Our group performs research on theoretical aspects of quantum materials, in

particular topologically nontrivial phases of matter and applications in topological quantum information processing. Our work is embedded in the following research networks:

**DFG Sonderforschungsbereich CRC Transregio 183**

"Entangled States of Matter"

(mit Univ. zu Köln, FU Berlin, Niels Bohr Institute Copenhagen, Weizmann Institute)

http://crc183.uni-koeln.de/

**DFG Exzellenzcluster**

"Matter and Light for Quantum Computing (ML4Q)"

(mit Univ. Köln, RWTH Aachen, FZ Jülich, Univ. Bonn)

https://ml4q.de/

### Examples:

**Quantum spin liquids**

- CRC TR183 Online Conference 2020, Talk "Electrical manipulations of Kitaev quantum spin liquids" [pdf]

**Topological insulators and superconductors**

- CRC TR183 Online Workshop 2021, Talk "Driven dissipative Majorana dark states and dark spaces" [pdf]
- ML4Q Online Workshop 2021, Talk "Driven dissipative Majorana qubits" (non-technical) [pdf]
- ICTP Trieste Conference 2019, Talk "Quantum measurements of Majorana qubits" [pdf]
- Luxemburg Conference 2018, Talk "Transport in Majorana box networks" [pdf]
- Miraflores Summer School 2017, Lecture "Majorana box qubits and Majorana surface code" [pdf]
- 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]

Lectures on Youtube:

Topological Kondo Effect in Majorana Devices (Lecture 1)

Topological Kondo Effect in Majorana Devices (Lecture 2)

Topological Kondo Effect in Majorana Devices

Topological Kondo Effect in Majorana Devices - Talk "Majorana fermions" at workshop "Topology and Nonequilibrium", MPI Dresden, September 2013 [pdf]
- "Electron transport in topological insulators" (Talk, Triest, November 2011) [pdf]

**Superconducting transport through molecular quantum dots **

- Budapest Memorial Conference for A. Zawadowski 2019, Talk "Fermi liquid theory for superconducting Kondo problems" [pdf]
- "Superconducting molecular quantum dots", Overview talk, 2010 [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.

- Colloquium Prof. Pereira, HHU 2019, "From quantum spin chains to chiral spin liquids" [pdf]

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)

**Orbital ferromagnetism in Rashba dots **

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

**Graphene**

- Mathematical physics conference, Hagen, 2019, Talk "Electric dipole problem and supercriticality in graphene" [pdf]
- "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]

**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)

**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)