Quantum dots in the quantum Hall regime

S. Baer, C. Rössler, T. Ihn, K. Ensslin, C. Reichl, and W. Wegscheider

Solid State Physics Laboratory, ETH Zurich, 8093 Zurich, Switzerland

Two-dimensional electron systems at low temperatures and in strong magnetic fields show a rich spectrum of highly degenerate, incompressible ground states. Fractional quantum Hall states, occurring at a fractional filling factor with an odd denominator, are well described by the Laughlin wavefunction. There exists a prominent exception from this hierarchy: The \nu = 5/2 state, which is believed to obey non-abelian statistics. This remarkable property could make it an interesting candidate for the realization of a topological qubit. Theoretical ideas for probing the statistics of the \nu = 5/2 state are based on quantum dots, operated as Fabry-Pérot interferometers as a basic building block.
In the presence of a strong magnetic field, Coulomb blockade (CB) oscillations can no longer be described within a single particle picture. Alternating compressible and incompressible regions inside the dot are formed, which can strongly modify the CB oscillations.
We present measurements of a large quantum dot with adjacent charge detector, fabricated on a high-mobility 2DEG. Magnetoresistance oscillations, measured as a function of magnetic field and gate voltages in the quantum Hall regime, arise from a Coulomb blockade mechanism. In a pinched-off regime, different coupling strengths of edge states inside the dot can directly be extracted, both from direct transport, as well as from measurements using charge detection techniques. In this configuration, a CB amplitude modulation can be observed over a large parameter range for different filling factors. This effect is attributed to a double dot like behavior of two edge states inside the dot. We are able to directly measure the charge stability diagram of the capacitively and tunnel coupled edge states.  The edge states within the dot are non-cyclically depopulated, which can be explained by a simple capacitive model and allows to draw conclusions about the edge state geometry within the quantum dot.