Electron flying over a skyrmion lattice
The merging of two magnetic whirls is described by an artificial magnetic monopole.

Research Interests

We work on a wide range of problems in modern condensed matter theory. These range from strongly correlated systems, open and driven quantum systems, topological matter, magnetic skyrmions, and many more. Our goal is to unravel new phenomena. Technically, we use a wide range of analytical and numerical methods. A sizable fraction of our work is done in close collaboration with experimental groups.

Research Highlights (updatet 6/13)

Artificial magnetic monopoles (6/13)
In a joint theoretical/experimental study we have investigated how the topology of a magnetic structure can be changed. We studied the fate of a lattice of topologically quantized magnetic whirls, so-called skyrmions (see below), when the the phase is destroyed by reducing a small external magnetic field. Our collaborators in Dresden (Peter Milde in the ???group of Lukas Eng) observed with magnetic force microscopy that the skyrmions coalesce in this process. Our simulations (see movie ) showed that a similar process occurs in the bulk, which was also confirmed by neutron scattering exeriments in the group of Christian Pfleiderer in Munich.
This phenomenon is best understood by observing that each magnetic whirl can be described by one flux quantum of an artifical magnetic field, which describes the Berry-phase forces of the magnetic whirls on electrons. The merging of skyrmions implies therefore the creation or destruction of one quantum of this artificial magnetic flux. The corresponding magnetic defect (a hedgehog defect) is can therefore be interpreted as a magnetic charge. It is an artificial magnetic monopole.
Magnetic monopoles have been postulated in 1931 by Paul Dirac as a fundamental particle to explain why electrons and protons carry electrical charges of exactly the same size. These postulated particles have never be found but are an essential element of many theories. The newly discovered artificial monopoles fulfil exactly the quantization condition of Dirac but do not solve the problem of charge quantization - they are not sources of the "real" magnetic field.
For more information, see our article in Science. Some press coverage can be found, e.g., here or in German on pro-physik.

Emergent electrodynamics of skyrmions in a chiral magnet (2/12)
In solid state physics we often observe the emergence of new degrees of freedom at low energies. These degrees of freedom are not directly encoded in the Hamiltonian but they arise "naturally" when describing low-energy excitations. In a collaborations with experimentalist from Munich, we have studied a beautiful example for this: the emergence of magnetic and electric fields. Here we are not talking about "real" electric and magnetic fields, but about "artificial" ones which arise naturally when describing the dynamics of electrons flying across a complex magnetic texture. More precisely, we study certain magnetic whirls (skyrmions, see below). Electrons flying across such whirls "feel" such an artificial magnetic field. Thus it is not surprising that when the whirls start to move, also an artificial "emergent" electric field is generated, as is well known from the Faraday effect of electromagnetism. For a more complete discussion of the interplay of topology and emergent electromagnetism, see our article in Nature Physics.

Breakdown of hydrodynamics for expanding atoms in an optical lattice (2/12)
Together with experimentalists from Munich (Bloch group), we have investigated how a cloud of atoms expands in an optical lattice. A surprising result was that the relevant hydrodynamic equations are so singular in the tails of the cloud, that the physics in these tails strongly feed backs on the center. In the experiment the different behavior of diffusive center and ballistic tails could be beautifully seen from the shape of the cloud. The article has been published in Nature Physics. For a more popular discussion (in German) see

Manipulating magnetic nano-whirls by small currents (12/10)
In a collaboration with the experimental group of Christian Pfleiderer in Munich, we have shown that periodic arrangements of a certain type of magnetic whirls (skyrmions, see see figure on right) can be manipulated with electric current using current densities more than 100.000 times smaller than in other experiments of the fields (see Science 330, 1648 (2010) or arXiv:1012.3496). These magnetic whirls couple especially efficiently to currents by an effect known under the name Berry phase: the spin of an electron flying over the skyrmion lattice adjust to the magnetic structure. The spin direction therefore performs a characteristic dance. While doing so, it picks up a quantum mechanical face which on the one hand deflects the current and on the other hand transfers a force to the magnetic structure.

