Electronic band structure of pseudo-binary AlB 2 -like hexagonal silicides SrNi x Si 2  x as novel low-T C superconductors I.R. Shein, A.L. Ivanovskii n Institute of Solid State Chemistry, Ural Branch of the Russian Academy of Sciences, 620990 Ekaterinburg, Russia article info Article history: Received 16 July 2012 Accepted 16 August 2012 Available online 5 September 2012 Keywords: Ni-doped SrSi 2 Electronic band structure Ab initio calculations abstract The very recently discovered pseudo-binary hexagonal silicide SrNi x Si 2x , which exhibits low-T C superconductivity, was examined theoretically to understand the effect of the unusual doping type (partial replacement of Si by Ni) on the electronic band structure of this material. Besides, the possible factors of the stabilization of the hexagonal AlB 2 -type structure of SrSi 2 upon substitution of Ni for Si, and the solubility limit of Ni in SrNi x Si 2 x are discussed in terms of competing Si–Si, Si–Ni, and Ni–Ni bonds. & 2012 Elsevier B.V. All rights reserved. 1. Introduction The phenomenon of the emergence of superconductivity near the lattice instability border is now widely used for search of novel superconducting materials, and the systems which exhibit rich polymorphism attract tremendous attention. These systems include binary disilicides of alkaline-earth metals (Ca,Sr,Ba)Si 2 , for which up to six polymorphs were found, see for example Refs. [1–3] and References therein. Some of these binaries are superconducting, see the review [4]. Besides, for these silicides the non-conventional AlB 2 -like phase may be stabilized by partial replacement of Si by sp metals (Al or Ga); in turn, for pseudo- binary silicides Sr(Al,Ge) x Si 2 x , superconducting transitions (with T C to 5.1 K) were also found [5–7]. Very recently (2012, [8]), novel pseudo-binary hexagonal silicides SrNi x Si 2 x (0.1 ox o0.7) were prepared by arc-melting, and superconductivity with T C to 2.6 K was detected. The most intriguing feature of these novel materials is the role of Ni which acts as a non-magnetic dopant, stabilizing the AlB 2 -like phase and simultaneously promoting the emergence of superconductivity for SrNi x Si 2 x . As far as we know, no data about the peculiarities of the electronic properties of Ni-doped SrSi 2 were available till now. In view of these circumstances, we present here first- principles FLAPW-GGA calculations of a series of pseudo-binary hexagonal SrNi x Si 2 x in order to understand the effect of the unusual doping type (partial replacement of Si by Ni) on the electronic band structure of these novel low-T C superconductors. 2. Models and computational aspects At the first step we considered the hexagonal (AlB 2 -like, space group P6/mmm) disilicide SrSi 2 . The lattice contains close-packed Sr layers alternating with graphene-like Si sheets in the sequence ..AHAHAH.. perpendicularly to the c direction, as depicted in Fig. 1. For SrNi x Si 2 x , we used the model of the periodic 12-atomic supercell 2  2  1 in the structure of hexagonal disilicide SrSi 2 . Then, replacing silicon atoms (in the cell) consistently by one, two or three Ni atoms, a series of pseudo-binary silicides SrNi x Si 2 x , where x ¼ 0.125, 0.25, and 0.375, was simulated. Moreover, in the example of SrNi 0.25 Si 1.75 , we probed the effect of Ni/Si atomic distributions on the stability of this pseudo-binary silicide (variants 2–4, Fig. 1) and its possible magnetization as a result of ‘‘clustering’’ of Ni impurities in this matrix. Our calculations were performed by means of the full- potential method within mixed basis APWþ lo (FLAPW) imple- mented in the WIEN2k suite of programs [9]. The generalized gradient correction (GGA) to exchange-correlation potential in the PBE form [10] was used. The basis set inside each muffin tin (MT) sphere was split into core and valence subsets. The core states were treated within the spherical part of the potential only, and were assumed to have a spherically symmetric charge density in MT spheres. The valence part was treated with the potential expanded into spherical harmonics to l ¼ 4. The valence wave functions inside the spheres were expanded to l ¼ 12. The plane-wave expansion was taken to R MT  K MAX equal to 7, and the k sampling with 8  8  13 k-points in the Brillouin zone was used. The densities of states (DOSs) were obtained by the modified tetrahedron method [11]. Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/physb Physica B 0921-4526/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physb.2012.08.020 n Corresponding author. Tel.: þ7 3433745331; fax: þ7 343 3744495. E-mail address: ivanovskii@ihim.uran.ru (A.L. Ivanovskii). Physica B 407 (2012) 4592–4594