Highly convergent schemes for the calculation of bulk and surface Green functions

Sancho, M. P. López; Sancho, Javier; Rubió, J.

doi:10.1088/0305-4608/15/4/009

Cited by 1,815 publications

(1,003 citation statements)

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“…The MLWF hopping parameters for the bulk part can be constructed from the bulk ab initio calculation, and the ones for the surface slab can be constructed from the ab initio calculation of the slab, in which the surface correction to the lattice constants and band structure have been considered self-consistently and the chemical potential is determined by the charge neutrality condition. With these bulk and surface MLWF hopping parameters, we use an iterative method 23,24 to obtain the surface Green's function of the semi-infinite system. The imaginary part of the surface Green's function is the local density of states (LDOS), from which we can obtain the dispersion of the surface states.…”

Section: Topological Surface Statesmentioning

confidence: 99%

Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface

et al. 2009

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Topological insulators are new states of quantum matter in which surface states residing in the bulk insulating gap of such systems are protected by time-reversal symmetry. The study of such states was originally inspired by the robustness to scattering of conducting edge states in quantum Hall systems. Recently, such analogies have resulted in the discovery of topologically protected states in two-dimensional and three-dimensional band insulators with large spin-orbit coupling. So far, the only known three-dimensional topological insulator is Bi R ecently, the subject of time-reversal-invariant topological insulators has attracted great attention in condensed-matter physics [1][2][3][4][5][6][7][8][9][10][11][12] . Topological insulators in two or three dimensions have insulating energy gaps in the bulk, and gapless edge or surface states on the sample boundary that are protected by time-reversal symmetry. The surface states of a three-dimensional (3D) topological insulator consist of an odd number of massless Dirac cones, with a single Dirac cone being the simplest case. The existence of an odd number of massless Dirac cones on the surface is ensured by the Z 2 topological invariant 7-9 of the bulk. Furthermore, owing to the Kramers theorem, no time-reversalinvariant perturbation can open up an insulating gap at the Dirac point on the surface. However, a topological insulator can become fully insulating both in the bulk and on the surface if a timereversal-breaking perturbation is introduced on the surface. In this case, the electromagnetic response of three-dimensional (3D) topological insulators is described by the topological θ term of the form S θ = (θ /2π)(α/2π) d 3 x dt E · B, where E and B are the conventional electromagnetic fields and α is the fine-structure constant 10 . θ = 0 describes a conventional insulator, whereas θ = π describes topological insulators. Such a physically measurable and topologically non-trivial response originates from the odd number of Dirac fermions on the surface of a topological insulator.Soon after the theoretical prediction 5 , the 2D topological insulator exhibiting the quantum spin Hall effect was experimentally observed in HgTe quantum wells 6 . The electronic states of the 2D HgTe quantum wells are well described by a 2 + 1-dimensional Dirac equation where the mass term is continuously tunable by the thickness of the quantum well. Beyond a critical thickness, the Dirac mass term of the 2D quantum well changes sign from being positive to negative, and a pair of gapless helical edge states appears inside the bulk energy gap. This microscopic mechanism for obtaining topological insulators by inverting the bulk Dirac gap spectrum can also be generalized to other 2D and 3D systems. The guiding principle is to search for insulators where the

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Section: Topological Surface Statesmentioning

confidence: 99%

Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface

et al. 2009

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“…The surface band structures are calculated in an semiinfinite geometry by using the recursive Green's function method [67] based on the previous tight-binding model.…”