Negative temperatures in optical lattices (11/10)
Nothing can be colder than the absolute minimum of temperature located at -273.15 degrees of Celsius or -459.67 degrees of Fahrenheit. Absolute temperatures, measured in Kelvin with T=0 Kelvin at the minimum of temperature, are therefore usually positive. However, the laws of thermodyna mics can also be extended to negative absolute temperatures, T < 0. They describe states which have a higher energy than an infinitely hot system: they are hotter than infinitely hot. Such states have first been realized with nuclear spins and are also important to understand lasers. Systems with negative T show many counter-intuitive phenomena. For example, to hold together a cloud of atoms at negative temperatures, one needs external forces which try to pull the cloud apart. In Phys. Rev. Lett. 105, 220405 (2010), we show theoretically how such states can be realized using ultraslow atoms captured in a lattice made out of light. We suggest that an exotic type of superfluidity can be used to identify experimentally negative temperatures using a simple imaging technique. We also discuss, how long it takes to reach equilibrium. Here it is important to realize that the essential point is that energy and particles have to be transported over large distances.
for press coverage see e.g. How to create temperatures below absolute zero, David Shiga, New Scientist, 2789, p.15 (2010). or Negative temperature, infinitely hot, Science News

Skyrmion Lattice in a Chiral Magnet (2/09)
In the early 1960th the British physicist J. Skyrme showed that a certain knot or whirl in pion fields could be interpreted as a neutron or proton. Since then, the idea of topological solitons, i.e. of stable non-linear field configurations, has been a powerful paradigm in many fields of physics. For example, corresponding whirls in the spin configuration of electrons (now called "skyrmions"), play an important role for field-effect transistors in large magnetic field showing the quantum hall effect. However, these skyrmions have only been observed indirectly. Our collegues from the group of C. Pfleiderer and P. B??ni from the TU Munich have now observed with neutron scattering a peculiar magnetic structure in the metallic magnet MnSi. Our theoretical calculations show rather unambiguously that this structure can be interpreted as a lattice of skyrmion tubes. To stabilize this strange state of matter, an important element is that MnSi crystals are chiral, i.e. the crystal and its mirror image are different. Therefore magnetic structures tend to get twisted, for example, more to the right than to the left which helps to form the skyrmions, see Science 323, 915 (2009) or arXiv:0902.1968 for more details
[see also Perspectives article by J. Zaanen, Science 323, 888 (2009),
C. Day in Physics Today 62, 12 (2009)
Spektrum der Wissenschaften
Deutschlandfunk (German national radio) in Forschung aktuell, 24.02.09, [ audio ] and in Von der Schneeflocke zum Quantencomputer, 29.8.2010, [ audio ]
An experimental proof of the topological nature of the skyrmions and the corresponding Berry phase is possible by measuring the Hall effect, see arXiv:0902.1933.

Quantum simulator for Mott transition (12/08)
In many materials an interesting effect can be observed: when the interactions are increased the system switches from a metallic state to an insulating state. The group of Immanuel Bloch in Mainz succeeded to simulate this physics by placing ultracold K atoms in an artifical lattice made of standing waves of laser light. To detect this state they observed how the radius of the atomar cloud changes when it is compressed by an external potential. The measurements where compared to our calculations (in a collaboration with T. Costi from J??lich) using the dynamical mean field theory. To our knowledge, this is also the first direct experimental text of dynamical mean field theory without using any fitting parameters. The cold atoms in the optical lattice can be described with high precision with the Hubbard model with known hopping rates and local repulsions. We expect that in future it will be possible to simulate more and more solid state phenomena (including magnetism, high-temperature superconductivity,...) using cold atoms in optical lattices.
Metallic and Insulating Phases of Repulsively Interacting Fermions in
a 3D Optical Lattice

U. Schneider, L. Hackermuller, S. Will, Th. Best, I. Bloch, T. A. Costi, R. W. Helmes,
D. Rasch, A. Rosch, Science 322, 1520 (2008) or arXiv:0809.1464
(see also Perspectives article by L. Fallani and M. Inguscio Science 322, 1480 (2008)
Deutschlandfunk (German national radio) in Forschung aktuell, 5.12.08, audio,
S. Wessel in Physik Journal 3, 20 (2009)).

for an example, how novel states of matter can be realized with atoms in optical lattices see
Metastable superfluidity of repulsive fermionic atoms in optical lattices
A. Rosch, D. Rasch, B. Binz, M. Vojta, Phys. Rev. Lett. 101, 265301 (2008) or arXiv:0809.0505