Electronic Structure of A IV B VI · m A 2 V B 3 VI (A IV = Ge,Sn,Pb; A V = Bi,Sb; B VI = Te,Se; m=1-3) Topological Insulators S.V. Eremeev, T.V. Menshchikova, Yu.M. Koroteev, E.V. Chulkov

Outline 1- Introduction to topological insulators 2- Motivation 3- New family of ternary topological insulators 4- Summary and conclusions

Introduction Topological insulators are one of the materials of the moment. In these unusual substances, the bulk behaves like an insulator, whereas the surface acts like a conductor. In addition to a host of practical applications, topological insulators are particularly important because they enable scientists to investigate a plethora of exotic states. Electrons in topological insulators are able to flow only at the edges of the material, not in the bulk. NPG Asia Materials featured highlight doi: /asiamat

Introduction ✔ Classification of materials according to band theory, ✔ But the quantum world can present more complex materials like, * Superconductors * Magnetic Materials * Topological Insulators EFEF Metals l Semi-metals l Insulators l E(k) k

Introduction

- Insulating bulk but metallic surface due to strong spin-orbit interaction. - Unique surface state that make surface conducting, with linear dispersion forming a Dirac Cone with a crossing point at the Fermi level. - Helical spin structure with the spin of the electron perpendicular to its momentum. Exotic properties - Electrons in this surface state are protected against scattering. - Very promising for spintronics or quantum computing applications.

Discovery of TI and motivation 1 st Generation : HgTe Q. Wells (2D), Bi x Sb 1-x (3D) Bernevig et al. Science 314(2006), Koenig et al. Science 318(2007), Fu and Kane PRB 76(2007), Hsieh et al. Nature 452(2008) 2 nd Generation: Bi 2 Se 3, Bi 2 Te 3, Sb 2 Te 3 3D crystals Zhang et al. Nat. Phys. 5(2009), Xiao et al. Nat. Phys. 5(2009), Chen et al. Science 325(2009) 3 rd Generation: Ternary Bi 2 Se 3 - and Bi 2 Te 3 -based compounds (Bi 2 Te 2 Se, PbBi 2 Te 4 …), Heusler Compounds (Li 2 AgSb, NdPtBi…), Tl-based Bi chalcogenides (TlBiSe 2, TlBiTe 2 ), antiperovskite nitride (M) 3 BiN (M = Ca, Sr, Ba), honeycomb-lattice chalcogenides LiAgSe and NaAgSe, Pyrochlores…

Discovery of TI and motivation 2 nd Generation: Bi 2 Se 3, Bi 2 Te 3, Sb 2 Te 3 3D crystals Zhang et al. Nat. Phys. 5(2009), Chen et al. Science 325(2009)

Discovery of TI and motivation Why look for more Topological Insulators??? - Bi 2 Se 3 Dirac Point is close to the Bulk Valence Band maximum  scattering channels (S. Kim et al, PRL 107, (2011)) - hexagonal warping of the Dirac cone: - more accurate quasi-particle GW approach reveals several cases where DFT identifications of TI phases are false Intrapair scatterings in (a) and (b) are forbidden by timereversal symmetry. But interpair scatterings in (b), for example, those between k2 and k3, are allowed. ( L.Fu, PRL 103, (2009) ) J. Vidal et al, PRB 84, (R) (2011)

A IV B VI · m A 2 V B 3 VI (A IV = Ge,Sn,Pb; A V = Bi,Sb; B VI = Te,Se; m=1-3) ternary compounds In this work the electronic structure of A IV B VI · m A 2 V B 3 VI (A IV = Ge,Sn,Pb; A V = Bi,Sb; B VI = Te,Se; m=1-3) series of ternary compounds are analyzed. The electronic structure was calculated in the density functional theory formalism as implemented in VASP. Like A 2 V B 3 VI these compounds have layered structure with ionic-covalent bonding within layers and van der Waals gaps between them, but unlike the parent compounds with simple quintuple layers structure, the structure of the ternary compounds contains alternating in various sequences quintuple and septuple layers. Peculiarities of bulk spectrum of these more complex materials give rise to more complicated surface band structure that depends on surface termination, which can be quintuple- or septuple-layer terminated. We predict the existence of exotic buried topological surface states which are characterized by a deep subsurface localization and Dirac states with the Dirac point in the valence band gap. Beside the Dirac cone states, which are peculiar to topological insulators, unoccupied Rashba-type spin-split state and occupied surface states can reside in these systems. We analyze dispersion and spatial charge density localization of the surface states. We also performed a layer-by-layer analysis of the spin distribution in the surface states.

