**Abstract:**

In the first part of the presentation we will discuss electron spin control in fluorinated graphene [1]. The spin-orbit interactions in pristine graphene are excluded due to high symmetry of the crystal structure [2]. The symmetry may be lifted by e.g. adatoms. In particular a fluorine adatom breaks the symmetry introducing a local spin-orbit Rashba interaction [3]. Using tight-binding Hamiltonian [4] which describes spin-orbit coupling near fluorine adatoms in a dilute concentration we show that spin inversion in fluorinated graphene nanoribbons is possible. The spin of the electron moving near the adatom is subject to the effective Rashba internal magnetic field. As the result of the electron passage near the adatom the spin undergoes a precession by a small angle. If external magnetic field is absent the electron backscattering cancels the local spin precession effects.

In the second part we will present our recent studies of the spin control in the silicene nanoribbons. Silicene belongs to the class of two-dimensional topological insulators due to the quantum spin Hall (QSH) phase, that occurs for Fermi energies close to the charge neutrality point. In our studies we propose double-slit electron interferometer in silicene that can be used in detection whether electron transport is normal or reveals topological-insulating character [5]. In our calculations we use tight-binding model with Hamiltonian [6] for pristine silicene along with the wave function matching method applied to the scattering matrix. We show that in dependence of increasing external magnetic field amplitude, the topological transport is characterized by sharp peaks in conductance, however, the normal state transport can be distingished by smooth Aharanov-Bohm oscillations.

This work was supported by the National Science Centre (NCN) according to decision No. DEC-2015/17/B/ST3/01161.

**References:**

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[2] A. Manchon, H.C. Koo, J. Nitta, S.M. Frolov, R.A. Duine, Nature Materials 14, 871. (2015)

[3] E.A. Laird, F. Kuemmeth, G. Steele, K. Grove-Rasmussen, J. Nygård, K. Flensberg, L.P. Kouwenhoven, Rev. Mod. Phys. 87, 703 (2015).

[4] S. Irmer, T. Frank, S. Putz, M. Gmitra, D.Kochan, and J. Fabian, Phys. Rev. B 91, 115141 (2015).

[5] B. Rzeszotarski, A. Mrenca-Kolasinska, and B. Szafran, Phys. Rev. B 99, 165426 (2019).

[6] C.-C. Liu, H. Jiang, and Y. Yao, Phys. Rev. B 84, 195430 (2011)