We investigate nanoscale and nanostructured systems in the framework of theoretical physics. The main focus of research is on electronic transport properties of nanosystems, including effects of quantum interference, strong interaction, disorder, and systems far from equilibrium. We are in particular interested in identifying novel behavior, which is of potential use in applications. We develop and employ most advanced analytical (field-theoretical) approaches, as well as modern numerical methods, including ab initio theories of nanosystems in the framework of quantum chemistry. The following describes some of our projects in more detail.

Electron Transport in Quantum Wires and Nanotubes

We develop a theory of transport properties of strongly interacting electrons in quantum wires; experimental realizations include carbon nanotubes, semiconductor, metallic, and polymer nanowires. In particular, we investigate conductivity of quantum wires with impurities, quantum interference phenomena, and transport properties far from equilibrium.

Scheme of the tunneling experiment with a voltage biased quantum wire. Right moving electrons have a larger chemical potential relative to left moving electrons.

Electronic Properties of Graphene

We study transport  in graphene structures, including conductivity for different types of scatterers, quantum interference phenomena, transport regimes (ballistics, localization, diffusion, criticality), interaction effects, and non-equilibrium physics. We also study related systems with Dirac-type carriers, such as topologically protected metals at boundaries of topological insulators.

Ballistic graphene setup with various strong scatterers. Vacancies as well as atomic or molecular impurities can create midgap states. Metallic islands support quasibound states that can be tuned to the resonance.	Graphene conductivity versus the concentration of vacancies. The resulting conductivity substantially depends on the distribution of vacancies among two graphene sublattices.

Topological Insulators and Superconductors

We investigate the properties of the electronic states both at the surface of 3D and at the edge of 2D topological insulators. Particular focus is on the quantum interference phenomena in the presence and interplay of both disorder and interaction effects. Possible superconducting properties of such topological materials, either intrinsic or induced via proximity effect, are also studied. We also  consider topological excitations (Majorana bound states) in the junctions between topological insulators and superconductors, and their prospective application to the quantum information processing.

Scaling functions for the conductivity of a two dimensional disordered electronic system with strong spin-orbit interaction. The four curves correspond to either presence or absence of the Coulomb interaction as well as to topologically either trivial or non-trivial (Dirac fermions) spectrum. In the case of Dirac fermions with Coulomb interaction a novel self-organized quantum critical state emerges.

Mesoscopic superconductivity

We study various electronic properties of the mesoscopic superconducting systems. The main focus is on the low-dimensional structures including various chains of Josephson junctions and dirty interacting thin films. Strong quantum effects give rise to a number of unusual physical phenomena. As an example, the interplay of strong disorder and Coulomb interaction counterintuitively enhances the superconducting properties of two-dimensional films.

Measurement circuit with 6-SQUID chain inserted in a superconducting loop. The phase difference and magnetic fluxes through SQUIDS are independently controlled by two external coils.	Temperature dependence of resistivity near the superconductor-insulator transition. Inset: phase diagram in the disorder strength - temperature plane.

Transport in Quantum Hall Structures

Electronic transport in 2D electron systems in transverse magnetic fields is explored. One research direction is related to non-equilibrium properties of quantum Hall systems subjected to microwave or strong dc fields. Another project is devoted to properties of integer and fractional quantum Hall edge states, in particular, quantum Hall Mach-Zehnder interferometers.

Resistivity of the microwave-irradiated 2D electron gas oscillates as a function of magnetic field. At strong fields, zero resistance states (ZRS) develop.	Scheme of an electronic Mach-Zehnder interferometer built on quantum Hall edge states. Quantum point contacts partially mix edge channels.

Anderson Localization and Metal-Insulator Transitions

We study Anderson localization phenomena in disordered electronic systems, in particular, of low dimensionality. The focus is on phase diagrams for various types of disorder, metal-insulator transitions and critical behaviour, and statistical properties of key observables.

Multifractal electron wave function at the quantum Hall transition critical state.

New Methods for Quantum Transport in Nanostructures

Leader: Prof. Dr. Peter Wölfle

We develop renormalization group methods in fermionic representation in order to obtain a realistic description of transport in interacting 1D systems. The transport through quantum dots in the Kondo regime, including the noise spectrum, is studied within the functional renormalization group.

Entwicklung von Renormierungsgruppenmethoden für beliebig starke Kopplung zur Berechnung von Transporteigenschaften durch Kontakte von zwei oder mehrerenQuantendrähten im Luttingermodell. Bestimmung der Fixpunktstruktur und der Leitwertmatrix sowie des Stromrauschens im linearen und nichtlinearen Responsebereich.

Formulierung einer analytischen Renormierungsgruppentheorie für den Transport durch Kondo-Quantenpunkte auch im Bereich starker Kopplung und Berechnung des Leitwerts und der Spektralfunktionen im linearen und nichtlinearen Bereich.

Theory and Simulation of Molecular Nanosystems (Evers Group)

We develop the ab initio - theory of transport through single molecules  with functionality ("Molecular electronics"), more generally of properties and function of atomic, molecular and nanostructured matter, in particular graphene and meta materials. Simulation and model calculations of transport- and statistical properties of disordered electron systems ("Anderson localization") are also studied.

The charge transport through molecules is sensitive to the molecular geometry. Hence a manipulation of this geometry, for instance by a pulse in the bias voltage, can trigger a hysteresis lop in the current-voltage curve, which is a prerequisite for a molecular memory element.

For more information on the research activities see web-page of the Group Evers. 

Numerical Simulations of Transport in Nanostructures

Leader: Dr. Peter Schmitteckert

We develop methods in the framework of the density matrix renormalization theory (DMRG) for calculating transport properties of strongly interacting systems in quasi-1D nanostructures. Among those are simulations in real time of the nonlinear conductance, and the motion of wave packets in electron and photon systems.

Analytical and numerical (DMRG) results for the current-voltage dependence of the self-dual interacting resonant level model.