## Nanostructures and quantum transport

**The continuing miniaturization of electronic circuits has brought transistor sizes down below 30 nanometers. At these scales, the quantum wave nature of electrons becomes noticeable. Low-temperature experiments on semiconductor devices show quantum effects such as flux quantization and interference. Novel materials featuring high electron mobility allow the realization of quantum effects already at room temperatures and thus opening up a pathway for devices that exploit quantum effects. **

**We model the electronic structure of nanodevices using quantum mechanics, from density functional theory to large-scale tight binding calculations that allow for the simulation of an entire nanodevice. We can predict transport properties, investigate the role of dopants or defects, and study details of the crossover from classical to quantum transport. **

**Graphene**

Since its first experimental realization in 2004, graphene, a one-atom-thin honeycomb lattice of carbon atoms, has given rise to a rapidly growing new field. Graphene is optically transparent, and an excellent conductor, making it a prime candidate for flexible displays. Indeed, mobile phones with graphene-based touch screens are already in the prototype stage. The special double-cone structure of the band structure of graphene mimics the linear dispersion relation of ultrarelativistic Dirac fermions. The resulting band topology results in reduced back-scattering, high mobilities and long spin coherence times, suggesting nanoelectronic applications. We investigate the electronic structure and transport properties of graphene nanodevices using density functional theory and tight binding. Combining graphen with other two-dimensional crystals such as hexagonal boron nitride or molybdenium disulfide allows for new exciting applications, such as photovoltaic cells or efficient nanotransistors. This research is done in collaboration with Prof. Stampfer and Prof. Morgenstern from RWTH Achen.

Selected publications:

Wave-Function Mapping of Graphene Quantum Dots with Soft Confinement

D. Subramaniam, Florian Libisch et al. Physical Review Letters 108, 046801 (2012)

**Quantum billiards**

The continued reduction of size in semiconductor electronic devices ultimately leads to a regime where quantum mechanics governs electronic transport. Paradigmatic systems have been termed quantum billiards or quantum dots and have been realized in semiconductor heterostructures where a two-dimensional electron gas is responsible for the current. New phenomena in electron transport have been found both experimentally as well as numerically such as conductance fluctuations and weak localization. These phenomena have been traced back to the quantum interference of distinct classical paths in the spirit of Feynman's path integral and it has been shown that quantum billiards behave in a distinctly different way if their classical phase space is regular or chaotic. We have developed a semiclassical theory which gives an intuitive, and for the first time, also a quantitatively correct picture of such phenomena as weak localization, conductance fluctuations, and shot noise. The theory contains a sum over piecewise classical paths. These classical paths are linked via diffraction effects at the lead junctions. Including millions of such paths with the correct phase and amplitude we managed to reconstruct even the scattering state itself.

Selected publications: