## Research Topics

# Topological insulators and superconductors

- Talk "Majorana Surface Code" at MPI conference in Dresden, September 2015 [pdf]
- "Introduction to Topological Kondo effect in Majorana devices"

Lecture notes at summer school in Natal/Brazil, August 2015 [pdf]- Talk "Majorana fermions" at workshop "Topology and Nonequilibrium", MPI Dresden, September 2013 [pdf]
- "Electron transport in topological insulators" (Talk, Triest, November 2011)

# Orbital ferromagnetism in Rashba dots

- Talk at NanoPeter, St. Petersburg, July 2014 [pdf]

Graphene

- "Efimov universality and interaction-induced zero mode transport in graphene", Natal, August 2015

Talk (pdf)- Talk on interaction effects in graphene, Antwerp workshop, May 2013 [pdf]

See also:- "Physical properties of graphene", colloquium, 2011

Talk (pdf)- "Spin-Bahn-Kopplungseffekte in Graphene" (Talk CSPIN11, Dresden, Oktober 2011)

Talk (pdf)- "Magnetic barriers in graphene", talk, 2007

Talk (pdf)

# Fluctuation relations for mesoscopic nonequilibrium transport

- "Transient fluctuation relations for particle transport", talk at ESF conference in Stockhom, Sep. 2010

Talk (pdf)

# Current-induces forces in mesoscopic systems

- Talk Bad Honnef, WE Heraeus Seminar, October 2013 [pdf]

# Superconducting transport through molecular quantum dots** **

- "Superconducting molecular quantum dots", Overview talk, 2010

Talk (pdf)

# ISPI and nonequilibrium quantum transport

We have developed a numerical approach to compute real-time path integral expressions for quantum transport problems out of equilibrium. The scheme is based on a deterministic iterative summation of the path integral (ISPI) for the generating function of the nonequilibrium current. Self-energies due to the leads, being non-local in time, are fully taken into account within a finite memory time, thereby including non-Markovian effects, and numerical results are extrapolated both to vanishing (Trotter) time discretization and to infinite memory time. This extrapolation scheme converges except at very low temperatures, and the results are then numerically exact. The method is applied to nonequilibrium transport through an Anderson dot.

- "Iterative real-time path integral approach to nonequilibrium quantum transport", talk, 2008

Talk (pdf)

# Quantum transport with time-dependent voltages

See also:

- "Interaction-induced harmonic frequency mixing in quantum dots", Moriond, 2008

Talk (pdf)

# Interacting one-dimensional systems and carbon nanotubes

Electronic properties in one-dimensional metals cannot be described in terms of conventional Fermi liquid theory but instead by Luttinger liquid theory. We are interested in correlation effects in such conductors, which are especially important in transport phenomena. Recently, our theoretical prediction of Luttinger liquid behavior in carbon nanotubes has been verified in a number of experiments. Current work focuses on spin transport, scanning tunneling microscopy, and disorder effects in carbon nanotubes. Methods employed in our studies include, e.g. bosonization, refermionization, boundary conformal field theory, and quantum Monte Carlo techniques.

See also:

- Overview seminar on Spin-orbit coupling in graphene and nanotubes, DPG-Tagung, 2009

Talk (pdf) - "Transport in disordered interacting nanotubes", talk given at SCEN06, Pisa, June 2006

Talk (pdf) - Talk on Correlated Sequential Tunneling, Symposium on "Molecular Electronics", Kopenhagen 2005

Talk (pdf) - Overview seminar on Theory of electronic transport in Carbon nanotubes, Les Houches Summer School on "Nanoscopic Quantum Transport", 2004

Lecture (pdf) - Talk on Superconductivity in Nanotubes, invited talk APS March Meeting, Montreal 2004

Talk (pdf)

# Theory of ultracold atoms

We study theoretical aspects related to the behavior of ultracold atoms in confined geometries. In particular, the effects due to interactions and/or disorder are of interest in these exciting systems, where essentially full control over the system can be gained. Recent work by our group includes studies of interference in 1D Bose gases, and the complete solution of the three-body problem for binary Fermi gases in 1D confinement. This allows to characterize atom-dimer scattering processes, which are also of relevance in the theory of the Bose-Einstein-to-BCS crossover. Theoretical methods include field theory as well as exact few-body calculations (integral equations, scattering theory). For related experiments, see group of A. Görlitz.

