Magnetoresistance of a 2D Electron Gas Caused by Electron Interactions in the Transition from the Diffusive to the Ballistic Regime

Abstract

On a high-mobility 2D electron gas we have observed, in strong magnetic fields (ωcτ > 1), a parabolic negative magnetoresistance caused by electron-electron interactions in the regime of kBT τ / ∼ 1, which is the transition from the diffusive to the ballistic regime. From the temperature dependence of this magnetoresistance the interaction correction to the conductivity δσ Electron-electron interaction (EEI) corrections to the Drude conductivity σ 0 of 2D systems have been intensively studied over two decades. These studies were based on the theory of interactions in the diffusive regime,. Physically this condition implies that the effective interaction time, /k B T , is larger than the momentum relaxation time τ and therefore the two interacting electrons experience scattering by many impurities. In the ballistic regime, k B T τ / > 1, electrons interact when scattered by a single impurity. A theory of the interaction correction for such a case was only recently developed [2], and there have already been several experimental attempts to apply it to the conductance of high-mobility (large τ ) semiconductor structures [3,4,5,6,7,8]. An essential feature of this theory is that the impurities are treated as point-like scatterersthe condition which is not satisfied in structures where the impurities are separated from the 2D channel by an undoped spacer (unless the spacer is thick enough for the background impurities to dominate the scattering). There is then a question of how the interaction correction in the ballistic regime manifests itself in a smooth fluctuation potential.Introducing a long-range scattering potential is expected to suppress the interaction correction in the ballistic regime considered in [2]. This correction is caused by electron back-scattering, but in the case of a smooth potential the backscattering is significantly reduced. However, as shown in [9,10], applying a strong magnetic field increases the probability of an electron to return back and restores the interaction correction.

Conductivity of a two-dimensional electron gas in a Si/SiGe heterostructure near the metal-insulator transition: Role of the short- and long-range scattering potential

“…In our opinion the explanation why in contrast to Ref. 8 we don't find a good agreement with Ref. 7 in our experiment may lie with the fact that theory 7 was developed with only the long-range component of the disorder potential taken into account.…”

“…The structures studied in Ref. 8 were of a higher mobility than ours and with a more important role of the longrange scattering potential compared to that of the pointlike scatterers. Probably in that case the approximation made in Ref.…”

“…Soon afterwards the results of Ref. 7 have been tested in an experiment on magnetoresistance in a GaAs/AlGaAs heterostructure with a 2DEG and a good agreement with theory 7 has been found 8 .…”

Interaction-induced magnetoresistance in a two-dimensional electron gas

“…Indeed, a T -dependent negative MR was observed in experiments 12,13,14,15,16 and attributed to the interaction effect. However, the majority of experiments 12,13,14 cannot be directly compared with the theory 1,10,11 since they were performed at higher temperatures, T τ 1.…”

“…However, the majority of experiments 12,13,14 cannot be directly compared with the theory 1,10,11 since they were performed at higher temperatures, T τ 1. (In high-mobility GaAs heterostructures conventionally used in MR experiments, 1/τ is typically ∼ 100 mK and becomes even smaller with improving quality of samples.)…”