# Research Projects

## Quantum Dot Systems

Quantum dots are structures that have a size in all three dimensions comparable to the electronic wavelength. Therefore they are also described as 0D-systems. Due to the similarity to atoms with no free motion for bound electrons, quantum dots are also called “artificial atoms”. The confinement of electrons in all directions has two principle consequences. On one hand, the quantization of the elementary charge becomes visible, on the other hand, the electronic wave can be investigated, resulting in discrete energy levels like in real atoms. Both effects can lead to future electronic devices up to quantum computers, but are also subject to intensive basic research, which our group is focused on. Especially coupled systems are of growing interest. If several quantum dots are coupled, “artificial molecules” are created with binding and antibinding states. The complexity of these systems, regarding tuning parameters and physical effects, increases with the number of dots. By now we have achieved to couple three quantum dots and for the first time to completely measure the so called stability diagram, the map of charge states.

### Charge Detection

In addition to direct electronic transport through quantum dots, a second method can be used, the detection of charge rearrangements using a quantum point contact, that is coupled to the quantum dot via Coulomb interaction. This technique has been used successfully in our group for many years to detect transitions within quantum dots, that either feature a direct transport too small to be measured, or appear due to internal charge rearrangements without any transport at all. Especially in complex systems like double or triple quantum dots, the observable parameter space is widely enlarged. Furthermore it is possible to detect the absolute number of electrons or to investigate tunneling rates.

### Spins in Quantum Dots

A special focus lies on the research of the electronic spin in quantum dots. The system of the two states spin up and spin down of an electron on a quantum dot could be the core element for the development of quantum computers, for which the two spin states could work as quantummechanical bit (qbit). Furthermore the interplay of single spins in coupled systems is of high interest. How do spins interact in multiple quantum dots? Which effects can be found for the interplay between dots and two dimensional leads? In our group, many observations have been made in this field like e.g. spin blockade, Kondo effect or RKKY effect.

### Many-body interaction Effects

The observation of Kondo effect in Single Electron Transistors (SETs) is a remarkable experimental achievement, underlining the fast progress in nanoelectronics, and is an important research direction today. One of the main focuses of our group is the study of the quantum entanglement between Kondo impurities via indirect spin-spin exchange interactions, like Rudermann-Kittel-Kasuya-Yoshida (RKKY). Being a form of non-local spin control, the study of the RKKY interaction has important implications in quantum information processing and the development of the next generation quantum computer.

## Electron Dynamics

The analysis of current fluctuations offers insight in the dynamics of electron transport which in contrast are unavailable in the observation of the average current. Our group has profound experience both in Shot Noise measurements (high frequency) and Full Counting Statistics (low frequency regime).

### Shot Noise Measurements

At low temperatures one of the most prominent current fluctuation phenomena is the so called shot noise. It occurs at low transmission probabilities - e.g. transport through quantum dots or tunneling barriers - and has its origin in the discreteness of the electronic charge. Electron-electron interaction effects lead to an enhancement or suppression of the shot noise power allowing us to draw detailed conclusions about e.g. transmission probabilities, Coulomb blockade, or even many-body interaction effects like the Femi edge singularity effect.

### Full Counting Statistics

While the shot noise offers insight about correlations in electronic transport through semiconductor heterostrucure devices it is a demanding task to extract higher moments directly from these measurements. In contrast those moments are naturally accessible in the context of Full Counting Statistics (FCS). Using a quantum point contact as a non-invasive detector we are able to directly count the number of electrons leaving or entering a quantum dot system allowing us to extract cumulants of the distribution up to the 20th order.

### Single Electron Pump

In addition noise measurements in collaboration with the PTB Braunschweig are utilized to characterise non-adiabatic single electron pumps; devices which promise to define the current standard in the coming years. These single electron pumps consist mainly of a quantum wire tuned by two top gates forming a quantum dot. An additional AC voltage coupled onto one of the top gates leads to a cyclic change of transmission probabilities and quantised quantum dot states. For a distinct set of control parameters a fixed number of electrons can be transferred per cycle. Noise measurements on these pumps fulfill two important tasks: detecting pumping errors and giving distinct proof of a fully quantised current.

## Graphene

Ultrathin layers of carbon atoms, called graphene, provide the possibility to study freestanding two dimensional systems. Due to their hexagonal lattice structure, monolayer graphene exhibit extraordinary properties including a Dirac type bandstructure in the vicinity of the neutrality point. The carrier concentrations can be tuned from electrons to holes.

In our group single, bi- and multilayer graphene samples are prepared and investigated using magneto transport measurements and atomic force microscopy.

### Decoupled Monolayer

Folded monolayer graphene forms a system of two very closely spaced layers, decoupled due to the misorientation. Magneto–transport measurements on this decoupled monolayers conducting in parallel are performed variing perpendicular applied magnetic field, backgate voltage and temperature. From the Shubnikov–de Haas oscillations, carrier densities are obtained, being different for the two layers due to screening. Mobilities and scattering times show significantly higher values in the top layer, indicating weaker substrate influence. Additionally, reduced Fermi velocities can be observed in such twisted layers.

### Graphene Nanostructures

Graphene can be used as a two dimensional base material for various nanostructures. E-beam lithography is used to define certain areas in which the graphene is etched away with a reactive oxigene plasma. The remaining parts form devices such as Hall-bars or ring-like structures in which electronic transport is investigated. Applied gate voltages are used to adjust the concentration and type of charge carriers in this nanostructures.

## Quantum Hall Effect (QHE) and Fractional QHE

The Quantum Hall effect (QHE) is one of the fundamental phenomena occurring in two-dimensional electron systems (2DES). Although it has been investigated for more than three decades we are still far away from complete understanding of this effect. In our working group we study the Fractional Quantum Hall Effect (FQHE) in very high mobility 2DES. On the basis of high mobility 2DES we study the interesting filling factor μ=5/2, which would realize the construction of a topological quantum computer. We also study new effects caused by the high mobility.