S. Lüscher

Energy spectra of quantum rings.

Quantum mechanical experiments in ring geometries have long fascinated physicists. Open rings connected to leads, for example, allow the observation of the Aharonov–Bohm effect, one of the best examples of quantum mechanical phase coherence. The phase coherence of electrons travelling through a quantum dot embedded in one arm of an open ring has also been demonstrated. The energy spectra of closed rings have only recently been studied by optical spectroscopy. The prediction that they allow persistent current has been explored in various experiments. Here we report magnetotransport experiments on closed rings in the Coulomb blockade regime. Our experiments show that a microscopic understanding of energy levels, so far limited to few-electron quantum dots, can be extended to a many-electron system. A semiclassical interpretation of our results indicates that electron motion in the rings is governed by regular rather than chaotic motion, an unexplored regime in many-electron quantum dots. This opens a way to experiments where even more complex structures can be investigated at a quantum mechanical level.

Signatures of spin pairing in chaotic quantum dots.

Coulomb blockade resonances are measured in a GaAs quantum dot in which both shape deformations and interactions are small. The parametric evolution of the Coulomb blockade peaks shows a pronounced pair correlation in both position and amplitude, which is interpreted as spin pairing. As a consequence, the nearest-neighbor distribution of peak spacings can be well approximated by a smeared bimodal Wigner surmise, provided that interactions which go beyond the constant interaction model are taken into account.

Fabricating tunable semiconductor devices with an atomic force microscope

We fabricated quantum wires of different geometries in Ga[Al]As heterostructures by local oxidation of the semiconductor surface with an atomic force microscope. By magnetotransport measurements at low temperatures on these wires the electronic width is determined and compared to the geometrical width. An extremely small lateral depletion length of the order of 15 nm and a high specularity of the scattering at the confining walls is found. Furthermore, we demonstrate experimentally that these quantum wires can be tuned by a combination of in-plane gates and top gates.

In-plane gate single-electron transistor in Ga[Al]As fabricated by scanning probe lithography

A single-electron transistor has been realized in a Ga[Al]As heterostructure by oxidizing lines in the GaAs cap layer with an atomic force microscope. The oxide lines define the boundaries of the quantum dot, the in-plane gate electrodes, and the contacts of the dot to source and drain. Both the number of electrons in the dot as well as its coupling to the leads can be tuned with an additional, homogeneous top gate electrode. Pronounced Coulomb blockade oscillations are observed as a function of voltages applied to different gates. We find that, for positive top-gate voltages, the lithographic pattern is transferred with high accuracy to the electron gas. Furthermore, the dot shape does not change significantly when in-plane voltages are tuned.

Transport properties of quantum dots with steep walls

Quantum dots are fabricated in a Ga[Al]As heterostructure by local oxidation with an atomic force microscope. This technique, in combination with top gate voltages, allows us to generate small lateral depletion lengths. The confinement is characterized by low-temperature magnetotransport measurements, from which the dots energy spectrum is reconstructed. We find that in small dots the addition spectrum can qualitatively be described within a Fock-Darwin model. For a quantitative analysis, however, a steep-wall confinement has to be considered. In large dots with small lateral depletion length, our measurements indicate that the density of states within Landau level 2 inside the dot is larger than that within Landau level 1, an effect that we interpret in terms of steep walls. Furthermore, we demonstrate that our interpretation is consistent within the charge-density model. The maximum wall steepness achieved is of the order of 0.4 meV/nm.

Electronic properties of nanostructures defined in Ga[Al]As heterostructures by local oxidation

Tunable nanostructures can be patterned in Ga[Al]As heterostructures with an atomic force microscope (AFM). Oxidizing the GaAs cap layer locally by applying a voltage to the AFM tip leads to depletion of the electron gas underneath the oxide. Here, we describe this type of AFM lithography as a tool to fabricate tunable nanostructures and characterize the electronic properties of the resulting confinement. As an example for the versatility of this technique, we present conductance measurements on a quantum wire as a function of its position. Conductance fluctuations in real space with a characteristic period of 2 nm are observed and interpreted in terms of individual peaks in the potential landscape the wire hits as it moves through the host crystal.

Single-hole transistor in a p-Si/SiGe quantum well

A single-hole transistor is patterned in a p-Si/SiGe quantum well by applying voltages to nanostructured top gate electrodes. Gating is achieved by oxidizing the etched semiconductor surface and the mesa walls before evaporation of the top gates. Pronounced Coulomb blockade effects are observed at small coupling of the transistor island to source and drain.

Quantum wires and quantum dots defined by lithography with an atomic force microscope

Semiconductor nanostructures are realized by patterning AlGaAs/GaAs heterostructures with an atomic force microscope. Steep potential walls, precise pattern transfer and a combination of in-plane and top gates can be achieved with this technique. The electronic properties of nanostructures defined in this way are discussed on two examples, namely a quantum point contact and a single electron transistor. For the quantum point contact we demonstrate quantized conductance at temperatures of 4 K and above. This indicates the strong confinement energy in this system. For the single electron transistor, the realization of special potential shapes and the observation of high-quality Coulomb blockade is shown.

Energy spectra of quantum rings

High quality quantum rings are fabricated by nano-lithography with a scanning force microscope. The electron occupancy as well the tunneling contacts to source and drain are controlled by in-plane and top gate voltages. Coulomb blockade oscillations in the conductance through the quantum ring give information about the energy spectrum and the wave functions. The Coulomb blockade peak positions as well as the amplitudes oscillate periodically as a function of magnetic field. The period is given by an Aharonov-Bohm-type argument, i.e., one flux quantum h/e through the area defined by the ring. Some states show a pronounced zig-zag behavior as a function of field in agreement with the energy spectrum of a perfect ring. Other states display a rather flat magnetic field dispersion. We argue that the magnetic field behavior of a given state depends on the degree to which its wave function is localized or extended along the circumference around the quantum ring.

Shifting a Quantum Wire through a Disordered Crystal: Observation of Conductance Fluctuations in Real Space

A quantum wire is spatially displaced by suitable electric fields with respect to the scattering potentials inside a semiconductor crystal. As a function of the wire position, the low-temperature conductance shows reproducible fluctuations. Their characteristic temperature scale is a few hundred millikelvin, indicating a phase-coherent effect. One fluctuation is attributed to a single bump in the scattering potential entering or leaving the wire.