It is shown that the collective spin rotation of a single Skyrmion in quantum Hall ferromagnet can be regarded as precession of the entire spin texture in the external magnetic field, with an effective moment of inertia which becomes infinite in the
zero g-factor limit. This low-lying spin excitation may dramatically enhance the nuclear spin relaxation rate via the hyperfine interaction in the quantum well slightly away from filling factor equal one.
A coherent superposition of many nuclear spin states can be prepared and manipulated via the hyperfine interaction with the electronic spins by varying the Landau level filling factor through the gate voltage in appropriately designed Quantum Hall Fe
rromagnet. During the manipulation periods the 2D electron system forms spatially large Skyrmionic spin textures, where many nuclear spins follow locally the electron spin polarization. It is shown that the collective spin rotation of a single spin texture is gapless in the limit of zero Zeeman splitting, and may dominate the nuclear spins relaxation and decoherence processes in the quantum well.
We present a theoretical study of the influence of the nuclear ferromagnetism on superconductivity in the presence of the electron-nuclear spin interaction. It is demonstrated that in some metals, e.g. Rh, W, the BCS condensate imbedded in a matrix o
f ferromagneticaly ordered nuclear spins should manifest the FFLO (Fulde-Ferel-Larkin-Ovchinniov) state. We outline that the optimal experimental conditions for observation of FFLO could be achieved by creation, via adiabatic nuclear demagnetization, of the negative nuclear spin temperatures. In this case the nuclear polarization points in the opposite to the external magnetic field direction and the electromagnetic part of the nuclear spin magnetization compensates the external magnetic field, while the exchange part creates the nonhomogeneous superconducting order parameter.
Electron transport in a new low-dimensional structure - the nuclear spin polarization induced quantum wire (NSPI QW) is theoretically studied. In the proposed system the local nuclear spin polarization creates the effective hyperfine field which conf
ines the electrons with the spins opposite to the hyperfine field to the regions of maximal nuclear spin polarization. The influence of the nuclear spin relaxation and diffusion on the electron energy spectrum and on the conductance of the quantum wire is calculated and the experimental feasibility is discussed.
The idea of quantum computation is the most promising recent developments in the high-tech domain, while experimental realization of a quantum computer poses a formidable challenge. Among the proposed models especially attractive are semiconductor ba
sed nuclear spin quantum computers (S-NSQC), where nuclear spins are used as quantum bistable elements, qubits, coupled to the electron spin and orbital dynamics. We propose here a scheme for implementation of basic elements for S-NSQCs which are realizable within achievements of the modern nanotechnology. These elements are expected to be based on a nuclear-spin-controlled isotopically engineered Si/SiGe heterojunction, because in these semiconductors one can vary the abundance of nuclear spins by engineering the isotopic composition. A specific device is suggested, which allows one to model the processes of recording, reading and information transfer on a quantum level using the technique of electrical detection of the magnetic state of nuclear spins. Improvement of this technique for a semiconductor system with a relatively small number of nuclei might be applied to the manipulation of nuclear spin qubits in the future S-NSQC.
A scenario of quantum computing process based on the manipulation of a large number of nuclear spins in Quantum Hall (QH) ferromagnet is presented. It is found that vacuum quantum fluctuations in the QH ferromagnetic ground state at filling factor $
u =1$, associated with the virtual excitations of spin waves, lead to fast incomplete decoherence of the nuclear spins. A fundamental upper bound on the length of the computer memory is set by this fluctuation effect.
The de Haas - van Alphen effect in two-dimensional (2D) metals is investigated at different conditions and with different shapes of Landau levels (LLs). The analytical calculations can be done when many LLs are occupied. We consider the cases of fixe
d particle number ($N=const$), fixed chemical potential ($mu =const$) and the intermediate situation of finite electron reservoir. The last case takes place in organic metals due to quasi-one-dimensional sheets of Fermi surface. We obtained the envelopes of magnetization oscillations in all these cases in the limit of low temperature and Dingle temperature, where the oscillations can not be approximated by few first terms in the harmonic expansion. The results are compared and shown to be substantially different for different shapes of LLs. The simple relation between the shape of LLs and the wave form of magnetization oscillations is found. It allows to obtain the density of states distribution at arbitrary magnetic field and spin-splitting using the measurement of the magnetization curve. The analytical formula for the magnetization at $mu =const$ and the Lorentzian shape of LLs at arbitrary temperature, Dingle temperature and spin splitting is obtained and used to examine the possibility of the diamagnetic phase transition in 2D metals.
We show that scattering of the conduction electrons by nuclear spins via the hyperfine interaction may lead the upper limit on the mean free path in clean metals. Nuclear spins with s >1/2 may cause a strong dephasing in dirty limit due to the quadru
pole coupling to the random potential fluctuations caused by static impurities and lattice imperfections.
