## Introduction

I am working in the area of physics which is known as condensed matter physics. In particular, I am interested in the physics of quasi-low dimensional materials in which phase space is reduced and correlations are strong. Enhanced correlations often invalidate a single-particle picture and concepts like Landau's Fermi-liquid picture can break down. The question of when and how this happens is of particular interest. Below you find a few examples of my recent research.

## Unraveling the Mott transition in organic conductors

Preparing a good cup of tea (or coffee, if you prefer) by boiling water,
we all experience phase transitions on a daily basis. Interesting phase
transitions can also be observed in a large number of materials,
including some organic conductors. As pointed out in a recent
Letter with coauthors M. de Souza and M. Lang,
the transition from a conductor to an insulator
in some organic materials could be more liquid-gas like than previously
thought by researchers in the field. Similarly to the liquid-gas phase
transition of water, this so-called metal-to-Mott insulator transition
can be controlled in a number of organic crystals by varying temperature
and pressure. Clear signatures in the change of the crystal's volume are
expected directly at the phase transition. While a standard procedure
relates the change of the crystal volume to the amount of heat required
to change its temperature, this well-known relation is shown to break down
near a finite-temperature
critical end point, above which there is no clear distinction between
the two phases. Experiments concerned with the thermal expansion of a
BEDT-TTF-based organic crystal are described quite well by our
scaling theory, and a few predictions are made. It is now left to future
experiments to show that the liquid-gas analogy also holds for the most
critical region of the metal-to-Mott insulator transition. To find out more,
have a look at the
recommendation with a commentary by
Jörg Schmalian in the
Journal Club for Condensed Matter Physics and
read the
paper [Phys. Rev. Lett. **104**, 245701 (2010)].

## Quantum dynamics of vortices in superfluids

While the possible breakdown of Landau's Fermi liquid picture in
reduced dimensions has been apparent for a long time, it has recently
also been pointed out that not all second order quantum phase
transition nicely fit in the Landau-Ginzburg-Wilson framework. In
collaboration with Leon Balents, Anton Burkov, Subir Sachdev, and
Krishnendu Sengupta I have studied competing orders near the Bose Mott
transition in two dimensions. From a dual perspective, vortices and
antivortices are the elementary excitations of a superfluid and it is
their condensation which leads to the (Mott) insulating state.
Interestingly, if we consider bosons on a lattice at fractional filling
the condensation of vortices and antivortices automatically leads to
some kind of density wave order. This has applications to the cuprate
superconductors where scanning tunneling microscopy studies reveal a
checkerboard pattern in the tunneling density of states with a
wavelength of approximately four times the lattice spacing. This is
nicely explained within our theory which links the occurrence of the
checkerboard pattern to the closeness of these systems to a Mott
insulting state at doping 1/8 where, according to our theory, we expect
4 x 4 = 16 flavors of vortices. Details can be found in our papers, the
most important one being Phys. Rev. B **71**, 144508 (2005).

## Attractive two-component Fermi gas

Another recent discovery involves the BCS-BEC crossover of the
attractive two-component Fermi gas which due to remarkable experiments
with ultracold atoms has recently received renewed interest.
In collaboration with Nils Lerch and Peter Kopietz I have looked at the
fermionic single-particle excitations. Here we could show that even in
three dimensions the coupling of the fermionic degrees of freedom to
the gapless Bogoliubov-Anderson mode leads to the absence of well
defined Landau quasi particles. While this result is expected to hold
in the entire BCS-BEC regime including the Feshbach resonance it is
important to note that its validity hinges on the short ranged
attractive interactions. To find out more read the paper: Phys. Rev. Lett. **100**, 050403 (2008).

## Research areas

- Quantum theory of magnetism and antiferromagnetism
- Quantum critical phenomena
- High temperature superconductors
- Superfluid-insulator transition in bosonic systems
- Organic conductors
- Functional renormalization group
- Ultracold atomic gases
- Coupled chains of Luttinger liquids
- Higher dimensional Luttinger liquids
- Charge density wave materials
- Disorder and electron-electron interactions in metallic systems

## Methods

- (Higher dimensional) bosonization
- Phase formalism
- Transfer matrix method
- Functional renormalization group
- Duality mappings
- Numerical methods

## Publications

Here you can find a complete list of publications.