Resonant scattering at the atomic absorbates in graphene was investigated recently in relation with the transport and gap opening problems. Attaching an impurity atom to graphene is believed to lead to the creation of unusual zero energy localized el
ectron states. This paper aims to describe the behavior of the localized impurity-induced levels in graphene in a quantizing magnetic field. It is shown that in the magnetic field the impurity level effectively hybridizes with one of the n=0 Landau level states and splits into two opposite-energy states. The new hybridized state is doubly occupied, forming a spin-singlet and reducing the polarization of a Quantum Hall ferromagnet in undoped graphene. Taking into account the electron-electron interaction changes radically the spectrum of the electrons surrounding the impurity, which should be seen experimentally. While existing publications investigate graphene uniformly covered by adatoms, here we address a possibly even more experimentally relevant case of the clusterized impurity distribution. The limit of a dense bunch of the impurity atoms is considered, and it is shown, how such a bunch changes the spectrum and spin polarization of a large dense electron droplet surrounding it. The droplet is encircled by an edge state carrying a persistent current.
The Wigner-crystal phase of two-dimensional electrons interacting via the Coulomb repulsion and subject to a strong Rashba spin-orbit coupling is investigated. For low enough electronic densities the spin-orbit band splitting can be larger than the z
ero-point energy of the lattice vibrations. Then the degeneracy of the lower subband results in a spontaneous symmetry breaking of the vibrational ground state. The $60^{circ}-$rotational symmetry of the triangular (spin-orbit coupling free) structure is lost, and the unit cell of the new lattice contains two electrons. Breaking the rotational symmetry also leads to a (slight) squeezing of the underlying triangular lattice.
We investigate the spin and charge densities of surface states of the three-dimensional topological insulator $Bi_2Se_3$, starting from the continuum description of the material [Zhang {em et al.}, Nat. Phys. 5, 438 (2009)]. The spin structure on sur
faces other than the 111 surface has additional complexity because of a misalignment of the contributions coming from the two sublattices of the crystal. For these surfaces we expect new features to be seen in the spin-resolved ARPES experiments, caused by a non-helical spin-polarization of electrons at the individual sublattices as well as by the interference of the electron waves emitted coherently from two sublattices. We also show that the position of the Dirac crossing in spectrum of surface states depends on the orientation of the interface. This leads to contact potentials and surface charge redistribution at edges between different facets of the crystal.
The phenomenon of mesoscopic Spin-Hall effect reveals in a nonequilibrium spin accumulation (driven by electric current) at the edges of a ballistic conductor or, more generally, in the regions with varying electron density. In this paper we review o
ur recent results on spin accumulation in ballistic two-dimensional semiconductor heterostructures with Rashba/Dresselhaus spin orbit interactions, and extend the method developed previously to predict the existince of spin-Hall effect on the surface of three-dimensional topological insulators. The major difference of the new Spin-Hall effect is its magnitude, which is predicted to be much stronger than in semiconductor heterostructures. This happens because in semiconductors the spin accumulation appears due to a small spin-orbit interaction, while the spin-orbit constitutes a leading term in the Hamiltonian of topological insulator.
