topological insulators (TIs). A thorough investigation of their properties could bring such materials from fundamental research to potential applications. Here, we report on theoretical investigations of the complex band structure (CBS) of two-dimensional (2D) TIs. We utilize the tight-binding form of the Bernevig, Hughes, and Zhang model as a prototype for a generic 2D TI. Based on this model, we outline the conditions that the CBS must satisfy in order to guarantee the presence of topologically protected edge states. Furthermore, we use the Green's function technique to show how these edge states are localized, highlighting the fact that the decay of the edge-state wave functions into the bulk of a TI is not necessarily monotonic and, in fact, can exhibit an oscillatory behavior that is consistent with the predicted CBS of the bulk TI. These results may have implications for electronic and spin transport across a TI when it is used as a tunnel barrier.

Topological insulators are very interesting from a fundamental point of view, and their unique properties may be useful for electronic and spintronic device applications. From the point of view of applications it is important to understand the decay behavior of carriers injected in the band gap of the topological insulator, which is determined by its complex band structure (CBS). Using first-principles calculations, we investigate the dispersion and symmetry of the complex bands of Bi2Se3 family of three-dimensional topological insulators. We compare the CBS of a band insulator and a topological insulator and follow the CBS evolution in both when the spin-orbit interaction is turned on. We find significant differences in the CBS linked to the topological band structure. In particular, our results demonstrate that the evanescent states in Bi2Se3 are non-trivially complex, i.e. contain both the real and imaginary contributions. This explains quantitatively the oscillatory behavior of the band gap obtained from Bi2Se3 (0 0 0 1) slab calculations.

Nodal line semimetals are characterized by symmetry-protected band crossing lines and are expected to exhibit nontrivial electronic properties. Connections of the multiple nodal lines, resulting in nodal nets, chains, or links, are envisioned to produce even more exotic quantum states. In this work, we propose a feasible approach to realize tunable nodal line connections in real materials. We show that certain space group symmetries support the coexistence of the planar symmetry enforced and accidental nodal lines, which are robust to spin-orbit coupling and can be tailored into intricate patterns by chemical substitution, pressure, or strain. Based on first-principles calculations, we identify non-symmorphic centrosymmetric quasi-one-dimensional compounds, K2SnBi and MX3 (M = Ti, Zr, Hf and X = Cl, Br, I), as materials hosting such tunable 2D Dirac nodal nets. Unique Landau levels are predicted for the nodal line semimetals with the 2D Dirac nodal nets. Our results provide a viable approach for realize the novel physics of the nodal line connections in practice.Quantum materials have recently become a promising platform for the discovery of new fermionic particles and novel quantum phenomena [1]. Among them are Weyl and Dirac semimetals, the three-dimensional (3D) materials with nontrivial band crossings at discrete points in the momentum space [ 2 , 3 ]. These materials support the quasiparticles resembling the relativistic Dirac (four-fold degenerate) and Weyl (doubly degenerate) fermions known from high-energy physics [2][3][4][5][6][7][8][9][10]. It has been demonstrated that the Dirac or Weyl cones can be tilted [11][12][13], the low-energy dispersion can be quadratic or cubic [14,15], and the fermionic quasiparticles can hold three-, six-, or eight-fold degeneracies [3,[16][17][18][19], which do not have analogy in high-energy physics.In addition to the nodal points, band crossings can also occur along the nodal lines [2,[20][21][22][23][24][25][26], resulting in unusual surface states and magneto-transport properties [21,27,28]. Importantly, the nodal lines can serve as the constituents for other nontrivial states. For example, the multiple nodal lines can form nodal chains [29][30][31][32], nets [33,34], and links [35][36][37][38]. Nodal lines intersections can produce triple or four-fold degenerate points in non-centrosymmetric materials [29,39] and support photoinduced Floquet multi-Weyl fermions [40,41].All the current studies of the interconnecting nodal line systems with non-negligible spin-orbit coupling (SOC), however, are limited to the nodal line connections with the permanent shapes, leaving possible transformations between the different nodal net textures unexplored. Materials with the tunable nodal line connections would allow engineering the desired spinfull fermionic properties of the nodal line semimetals, thus providing a promising platform to discover new physics and to design potential applications.In this work, we propose a feasible approach to realize tunable nodal line connections in...

The compound Bi 14 Rh 3 I 9 has recently been suggested as a weak 3D topological insulator (TI) on the basis of angle-resolved photoemission and scanning-tunneling experiments in combination with density-functional (DF) electronic structure calculations. These methods unanimously support the topological character of the headline compound, but a compelling confirmation could only be obtained by dedicated transport experiments. The latter, however, are biased by an intrinsic n-doping of the material's surface due to its polarity. Electronic reconstruction of the polar surface shifts the topological gap below the Fermi energy, which would also prevent any future device application. Here, we report the results of DF slab calculations for chemically gated and counter-doped surfaces of Bi 14 Rh 3 I 9. We demonstrate that both methods can be used to compensate the surface polarity without closing the electronic gap.tum spin Hall effect In recent years, topological insulators (TIs) have attracted enormous attention due to their intriguing properties. Of particular interest are their massless Dirac-cone-like surface states protected by time-reversal symmetry (TRS). 1-3 In a nutshell, TIs are characterized by these gapless surface states and a bulk energy gap. Three dimensional (3D) TIs are called strong or weak based on four Z 2 invariants (ν 0 ; ν 1 , ν 2 , ν 3). If ν 0 = 1, the material is a strong TI; if ν 0 = 0 and any of the indices (ν 1 , ν 2 , ν 3) is equal to one, it is a weak TI. 4,5 In the former case, including the well-known compounds Bi 2 Se 3 and Bi 2 Te 3 , 1,2 the TRS-protected surface states are present on all facets, while in the latter case, such surface states are present only on certain facets. Their peculiar properties bear the potential to enable novel types of information processing. 6-8 An important step toward so-called topological quantum computing is the recent observation of signatures of Majorana fermion modes. 9 In closer reach could be an application of the recently observed excellent thermoelectric properties of the title compound 10 or of the all-electrical detection of spin polarization by combination of quantum spin Hall and metallic spin Hall transport in a single device. 7 Weak 3D TIs suggested hitherto are usually hosted by layered crystal structures. 11 The strength of the related inter-layer coupling influences the bulk band structure: (i) In Bi 2 TeI with strong inter-layer coupling, this coupling is essential for the formation of the weak 3D TI state; 12 (ii) a weak interlayer coupling, on the other hand, results in a quasi two-dimensional (2D) band structure. This situation is found in KHgSb, 13 ZrTe 5 14 or Bi 14 Rh 3 I 9. 15,16 Weak 3D TIs of the second kind may allow to produce 2D TI structures that are expected to show the quantum spin-Hall (QSH) effect. This can be achieved by cleaving off thin layers from the bulk 3D TI as an alternative way to the fabrication of quantum wells. 17,18 Indeed, 2 a single, charge-compensated layer of Bi 14 Rh 3 I 9 was predicted to be a 2D T...