Non- Abelian gauge theory for Rashba and Dresselhaus Spin-Orbit Interaction

Abstract : A non-Abelian gauge formulation for the Rashba and Dresselhaus hamiltonians, relevant in spintronics of non-centrosymmetric materials, is studied. The gauge fields defined are proportional to the SU(2) generators and also to potential gradients of extrinsic and intrinsic origin which results in a U(1) × SU(2) formulation. We derived from the corresponding lagrangian the equations of motion and conserved spin currents. It is shown that the mandatory presence of a Proca mass type term fixes the gauge and solves in consequence the gauge dependence of the spin current and therefore the ambiguities of the spin current reported in the literature. The invariant gauge subgroup of this theory will be studied. We will analyze some topological consequences of the gauge formulation of Rashba and Dresselhaus focusing on interferometers models and quantization conditions similar to the integer quantum Hall effect. A Spin filtering device, through quantum spin interference, is addressed in a quasi-2 dimensional GaAs/AlGaAs electron gas that has both Rashba and Dresselhaus spin-orbit couplings and an applied external magnetic field. We propose an experimentally feasible electronic Mach Zehnder Interferometer that determines perfect spin filtering conditions. We find two spin filtering regimes, one where filtering is achieved in the original incoming quantization basis, that takes advantage of the purely non-Abelian nature of spin rotations, and the other, where one needs a tilted preferential axis to observe the polarized output spinor. We also address the electronic states of a mesoscopic ring in the presence of Rashba Spin Orbit coupling and a U(1) gauge field. Spin symmetric coupling to an ideal lead is implemented following Büttiker’s voltage probe. The spin and charge persistent currents are computed in the presence of the SO interaction and the reservoir coupling for two distinct scenarios of the electron filling fraction. The degradation of the persistent currents depends uniformly on the reservoir coupling but due to the fact that currents emerge from different depths of the fermi sea, they depend non uniformly in temperature, “shielding” the currents with a protective gap. Finally the problem of persistent charge and spin currents is addressed on a Corbino disk built from a graphene sheet. We consistently derive the Hamiltonian including kinetic, intrinsic (ISO) and Rashba spin-orbit interactions in cylindrical coordinates. The Hamiltonian is carefully considered to reflect hermiticity and covariance. We use the linear response definition in order to determine the charge persistent currents. We also determine the spin and pseudo spin polarizations associated with such equilibrium currents. For the intrinsic case one can also compute the correct currents by properly defining the bare velocity operator associated with ISO problem or alternatively the ISO group velocity operator associated with the free case. Charge currents for both SO couplings reach maximal values in the vicinity of half integer flux quanta. Such maximal currents are protected from thermal effects because contributing levels plunge (~1K) into the Fermi sea at half integer flux values. Such a mechanism, makes them observable at readily accessible temperatures. Spin currents only arise for the Rashba coupling, due to the spin symmetry of the ISO spectrum. For the Rashba coupling, spin currents are canceled at half integer fluxes but they remain finite in the vicinity, and the same scenario above protects spin currents
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  • HAL Id : tel-01751704, version 1

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Nelson Bolívar. Non- Abelian gauge theory for Rashba and Dresselhaus Spin-Orbit Interaction. Other [cond-mat.other]. Université de Lorraine, 2014. English. ⟨NNT : 2014LORR0356⟩. ⟨tel-01751704⟩

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