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.