Aharonov-Bohm effect in one-channel weakly disordered rings

Abstract

A new diagrammatic method, which is a reformulation of Berezinskii's technique, is constructed to study the density of electronic states ρ(ǫ, φ) of a one-channel weakly disordered ring, threaded by an external magnetic flux. The exact result obtained for the density of states shows an oscillation of ρ(ǫ, φ) with a period of the flux quantum φ0 = hc e . As the sample length (or the impurity concentration) is reduced, a transition takes place from the weak localization regime (L ≫ l) to the ballistic one (L ≤ l). The analytical expression for the density of states shows the exact dependence of ρ(ǫ, φ) on the ring's circumference and on disorder strength for both regimes. 71.10.-w, 71.20.-b, 71.55.i, 73.23.-b The oscillation of physical properties of disordered metals has been studied intensively after the prediction of the Aharonov-Bohm effect in doubly connected dirty systems [1] with the period of half of a flux quantum and its observation [2] in a Mg cylinder.Today, a particular subject of intensive investigation is the persistent current, predicted in [3,4] for one-dimensional disordered rings. Recent advances in microstructure technology facilitate the fabrication of mesoscopic rings and the observation of thermodynamic currents therein [5][6][7]. The observed oscillatory responses in these experiments, which are consistent with a persistent current, differ in the period of oscillation.A similar controversy exists also in theory. According to fundamental physical principles all physical parameters, in particular the persistent current, of a one-channel metal ring should be periodic in an applied magnetic flux φ with period of a flux quantum φ 0 = hc e [3,4,[8][9][10]. However, the coherent backscattering mechanism with consequent interference effects in mesoscopic systems gives rise to conductance oscillations with the halved period φ 0 /2 [1, [11][12][13][14][15]. It is pertinent to notice that the attempt to explain the φ 0 /2 oscillation in a disordered ring by taking into account the electron-electron interaction [15][16][17][18][19] is also based on the "cooperon" propagation in the system. All these disputes in the theory seem to be connected with the absence of a consistent theory for a one-dimensional (1d) disordered ring in a magnetic field which goes beyond the diffusion approximation and can calculate not only average values of the physical parameters but also mesoscopic fluctuations of these parameters.It is well known that the physical parameters of a mesoscopic system with dimension L satisfying the condition l < L ≪ l in (where l is the mean free path and l in is the length over which the phase coherence of an electron wave is conserved) have random character, i.e. self-averaging is violated [20]. At T = 0 all systems become mesoscopic. In this case high moments give a considerable contribution, which results in strong differences between average value and typical one of the observed parameter [21], i.e. the average value loses its significance to characterize the experimental observation. F...

High-temperature Aharonov-Bohm effect in transport through a single-channel quantum ring

“…(32) The electrons passing through the ring acquire spin polarization. For the case of unpolarized incoming electron beam the spin polarization is calculated as , (33) and, therefore, is also expressed in terms of .…”

“…At low temperature T, the tunneling conductance of this device exhibits narrow resonant peaks [26][27][28][29][30][31][32][33]. The peak arises each time when one of the flux depen dent energy levels in the ring crosses the Fermi energy (AB resonances are also affected by the Coulomb blockade [34,35]).…”