General field of research

Realizing well designed phase-coherent quantum circuits with controllable potentials for manipulating individual electrons and their spin is at the heart of my research. Such circuits are fabricated on different material systems. Currently we are working on

• quantum dot - circuit QED hybrid architectures
  for implementing and investigating qubits.
• van der Waals materials,
  such as single- and bi-layer graphene and MoS₂,
• low-dimensional systems on III-V semiconductors,
  such as GaAs, InAs/GaSb, InAs, GaSb and InSb

Starting from two-dimensional systems, we fabricate micro- and nanostructures for transport experiments at temperatures down to 5 mK and in magnetic fields of up to 15 T. For sample fabrication, we employ the state-of-the-art nanofabrication techniques available in ETH's Center for Micro- and Nanoscience (FIRST), which allow us to realize, e.g., Hall-bars, quantum wires, quantum point contacts, quantum dots, quantum rings, and superconducting microwave resonators. With these samples, we study quantum interference effects of electrons under the influence of their mutual interaction and their interaction with the crystal lattice via spin-orbit fields, do time resolved detection of electron tunneling in quantum dots and detect and manipulate the spin states of the electrons. Of particular interest is also, how the electrons couple to other excitations, such as phonons, photons, or nuclear spins, and how we can control these interactions.

Electron and spin transport in quantum structures

Quantum dots are facinating objects in semiconductor research because they allow us to manipulate electrons and spins one by one due to the Coulomb blockade effect. Few-electron dots have become known as "artificial atoms" since they have exhibited a shell structure similar to real atoms. We fabricate and study such artificial atoms with electron numbers between one and about 50, and connect them by tunnel coupling to other dots or mesoscopic structures. In particular, we are interested in phase-coherence, decoherence, spin manipulation, and charge detection. We also address single-electron tunneling with real-time resolution, which allows us to investigate shot noise and full counting statistics in quantum dots, do single photon detection, and study detector back-action, irreversibility and modern fluctuation theorems at the level of single electrons.

Ring geometries have fascinated experimental and theoretical physicists over many years. Open rings connected to leads allow the observation of the Aharonov-Bohm effect, a paradigm of quantum mechanical phase coherence. Closed rings in a magnetic field give rise to the existence of persistent currents. We have defined quantum ring structures in various material systems, that can be tuned into the Coulomb blockade regime, open rings, rings with embedded quantum dots and quantum dot molecules, and a ring with a side coupled quantum dot.

Fig. 1(a): The figure shows from left to right, an AFM-lithography defined few electron dot, a quantum ring, a quantum dot molecule embedded in an Aharonov-Bohm interferometer, and an electron-beam lithography defined double quantum dot.

Fig. 1(b): Statistics of electron transport obtained by repeatedly counting individual electrons over a finite time-span. The histogram shows, how frequently a particular number n of electrons was transferred through the structure. Negative numbers indicate that electrons have moved upstream, i.e., against the direction of the applied bias (bi-directional counting). The two arrows indicate the mean electron number and its variance. The mean is proportional to the current through the structure, the variance is proportional to the noise of the current.

Local spectroscopy of semiconductor nanostructures with scanning probe techniques

Within this branch of my acitivities we have set out to locally investigate electron transport in semiconductor structures using scanning probe microscopes at cryogenic temperatures. For this purpose we have built scanning force microscopes based on piezoelectric tuning fork sensors for the operation at cryogenic temperatures. Currently we operate one microscope in a ³He-cryostat with a base temperature of 300 mK, and a second one in a dilution refrigerator with a base temperature of 30 mK. A sharp metallic tip attached to the tuning fork sensor acts as the local probe which couples capacitively to the electronic structure at or below the sample surface. The tip is used as a local gate electrode modifying the sample resistance.
1.7 K system: With this scanning gate technique potential fluctuations in quantum wires were locally investigated and edge-states in the quantum Hall effect could be made visible. These results were obtained within the PhD thesis of Jörg Rychen. The work has been continued by Andreas Baumgartner who investigated the classical and quantum Hall effect with the scanning gate technique. After the successful installation of the ³He-⁴He dilution refrigerator system (see below), we have discontinued to use this system.
³He-system: The microscope in this system has been built by Tobias Vancura within his PhD project. Later on, Alessandro Pioda and Slavo Kicin performed scanning gate measurements on quantum point contacts and quantum dots. In the latter, the Coulomb blockade effect can be manipulated in real space. The system has later been partially rebuilt, and Magdalena Hüfner was then able to perform scanning gate measurements of double quantum dots and superconducting SETs in the Coulomb blockade regime. Recently, Dr. Aleksey Kozikov and Richard Steinacher have investigated constrictions and phase coherent cavities in samples with mobilities of more than 8x10⁶ cm²/Vs. They observed branched electron flow in the vicinity of quantum point contacts, formed quantum point contact constrictions between the tip and gates, and observed the depopulation of magnetoelectric subbands in real space. Richard Steinacher has further investigated the imaging mechanisms of the scanning gate technique when transiting from open to closed structures. He also investigated the transition from the strongly to the weakly invasive imaging regime. The microscope is now operated by Carolin Gold.
³He-⁴He dilution refrigerator system: This microscope has been built in a joint effort by Arnd Gildemeister, Paul Studerus and Cecil Barengo. It is fully operational and has given nice results on quantum dots with an integrated charge readout. Arnd further measured the tip-induced potential with great spatial and energy resolution and showed how debris picked up by the tip during scanning can have a big effect on this potential. He also found ways to clean the tip in situ. His work was continued by Stephan Schnez, who measured Coulomb blockade in graphene quantum dots with spatial resolution. The microscope was then operated by Nikola Pascher, who imaged edge states in the integer and fractional quantum Hall regimes. This work was continued by Beat Braem, who is in charge for the system at present.

