Berry’s phase and persistent charge and spin currents in textured mesoscopic rings

Torsion effects on a relativistic position-dependent mass system

“…It can be found in the literature studies of persistent currents associated with the Berry phase [74,75], the Aharonov-Anandan quantum phase [76,77] and the Aharonov-Casher geometric quantum phase [78][79][80][81]. According to Refs.…”

Berry phase and adiabaticity of a spin diffusing in a nonuniform magnetic field

“…wheie we have assumed isotiopic scattenng (rate l/r (2 D =' We look for a stationary solution to the Boltzmann equation, so the left-hand side of Eq (2 5) is zero and we omit the argument t of P A stationary flux of paiticles with an isotropic velocity distnbution is mjected at x = 0, their spms all ahgned with the local magnetic field (so χ 2 method. The second is an approximate analytical solution using the diffusion approximation, valid for L>/*.…”

“…The adiabatic theorem of quantum mechamcs implies that the final state of a particle that moves slowly along a closed path is identical to the initial eigenstate-up to a phase factor The Berry phase is a time-mdependent contnbution to this phase, depending only on the geometry of the path ' A simple example is a spm-1/2 m a lotating magnetic field B, where the Berry phase equals half the solid angle swept by B It was proposed to measure the Berry phase m the conductance G of a mesoscopic ring m a spatially rotating magnetic field 2 3 Oscillations of G äs a function of the swept solid angle were piedicted, similar to the Aharonov-Bohm oscillations äs a function of the enclosed flux 4 An impoitant practical diffeience between the two effects is that the Aharonov-Bohm oscillations exist at arbitianly small magnetic fields, whereas for the oscillations due to the Berry phase the magnetic field should be sufficiently strong to allow the spin to adiabatically follow the changing dnection Generally speaking, adiabaticity requnes that the piecession frequency ω Β is large compaied to the reciprocal of the chaiactenstic time scale t c on which B changes direction We know that ω ϋ = gμ E B/2fί, with g the Lande factor and μ-Β the Bohr magneton The question is, what is i c 9 In a ballistic ring there is only one candidate, the cncumfeience L of the i mg divided by the Fermi velocity v (For simplicity we assume that L is also the scale on which the field dnection changes) In a diffusive nng theie are two candidates the elastic scattermg time τ and the diffusion time r d aiound the ring They differ by a factoi r A /r~(LI/^) 2 , where / = υ r is the mean fiee path Smce, by defimtion, LS>/ m a diffusive system, the two time scales aie fai apait Which of the two time scales is the relevant one is still undei debate 5 Stern's ongmal proposal 3 was that (11) is necessary to observe the Berry-phase oscillations For reahstic values of g this requires magnetic fields in the quantum Hall regime, outside the ränge of validity of the semiclassical theory We call Eq (11) the "pessimistic cntenon " In a later work, 6 Loss, Schoeller, and Goldbart (LSG) concluded that adiabaticity is reached already at much weaker magnetic fields, when i ι η 2 r Ι (12) This "optimistic cntenon" has motivated expenmentahsts to seaich foi the Berry-phase oscillations m disordered conductois, 7 and was invoked in a recent study of the conductivity of mesoscopic ferromagnets 8 In this paper, we reexarmne the sermclassical theory of LSG to resolve the controveisy The Berry-phase oscillations in the conductance result fiom a penodic modulation of the weak-locahzation correction, and icquire the solution of a diffusion equation for the Cooperon propagator To solve this problem we need to considei the coupled dynamics of four spin degrees of freedom (The Coopei on has four spin mdices) To gam insight we fiist examine m See Π the simplei problem of the dynamics of a single spin variable, by studymg the randomization of a spin-polanzed election gas by a nonuniform magnetic field We stau at the level of the Boltzmann equation and then make the diffusion approximation We show how the diffusion equation can be solved exactly foi the first two moments of the polanzation The same procedure is used in See III to aiTive at a dif...…”

Effect of spin-orbit coupling on zero-conductance resonances in asymmetrically coupled one-dimensional rings

“…In numerous investigations, the transmission properties of mesoscopic AB and AC-rings coupled to current leads were studied under various aspects such as AB-flux and coupling dependence of resonances 3 , geometric (Berry) phases [4][5][6][7][8] and spin flip, precession and interference effects [9][10][11][12][13] . Most of the investigated models use symmetrically coupled rings.…”