Magnetoresistance and dephasing in a two-dimensional electron gas at intermediate conductances

Abstract

We study, both theoretically and experimentally, the negative magnetoresistance (MR) of a twodimensional (2D) electron gas in a weak transverse magnetic field B. The analysis is carried out in a wide range of zero-B conductances g (measured in units of e 2 /h), including the range of intermediate conductances, g ∼ 1. Interpretation of the experimental results obtained for a 2D electron gas in GaAs/InxGa1−xAs/GaAs single quantum well structures is based on the theory which takes into account terms of higher orders in 1/g. We show that the standard weak localization (WL) theory is adequate for g 5. Calculating the corrections of second order in 1/g to the MR, stemming from both the interference contribution and the mutual effect of WL and Coulomb interaction, we expand the range of a quantitative agreement between the theory and experiment down to significantly lower conductances g ∼ 1. We demonstrate that at intermediate conductances the negative MR is described by the standard WL "digamma-functions" expression, but with a reduced prefactor α. We also show that at not very high g the second-loop corrections dominate over the contribution of the interaction in the Cooper channel, and therefore appear to be the main source of the lowering of the prefactor, α ≃ 1 − 2/πg. The fitting of the MR allows us to measure the true value of the phase breaking time within a wide conductance range, g 1. We further analyze the regime of a "weak insulator", when the zero-B conductance is low g(B = 0) < 1 due to the localization at low temperature, whereas the Drude conductance is high, g0 ≫ 1, so that a weak magnetic field delocalizes electronic states. In this regime, while the MR still can be fitted by the digamma-functions formula, the experimentally obtained value of the dephasing rate has nothing to do with the true one. The corresponding fitting parameter in the low-T limit is determined by the localization length and may therefore saturate at T → 0, even though the true dephasing rate vanishes.

Quantum coherence at low temperatures in mesoscopic systems: Effect of disorder

“…Such a temperature dependence is very similar to what has been observed in Ref. 74 for similar values of k F l e . In that work, 74 the exponent varied from p = −0.5 to −0.3 when reducing k F l e Ͻ 5 down to k F l e ϳ 1, similar to our observations.…”

“…[69][70][71][72][73][74][75][76][77] In such 2D systems, an estimation of the localization length loc 2D is given by 74,75 loc…”

Spatially varying electronic dephasing in three-dimensional topological insulators

“…The Hikami-Larkin Naganoka theory describing weak localization(and anti-localization) effects assumes diffusive motion of electrons, and predicts the magnitude of weak anti-localization to be αe 2 /(2π ), where α = 0.5 is a fixed constant per independent electronic channel. This is however not valid in the pseudo-diffsuive regime, where it has been shown that α = 0.5−2R/π, where R is the sample resistance in units of e 2 /h [68,69]. This suppression of α is a consequence of pseudo-diffusive transport where quantum corrections to conductance need to take into account terms in higher orders of the dimensionless conductance g = 1/R.…”

Superconducting fluctuations and characteristic time scales in amorphous WSi

“…where ( ) = ( 1 2 + 1 ) + ln with the limiting cases ( ) ≈ 2 /24 for ≪ 1 and for ≫ 1 ( ) ≈ ln − 2 ln 2 − + 2 2 ⁄ , with = 0.5772 is the Euler constant [24,29]. Moreover, since is much smaller than any other time scales here [25], the excess conductance can therefore be simplified to…”