Section: Z2 Invariant Protected By G * Tmentioning

confidence: 99%

Topological semimetals with helicoid surface states

et al. 2016

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Riemann surfaces are geometric constructions in complex analysis that may represent multi-valued holomorphic functions using multiple sheets of the complex plane. We show that the energy dispersion of surface states in topological semimetals can be represented by Riemann surfaces generated by holomorphic functions in the two-dimensional momentum space, whose constant height contours correspond to Fermi arcs. This correspondence is demonstrated in the recently discovered Weyl semimetals and leads us to predict new types of topological semimetals, whose surface states are represented by double-and quad-helicoid Riemann surfaces. The intersection of multiple helicoids, or the branch cut of the generating function, appears on high-symmetry lines in the surface Brillouin zone, where surface states are guaranteed to be doubly degenerate by a glide reflection symmetry. We predict the heterostructure superlattice [(SrIrO3)2(CaIrO3)2] to be a topological semimetal with double-helicoid Riemann surface states.Introduction The study of topological semimetals [1] has seen rapid progress since the theoretical proposal of a three-dimensional Weyl semimetal in a magnetic phase of pyrochlore iridates [2]. In general, topological semimetals are materials where the conduction and the valence bands cross in the Brillouin zone and the crossing cannot be removed by perturbations preserving certain crystalline symmetry such as the lattice translation. Bloch states in the vicinity of the band crossing possess a nonzero topological index, e.g., the Chern number in case of Weyl semimetals. The nontrivial topology gives rise to anomalous bulk properties of topological semimetals such as the chiral anomaly [3][4][5]. Several classes of topological semimetals have been theoretically proposed so far, including Weyl, [2,[6][7][8][9][10][11][12][13], Dirac [14][15][16][17] and nodal line semimetals [7,[17][18][19][20][21][22][23][24][25][26][27][28][29][30], some among which have been experimentally observed [31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47].Surface states of topological semimetals have attracted much attention. On the surface of a Weyl semimetal, the Fermi surface consists of open arcs connecting the projection of bulk Weyl points onto the surface Brillouin zone [2], instead of closed loops. The presence of Fermi arcs on the surface is a remarkable property that directly reflects the nontrivial topology of the bulk, and plays a key role in the experimental identification of Weyl semimetals [32,33,36]. In contrast, as shown by recent theoretical works [18,21,23,24,28,48,49], existing Dirac and nodal line semimetals do not have robust Fermi arcs that are stable against symmetry-allowed perturbations. Therefore, the general condition for protected Fermi arcs and their existence in topological semimetals beyond Weyl remain open questions.In this work, we report the discovery of a new topological semimetal phase in a wide variety of nonsymmorphic crystal structures with the glide reflection sym-

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“…To figure out the band topology of each phase, we employ the direct computation method of the Z 2 invariant on a lattice Brillouin zone (BZ) which is based on the recent development in the lattice gauge theory (23,24). Also, we examine the edge state dispersion from the edge Green's functions (25,26) and it is found to be consistent with the Z 2 invariants of the 2D bands. …”

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confidence: 99%

Topological quantum phase transitions driven by external electric fields in Sb ₂ Te ₃ thin films

Kim

et al. 2011

Proc. Natl. Acad. Sci. U.S.A.

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Using first-principles calculations, we show that topological quantum phase transitions are driven by external electric fields in thin films of Sb 2 Te 3 . The film, as the applied electric field normal to its surface increases, is transformed from a normal insulator to a topological insulator or vice versa depending on the film thickness. We identify the band topology by directly calculating the Z 2 invariant from electronic wave functions. The dispersion of edge states is also found to be consistent with the bulk band topology in view of the bulk-boundary correspondence. We present possible applications of the topological phase transition as an on/off switch of the topologically protected edge states in nano-scale devices.density functional theory | topological edge state T he concept of the topological order in condensed matter physics has provided a new perspective to the understanding of the origin of different phases and the exact quantization of Hall conductance in the quantum Hall effect (1, 2). Recently, nontrivial topological orders have been predicted theoretically and confirmed experimentally in both two-dimensional (2D) and threedimensional (3D) systems with the time-reversal invariance (3-11). These topologically nontrivial systems, called topological insulators (TIs), have intriguing properties that they develop robust conducting edge or surface states on the boundary with normal insulators (NIs) or vacuum following the bulk-boundary correspondence rule (12). These characteristic boundary states have a topological origin and are potentially useful for the design of nano-scale devices in spintronics or quantum computations.Manifestation of the nontrivial topology of occupied bands in a TI is attributed to the band inversion between occupied and unoccupied bands by large enough spin-orbit coupling (13). If the strength of the spin-orbit coupling should be reduced, the band topology would recover a trivial configuration via gap closing (14). Thus, modifying the spin-orbit strength can be a method to control the topology and induce a quantum phase transition between TI and NI phases. The band topology of a physical system may also be changed, for example, by adjusting lattice constants or internal atomic positions (15, 16). Based on this mechanism, a strain-induced topological phase transition can be driven if the original system is close to the phase boundary. In the case of 2D TIs (i.e., quantum spin Hall systems), still another factor affecting the band topology is an electrostatic scalar potential or an external electric field as an effective continuous model predicts that potential difference between upper and lower surfaces can transform topologically nontrivial thin films of Bi 2 Se 3 into topologically trivial ones (17,18). Actually, a model calculation shows that external electric fields can drive the quantum phase transition between TIs and NIs in HgTe quantum wells (19). It has been predicted that thin films of tetradymite semiconductors recently found to be 3D strong topological insulators...

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Highly convergent schemes for the calculation of bulk and surface Green functions

Cited by 1,815 publications

References 17 publications

Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface

Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface

Topological semimetals with helicoid surface states

Topological quantum phase transitions driven by external electric fields in Sb ₂ Te ₃ thin films

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Highly convergent schemes for the calculation of bulk and surface Green functions

Cited by 1,815 publications

References 17 publications

Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface

Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface

Topological semimetals with helicoid surface states

Topological quantum phase transitions driven by external electric fields in Sb 2 Te 3 thin films

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Topological quantum phase transitions driven by external electric fields in Sb ₂ Te ₃ thin films