Quantum transport in lateral superlattices

TLDR: In this article, the potential modulation of the Shubnikov-de Haas oscillations arising in the magneto-resistance at quantizing magnetic fields has been investigated and compared with theoretical predictions for the so-called Hofstadter butterfly energy spectrum.

Abstract: 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.