See also:

- Talk On Disordered Interacting Systems, Conference on "Electrical and Mechanical Properties of Nanowires", Venice 2004

Talk (pdf)

# Quantum-Monte-Carlo-Simulations without sign problem

Quantum Monte Carlo (QMC) simulations are one of the most important and broadly used methods in Computational Physics. We study in particular path-integral QMC techniques, where the quantities of interest are calculated by means of stochastic averaging over all possible system paths. In many cases, e.g. for fermions or dynamical problems, a fundamental problem known as the "sign problem" significantly hinders progress. We have developed methods in order to largely circumvent this problem, which allow to carry out stable simulations in practice. Successful applications include e.g. the real-time dynamics of the dissipative two-state system (spin boson problem), the conductance of a quantum wire with impurity, and the behavior of electrons in a strongly correlated quantum dot.

See also:

- Talk on Real Time-QMC Simulation of spin-boson model, Bad Honnef 2004

Talk (pdf)

# Quantum Dots in semiconductor heterostructures

Modern nanofabrication techniques allow the investigation of artificial atoms in the 2D electron gas of semiconductor heterostructures, where N electrons are spatially confined by a (typically parabolic) confinement potential. In contrast to conventional atoms, the shallow confinement implies that one is typically in a strongly correlated regime. We have studied equilibrium properties and the Wigner crystal formation in quantum dots by a novel path-integral Monte Carlo method based on the multi-level blocking approach to the Fermion sign problem. This technique allows to circumvent the sign problem to a large degree, and enables the simulation of this problem at low temperatures.

See also:

- Talk (in German) given at SFB Kolloquium Freiburg 2003

Talk (pdf)

# Spin-Boson Systems

The spin-boson model describes a system of two (or a few) quantum states coupled with a quantum-dissipative environment. In the model, the discrete quantum system is conveniently expressed in terms of Pauli spin matrices, while the environment is modeled by an ensemble of bosonic degrees of freedom. The model thus states a very general physical problem, that arises in many different areas of physics an chemistry. Typical applications of the model in condensed matter physics include the tunneling of impurities in solids, the Kondo problem, or low temperature flux transitions on Josephson junctions. Another prominent application of the spin-boson model are electron transfer reactions in condensed phase. In that case, the electronic donor and acceptor make up the quantum system, the "spin", while the polarizable environment is modeled by a harmonic bosonic bath that couples with the electronic system. This type of reaction has been under study in our group, where we have focussed on the primary charge transfer in the photosynthetic reaction center and electron transfer in aqueous mixed valence compounds. Without a dissipative environment, the system is governed by interference between the quantum states. In an electron transfer system, that would lead to resonant tunneling between the localized states. Existence of these interference effects is called "electronic coherence". In the presence of a dissipative environment, this coherence is believed to be destroyed and the transfer is incoherent. We have currently examined this question and concluded that whether the transfer is coherent or not depends crucially on the initial preparation of system and environment. For a certain class of non-equilibrium initial preparations, our calculations based on numerically exact Quantum Monte Carlo predict electronic coherence even in strongly polar environments, like water.

# Elastic defects in crystalline and plastic materials

The scattering of electrons on a screw dislocation shows an Aharonov-Bohm effect which is caused by the stair-case topology induced by the defect in the host material. One of our present activities concerns the question of a similar behavior in the scattering of sound waves on a screw dislocation. Another project is the investigation of heterogeneous nucleation of a new phase at linear and planar elastic defects. In the driven motion of such defects we have observed wetting-like phase transitions of the comoving nuclei. Moreover, these nuclei give rise to kinetic roughening and spinodal-like instabilities of the defects. We presently consider the question whether such instabilities also occur at the surface of a growing crystal.