Topological insulators are characterized by Dirac-cone surface states with electron spins locked perpendicular to their linear momenta. Recent theoretical and experimental work implied that this specific spin texture should enable control of photoelectron spins by circularly polarized light. However, these reports questioned the so far accepted interpretation of spin-resolved photoelectron spectroscopy. We solve this puzzle and show that vacuum ultraviolet photons (50-70 eV) with linear or circular polarization indeed probe the initial-state spin texture of Bi 2 Se 3 while circularly polarized 6-eV low-energy photons flip the electron spins out of plane and reverse their spin polarization, with its sign determined by the light helicity. Our photoemission calculations, taking into account the interplay between the varying probing depth, dipole-selection rules, and spin-dependent scattering effects involving initial and final states, explain these findings and reveal proper conditions for light-induced spin manipulation. Our results pave the way for future applications of topological insulators in optospintronic devices.

Three-dimensional topological insulators (TIs) are characterized by spin-polarized Dirac-cone surface states that are protected from backscattering by time-reversal symmetry. Control of the spin polarization of topological surface states (TSSs) using femtosecond light pulses opens novel perspectives for the generation and manipulation of dissipationless surface spin currents on ultrafast timescales. Using time-, spin-, and angle-resolved spectroscopy, we directly monitor for the first time the ultrafast response of the spin polarization of photoexcited TSSs to circularly-polarized femtosecond pulses of infrared light. We achieve all-optical switching of the transient out-of-plane spin polarization, which relaxes in about 1.2 ps. Our observations establish the feasibility of ultrafast optical control of spin-polarized Dirac fermions in TIs and pave the way for novel optospintronic applications at ultimate speeds.The emerging field of ultrafast spintronics in condensed-matter physics relies on the possibility of achieving efficient control of pure spin-currents, spinpolarized electrical currents and spin-configurations on ultrafast timescales [1][2][3]. One alternative for this purpose is the use of technologically relevant informationstorage devices which are composed by ferromagnetic layers, and utilize laser-assisted switching for ultrafast remagnetization. For instance, the use of circularlypolarized femtosecond (fs) laser pulses has been established as a promising route to excite and coherently control spin dynamics in magnets without involving spin precession or external magnetic fields [4]. The efficiency of such magnetic devices might be even enhanced by manipulation of isolated spins with pulses as short as the timescale of the exchange interaction, and within a single-photon shot [4].On the other hand, the growing demand of low-power consumption by using the least possible current in such devices, has motivated in recent years a completely different avenue to achieve generation and control of pure spin currents at ultimate speeds. This alternate pathway relies on the possibility of controlling carrier spins in lowdimensional systems through the spin-orbit interaction [5][6][7][8]. The process of spin-current generation and its manipulation on sub-picosecond (ps) timescales is based on non-magnetic materials, and control of the electron spin is achieved solely by optical means [2,9]. This method also allows for the generation of spin-polarized electrical currents where in addition to the spin there is net flow of charge. With the advent of new classes of electronic materials such as topological insulators (TIs) [10][11][12], this unique route towards ultrafast optical control of spin currents and spin-polarized electrical currents appears to be very promising as it might lead to much lower energy consumption as compared to devices entirely composed by ferromagnetic layers. The key difference resides on the fact that, while insulating in the bulk due to strong spin-orbit coupling, the surface electronic st...

By use of the conservation laws a four-site Hubbard model coupled to a particle bath within an external magnetic field in z-direction was diagonalized. The analytical dependence of both the eigenvalues and the eigenstates on the interaction strength, the chemical potential and magnetic field was calculated. It is demonstrated that the low temperature behaviour is determined by a delicate interplay between many-particle states differing in electron number and spin if the electron density is away from half-filling. The grand partition sum is calculated and the specific heat, the susceptibility as well as various correlation functions and spectral functions are given in dependence of the interaction strength, the electron occupation and the applied magnetic field. For both the grand canonical and the canonical ensemble the high-temperature crossing points of the specific heat are calculated. Whereas in the weak correlation regime the universal value calculated by second order perturbation theory for several Hubbard systems being in the thermodynamic limit is confirmed, these crossing points vanish for intermediate to strong correlation.

The Hubbard model extended by either nearest-neighbour Coulomb correlation and/or nearest neighbour Heisenberg exchange is solved analytically for a triangle and tetrahedron. All eigenvalues and eigenvectors are given as functions of the model parameters in a closed form. The groundstate crossings and degeneracies are discussed both for the canonical and grand-canonical energy levels. The grand canonical potential Ω(µ, T, h) and the electron occupation N (µ, T, h) of the related cluster gases were calculated for arbitrary values (attractive and repulsive) of the three interaction constants. In the pure Hubbard model we found various steps in N (µ, T = 0, h) higher than one. It is shown that the various degeneracies of the grand-canonical energy levels are partially lifted by an antiferromagnetic exchange interaction, whereas a moderate ferromagnetic exchange modifies only slightly the results of the pure Hubbard model. A repulsive nn Coulomb correlation lifts these degeneracies completely. The relation of the cluster gas results to extended systems is discussed.

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