New generation of two-dimensional spintronic systems realized by coupling of Rashba and Dirac fermions

www.nature.com/scientificreports OPEN received: 08 April 2015 accepted: 08 July 2015 Published: 04 August 2015 New generation of twodimensional spintronic systems realized by coupling of Rashba and Dirac fermions Sergey V. Eremeev1,2,3,4, Stepan S. Tsirkin2,3,4, Ilya A. Nechaev2,3, Pedro M. Echenique3,5,6 & Evgueni V. Chulkov2,3,4,5,6 Intriguing phenomena and novel physics predicted for two-dimensional (2D) systems formed by electrons in Dirac or Rashba states motivate an active search for new materials or combinations of the already revealed ones. Being very promising ingredients in themselves, interplaying Dirac and Rashba systems can provide a base for next generation of spintronics devices, to a considerable extent, by mixing their striking properties or by improving technically significant characteristics of each other. Here, we demonstrate that in BiTeI@PbSb2Te4 composed of a BiTeI trilayer on top of the topological insulator (TI) PbSb2Te4 weakly- and strongly-coupled Dirac-Rashba hybrid systems are realized. The coupling strength depends on both interface hexagonal stacking and trilayer-stacking order. The weakly-coupled system can serve as a prototype to examine, e.g., plasmonic excitations, frictional drag, spin-polarized transport, and charge-spin separation effect in multilayer helical metals. In the strongly-coupled regime, within ~100 meV energy interval of the bulk TI projected bandgap a helical state substituting for the TI surface state appears. This new state is characterized by a larger momentum, similar velocity, and strong localization within BiTeI. We anticipate that our findings pave the way for designing a new type of spintronics devices based on Rashba-Dirac coupled systems. Over the past few years, great attention is paid to 2D electron systems that hold helical (spin-momentum locked) electron states induced by spin-orbit interaction (SOI), such as giant-Rashba-split states or topological Dirac states1–5. Suitable Dirac systems are already routinely observed on surfaces of three-dimensional topological insulators. The main concern here is that the corresponding 2D backscattering-protected helical states are desirable to be energetically and spatially well separated from TI bulk states. It is seen as a way to refine on their remarkable characteristics, be it, e.g., the helical spin-polarized transport6–12 or the Dirac plasmon, which carry spin13,14 and, consequently, may lead to charge-spin separation effects expected for thin (about 100 nm) films of a TI15. Until recently, Rashba systems, which were mainly associated with 2D electron gases of semiconductor heterostructures and as such were extensively studied, e.g., in the context of spin-polarized transport, are inferior to Dirac systems, first and foremost, because of the very small magnitude of the SOI term. Now, the semiconductors BiTeX (with X =  Cl, Br, I) came into focus, because of the sizeable Rashba-type 1 Institute of Strength Physics and Materials Science, 634021, Tomsk, Russia. 2Tomsk State University, 634050, Tomsk, Russia. 3Donostia International Physics Center (DIPC), 20018 San Sebastián/Donostia, Basque Country, Spain. 4Saint Petersburg State University, Saint Petersburg, 198504, Russia. 5Departamento de Física de Materiales UPV/EHU, Facultad de Ciencias Químicas, UPV/EHU, Apdo. 1072, 20080 Sebastián/Donostia, Basque Country, Spain. 6Centro de Física de Materiales CFM - MPC, Centro Mixto CSIC-UPV/EHU, 20080 San Sebastián/ Donostia, Basque Country, Spain. Correspondence and requests for materials should be addressed to S.V.E. (email: ) Scientific Reports | 5:12819 | DOI: 10.1038/srep12819 1 www.nature.com/scientificreports/ Figure 1. Spin-resolved electronic structure (red and blue colors denote positive and negative values of in-plane spin, respectively, for mutually perpendicular Γ − M and Γ − K directions) of (a) freestanding BiTeI trilayer (TL); (b) PbSb2Te4 surface; (c) the system of BiTeI TL at distance of ≈ 7 Å above the PbSb2Te4 surface modeled by a six septuple-layer (SL) slab. Projected bulk band structure of PbSb2Te4 marked by brown areas. spin splitting of their bulk and surface states4,5,16–20, arising from a strong SOI and the material polarity. In this case, the SOI term is not a weak perturbation with respect to the band kinetic energy anymore. A promising combination of the 2D Rashba system formed by surface-state electrons of the BiTeX surface and the graphene Dirac system has been theoretically proposed in Ref. [21], though in this case original graphene Dirac state has no spin-momentum locking. To involve 2D helical Dirac states, one should treat a semi-infinite TI or a TI film as thick as about 10 its structure elements. Thus, we have a situation, when both desired Rashba and Dirac electron systems are provided by surfaces. However, in contrast to 2D spin-helical Dirac fermions, the 2D Rashba-fermion system with giant spin-orbit splitting can be represented merely by a structure element of BiTeX. Owing to three-layered (TL) structure of these compounds with the X-Bi-Te stacking within the TL, an ultrathin film of one-TL thickness can be exfoliated from the bulk crystal or grown epitaxially on suitable substrate. Among BiTeX, it is BiTeI, which provides us with the biggest Rashba interaction strength αR ≈  1.6 eVÅ, as calculated within density functional theory (DFT) (see details in Supplementary Section S1) for the conduction band of a single TL possessing the band gap of 750 meV [see Fig. 1(a)]. Such a strength is half as much as compared to the Te-terminated surface state of BiTeI, but it is still an order of magnitude greater than that in the conventional semiconducting heterostructures. A desired interplay of Dirac and Rashba fermions can thus be realized by depositing a BiTeI TL on top of a TI. The most geometrically suitable TI in this case is PbSb2Te422, whose in-plane hexagonal parameter matches perfectly with the parameter of BiTeI. This TI has a 220 meV calculated indirect band gap hosting the spin-helical Dirac surface state [see Fig. 1(b)]. As seen in Fig. 1(c) showing the electronic spectrum of a system composed of non-interacting TL and TI, energetically we have the fortunate alignment of the Dirac and Rashba bands within the projected band gap of the bulk PbSb2Te4; the degeneracy point of the Rashba state lies just a few meV above the Dirac point. Regarding the helicity of the Rashba and Dirac states, in the upper Dirac cone and in the outer Rashba branch the spin locked to the momentum can be in-plane polarized in the same or opposite directions, depending on how the TL is oriented relative to the TI. In that sense, we have two TI-TL interfaces: Te-I (hereafter marked as TII) with the same directions [as shown in Fig. 1(c)] and Te-Te (below we refer to it as to TTI) with the opposite directions. Thus, one can expect that the interacting picture should vary with the type of interface. In order to treat the TI-TL interaction properl (...truncated)