Classification of topological phases Three-dimensional materials with inversion symmetry are classified with four Z 2 topological invariants 0 ; ( 1, 2, 3 ), which can be determined by the parity  m (  i )=±1 of occupied bands at eight time-reversal invariant momenta (TRIM)  i =(n 1,n 2,n 3 ) = (n 1 b 2 + n 2 b 2 + n 3 b 3 )/2, where b 1, b 2, b 3 are primitive reciprocal lattice vectors, and n j = 0 or 1 [1, 2]. The Z 2 invariants are determined by the equations andwhere For rhombohedral lattice the TRIMs are ,Z, and three equivalent L and F points. 0 =1 characterize a strong topological insulators. [1] L. Fu, C.L. Kane, and E.J. Mele, Phys. Rev. Lett. 98, (2007). [2] L. Fu, and C.L. Kane, Phys. Rev. B 76, (2007).

Planar Perp. The topological number 0 for n A IV B VI · m A 2 V B 3 VI (n=1; m=1–3) compounds based on Bi 2 Te 3, Sb 2 Te 3 and Bi 2 Se 3 parent phases mBi 2 Te 3 0 Sb 2 Te 3 0 Bi 2 Se 3 0 1GeBi 2 Te 4 1GeSb 2 Te 4 1 SnBi 2 Te 4 1SnSb 2 Te 4 1SnBi 2 Se 4 0 PbBi 2 Te 4 1PbSb 2 Te 4 1PbBi 2 Se 4 1 2GeBi 4 Te 7 1GeSb 4 Te 7 1 SnBi 4 Te 7 1SnSb 4 Te 7 1 PbBi 4 Te 7 1PbSb 4 Te 7 1PbBi 4 Se 7 1 3GeBi 6 Te 10 1GeSb 6 Te 10 0 SnBi 6 Te 10 1 PbBi 6 Te 10 1

Crystal Structure of PBT compounds

parent compound Bi 2 Te 3 SOC-induced band inversion marked by green ellipse

surface band structure of Bi 2 Te 3 and spatial charge density distribution of the Dirac state parent compound Bi 2 Te 3 layer-resolved spin structure NATURE 460, 1101 (2009).

SOC-induced band-gap inversion in PbBi 2 Te 4 Bulk band structure of PBT compounds More complicated band structure in PbBi 4 Te 7

Surface band structure of PbBi 2 Te 4 Layer-resolved spin structure of the Dirac state in the topmost 7L block of PbBi 2 Te 4, given by spin projections Sx, Sy, and Sz at 30 and 90 meV above DP. counter-clockwise spin rotation in the topmost Te atom

Surface band structure of n A IV B VI · m A 2 V B 3 VI (n=1; m=1)

Surface band structure of 7L-terminated PbBi 4 Te 7 (0001) counter-clockwise spin rotation in the topmost Te atom The character of p states changes from dominating p y and p z in all subsurface layers to p x in the topmost Te layer which can change the spin-orbit interaction and reverse the spin orientation.

Surface band structure of 5L-terminated PbBi 4 Te 7 (0001) Charge density distribution of the occupied and unoccupied surface states integrated over xy planes

Surface band structure of 5L-terminated PbBi 4 Te 7 (0001) Spin projections for occupied SS Layer-resolved spin structure of the Dirac state at 5L-term PbBi 4 Te 7 (0001) at 100 meV.

Surface band structure of n A IV B VI · m A 2 V B 3 VI (n=1; m=2)

Surface band structure of 7L-terminated and 5L-terminated PbBi 6 Te 10 (0001)

PbBi 6 Te 10 (0001) with two 5L blocks on the top

Summary and conclusions — We have shown that, in the homologous series of ternary compounds based on Bi 2 Te 3, Bi 2 Se 3 and Sb 2 Te 3, most of the compounds A IV B VI · m A 2 V B 3 VI (A IV = Ge,Sn,Pb; A V = Bi,Sb; B VI = Te,Se; m=1-3) are 3D topological insulators. — Part of these systems (m = 2,3) represent naturally grown superlattices composed of 5L and 7L blocks, which demonstrate much richer physics than the parent TIs. — More complex surface electronic and spin structures, originating from peculiarities of the bulk spectrum of these materials, provides an efficient way to manipulate both the spin structure and the spatial localization of the conducting state. This subsequently may allow for a variation of the depth of the spin transport channel below the surface. References: С.В. Еремеев и др., Письма в ЖЭТФ, т. 92, с. 183 (2010), S.V. Eremeev et al., Nature Comm. 3:635, DOI: /ncomms1638 (2012), Kuroda et al. PRL (under reviewing)

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Prospective devices Structure of proposed memory cell, based on a TI block with a magnetically doped surface. A bit is stored by the perpendicular magnetization of the surface. T. Fujita et al., Applied Physics Express 4 (2011) Gate-tuned normal and superconducting transport at the surface of a topological insulator B. Sacepe et al., Nat. Comm (2011)