G Lütjering

Magnetotransport in antidot arrays

We study magnetotransport in lateral two-dimensional superlattices with periods on the order of 100 nm. Pronounced low-field transport anomalies reflect the interplay of two characteristic lengths of the system, the cyclotron radius Rc and the period a. Measurements at very low temperatures reveal quantum oscillations, periodic in the magnetic field B, which are superimposed upon the commensurability anomalies in the magnetoresistance pxx. We show that the latter effect can be interpreted in terms of quantized periodic orbits which takes into account the chaotic nature of the classical phase space.

Metal-non-metal transition at the crossover from antidots to quantum dots

A three-dimensionally structured gate resembling a pillared hall allows the exertion of a strong potential modulation on a two-dimensional electron gas in a GaAs/AlGaAs heterostructure. The system can be tuned over a wide range, from a metallic, open antidot lattice to an insulating system of disconnected dots, by a negative gate voltage. At threshold each dot typically contains 50 electrons. The conductance near threshold shows strongly activated behaviour at liquid helium temperatures, which can be modelled by considering tunnelling through a barrier between two dots.

Electrons in mesoscopically inhomogeneous magnetic fields

We investigated the low-field magnetoresistivity of a two-dimensional electron gas (2DEG) underneath microstructured ferromagnetic gratings. The strength and the direction of an externally applied magnetic field determines the strength and the shape of the micromagnets stray field. Commensurability effects due to the imposed periodic magnetic field are in competition with similar effects resulting from a strain-induced periodic electrostatic potential, associated with the patterned ferromagnets on top of the heterojunction. The presence of both a periodic magnetic field and a periodic electrostatic potential gives rise to the interesting interference phenomena presented here.

Weak localisation in ballistic cavities filled with antidot arrays

We present experimental data on the ballistic weak localisation in square cavities filled with antidot arrays. The weak localisation peak is cusp-like at mK temperatures and clearly deviates from a Lorentzian line shape, which is the theoretical prediction for a classical chaotic system. Although the ideal system, a Sinai billiard, is in principle purely chaotic, directly reflected, non-chaotic trajectories lead to the behaviour of a mixed system in experiment. We demonstrate this by detailed semiclassical analysis. In comparison, empty cavities of equal geometry show a sharper peak in the form of a Lorentzian. Here, imperfections of the experimental structure (boundary roughness, small-angle scattering) seem to change the dynamics of the nominally regular system to chaotic, contrary to the antidot case.

Nonequilibrium Quantum Transport in Antidot Arrays

We have studied the onset of dissipation in the quantum Hall effect (QHE) in different antidot arrays (periodic or aperiodic antidot arrays, and single lines of antidots), patterned on a two-dimensional electron system. In periodic arrays, the breakdown current is systematically reduced with increasing antidot density. In comparable aperiodic arrays, the breakdown current is markedly lower, and the electron temperature starts rising at lower currents than in periodic arrays. Single lines of antidots across the current channel cause only a small reduction of the breakdown current, indicating the relevance of avalanche electron heating. In arrays of very small antidots, a suppression of the electron heating due to additional scattering and a complete absence of hot-electron-induced hysteresis in the current–voltage characteristics were observed.

Evidence for quasi-classical transport of composite fermions in an inhomogeneous effective magnetic field

We report on transverse magnetic focusing experiments in arrays of equidistant constrictions with centre-to-centre constriction spacings L varying from 500 nm to in the vicinity of the Landau level filling factor of a two-dimensional electron system. Provided the composite fermion mean free path is comparable to L, focusing is observed for both effective magnetic field directions. The non-uniform electron distribution with a saddle point in the middle of each constriction, and the associated inhomogeneous effective magnetic field for the composite fermions, invokes characteristic differences in the composite fermion focusing spectra compared with the electron focusing spectra near zero magnetic field. These changes are well predicted by quasi-classical calculations of the composite fermion dynamics in the corresponding potential landscape.

Transport in Electric and Magnetic Lateral Superlattices

In this contribution a short outline of different types of lateral superlattices is given and the predominant phenomena, in particular due to the commensurability between the cyclotron radius R c and the period a, are briefly reviewed.