Quantum transport in lateral superlattices

Lateral superlattices with very small lattice periods approaching the Fermi wavelength in size are fabricated on AlGaAs heterostructures by electron beam lithography. The potential modulation is induced by a gate voltage applied to a laterally modulated gate electrode. In our samples the two-dimensional electron gas is located very close to the sample surface, thus allowing us to induce very small lattice periods with a relatively large amplitude of the potential modulation. For weak potential modulation, which can be tuned by the gate voltage, we observe a modulation of the amplitude of the Shubnikov-de Haas oscillations arising in the magneto-resistance at quantizing magnetic fields. For more negative gate voltages, i.e. larger amplitudes of the potential modulation, certain maxima of the Shubnikov-de Haas oscillations split up reflecting the energy spectrum that arises when a given number of flux quanta penetrates a unit cell of the lattice. We compare our experimental results with theoretical predictions for the so-called Hofstadter butterfly energy spectrum and we conclude that we can experimentally detect the major energy bands and gaps.