Quantum states and linear response in dc and electromagnetic fields for the charge current and spin polarization of electrons at the Bi/Si interface with the giant spin-orbit coupling

Abstract

An expansion of the nearly free-electron model constructed by Frantzeskakis, Pons and Grioni [Phys. Rev. B 82, 085440 (2010)] describing quantum states at Bi/Si(111) interface with giant spinorbit coupling is developed and applied for the band structure and spin polarization calculation, as well as for the linear response analysis for charge current and induced spin caused by dc field and by electromagnetic radiation. It is found that the large spin-orbit coupling in this system may allow resolving the spin-dependent properties even at room temperature and at realistic collision rate. The geometry of the atomic lattice combined with spin-orbit coupling leads to an anisotropic response both for current and spin components related to the orientation of the external field. The in-plane dc electric field produces only the in-plane components of spin in the sample while both the in-plane and out-of-plane spin components can be excited by normally propagating electromagnetic wave with different polarizations.

Edge States and Topological Properties of Electrons on the Bismuth on Silicon Surface With Giant Spin-Orbit Coupling

“…Our model for the 1D edge states is based on the 2D NFE model for the bulk states of 2DEG formed at the interface of the trimer Bi/Si(111) structure [46] developed for the description of the spectrum near the M-point of the BZ, and later extended for the modeling of the electron states in the whole BZ. [47] This model was compared with its expansion containing the anisotropic terms in the NFE model as well as with an empirical tightbinding model. [46] While the details of band structure and the quality of reproduction of experimental ARPES data on energy bands in Bi/Si vary from model to model, the simple NFE model allows to reconstruct the main properties of spin split bands including the magnitude of splitting, the energy gap, and the spin polarization.…”

“…, Γ 6 in the hexagonal lattice is shown in Fig.1a. In the model originally proposed [46] only the vectors G 1 , G 2 , G 6 were included in order to described the states near the M point, and later we expanded this model [47] with vectors G 3 , G 4 , G 5 for the description of the states in the whole BZ. The parameters of the hexagonal lattice in Fig.1a are ΓM = 0.54Å −1 and ΓK = 0.62…”

“…The parameters of both the H 0 and V are fitted as to provide the best correspondence between the model and the structure of the bands near the Fermi level experimentally known from ARPES measurements. [42][43][44]46] The typical values [46,47] are m = 0.8m 0 , α R = 1.1 eV • Å and V i = V 0 = 0.3 eV, although they should be treated as fitting parameters rather than measured material constants, and in the present paper we shall consider their variations in the range of 0.3 . .…”

“…This material is characterized by a giant SOC splitting which was predicted or observed experimentally also in a number of metal films or the combined materials of the "metal on semiconductor" type, [40][41][42][43][44][45][46] and recently described theoretically. [46,47] Its huge spin splitting together with the hexagonal type of the lattice creates a certain potential of manifestation of the TI properties, since the spin-resolved bands may evolve into spin-resolved edge states, and the hexagonal type of the lattice is favorable for the TI to exist. [28] The properties of 2DEG at the Bi/Si interface have been studied experimentally with the help of angleresolved photoemission spectroscopy (ARPES) [40-44, 46, 48-50] applied also to other materials.…”

“…[66] One can mention also new types of triple bulk compounds with strong SOC like GeBi 2 Te 4 , [67] BiTeI or other bismuth tellurohalides, [68][69][70] or recently discussed Bi 14 Rh 3 I 9 material. [71] In the present paper we adopt the nearly-free model of two-dimensional bulk states in Bi/Si developed earlier [46] and applied in the extended form in our previous pa-per for the description of spin polarization, charge conductance and optical properties of this promising material [47] for the calculation of the 1D edge states of the electrons on the Bi/Si interface in the finite strip geometry. We obtain both the explicit form of the edge wavefunctions and the edge energy spectrum, calculate their spin polarization, and link the possible topological stability of their properties to the Z 2 topological invariant studied by the analysis of the time reversal matrix elements behavior in the Brillouin zone.…”