Fig. 2: The left figure shows scanning gate measurements taken on a quantum dot in GaAs at 300 mK for different voltages applied to the scanning tip. The right figure shows the scanning gate measurement taken on a graphene quantum dot at 200 mK.

Transport in the two-dimensional topological insulator InAs/GaSb

It has been proposed that InAs/GaSb double quantum wells can realize a two-dimensional topological insulator, where the transition to a trivial insulator can be fully controlled by gate voltages. At the interface between InAs and GaSb, the GaSb valence band edge is higher in energy than the InAs conduction band edge, a situation called inverted band structure. At this interface, the in-plane dispersion relations for InAs conduction band electrons and GaSb valence band electrons hybridize, leading to the band gap that renders the double quantum well to be an insulator in the bulk. The hybridized states are superpositions of electron- and hole-like states. Indeed, electrons and holes have been demonstrated to coexist in this double quantum well structure already in the 1970s. By virtue of bulk-edge correspondence, conducting topological edge channels should appear at lateral interfaces of the 2D inverted system with a trivial insulator (such as the outside of the crystal) at zero magnetic field. Although edge conduction has been found in this material system, it is controversial, whether it is of trivial or of topological origin. The system is of interest and acquires some of the properties mentioned above, because strong spin-orbit interactions are present in both the InAs conduction band as well as the GaSb valence band. The spin-orbit interaction also complicates the Landau-level spectrum at finite magnetic field.

Fig. 3: Left: resistivity of an InAs/GaSb quantum well as a function of gate voltage and parallel magnetic field. The orange arrow labeled 'CNP' points at the resistivity peak arising at equal electron and hole densities, when the Fermi energy is in the topological gap. A magnetic field in the plane of the quantum wells suppresses this resistivity peak. Right: Landau fan of a InAs/GaSb double quantum well Hall bar structure showing very unconventional modulations of the Landau-level gaps. Gray numbers at the top of the image indicate electron- (positive) and hole- (negative) Landau level filling factors.

Two-dimensional van der Waals heterostructures

Graphene is a two-dimensional hexagonal crystal of carbon atoms. There are countless superlatives related to this material, and its peculiar band structure features so-called massless Dirac fermions. Techniques to deposit and to distinguish single- and bilayer graphene on substrates have been further developed since the Nobel-prize winning pioneering work of Geim and Novoselov in 2004. Nowadays, high quality graphene for transport studies at low temperatures is encapsulated between hexagonal boron nitride insulating layers. Graphite back gates can be added to screen the graphene layers of interest from the influence of impurities in the substrate. We fabricate such layered van der Waals heterostructures by mechanical exfoliation in a glove-box and apply standard lithography techniques to fabricate nanostructures, such as quantum rings and quantum dots. In the past we have investigated phase-coherence and quantum interference in mesoscopic wires and in Aharonov-Bohm rings, and transport through nanoribbons, single- and double quantum dots. We applied charge detection techniques and the scanning gate technique to graphene structures. The more recent high quality encapsulated graphene structures allowed for the detection of a Lifshitz-transition in bilayer graphene, and for the discovery of unexpected magnetoresistance oscillations in bilayer graphene. Recently, we have also started to investigate van der Waals heterostructures beyond graphene, such as MoS₂ and InSe.

Fig. 4: Conductance resonances of a graphene quantum dot in the Coulomb-blockade regime.