Research interests

Current: Novel High-Temperature-Superconductors: Iron pnictides

Figure: order parameter
Possible symmetries of the order parameter in iron-based superconductors (negative: red, positive: blue)
(Hirschfeld, et al., Rep. Prog. Phys. 74, 124508 (2011))
Figure: LiFeAs: Fermi surfage, Gap
Sketch of the anisotropic order parameter in LiFeAs (ARPES measurement)
(Borisenko, et al., Symmetry 4, 251 (2012))
Although the phenomena of superconductivity has been discovered experimentally more than 100 years ago by Kammerlingh Onnes in 1911, it is still subject to recent research in experiment and theory. A possible reason is that it appears in many different materials and a physical understanding hasn't been achieved in a universal theory yet. The effect of superconductivity which simply speaking manifests itself by complete expulsion of a magnetic field (Meißner effect) and conductance of electric current without loss is due to pairing of electrons to the so-called Cooper pairs. In conventional superconductors (which become superconducting at quite low temperatures below 23K) the attractive interaction is believed to be mediated by lattice vibrations and the essential physics has been understood quite some time ago in terms of the BCS theory.
Figure: highest critical temperature as function of time
Highest critical temperatures in various materials as function of time
Figure: Fermi surface KFe2-ySe2
The Fermi surface of KFe2-ySe2 consists in 2 patches centered around the X and Y point (color code: red: dxz orbital, green: dyz orbital, blue: dxy orbital).
Figure: multiband superconductor
Model of a multiband superconductor with anisotropic order parameter and linearized dispersion.
(Wang, et al., Phys. Rev. B 87, 094504 (2013))
However, the whole understanding got screwed up by two experimental discoveries: In 1986 Bednorz and Müller discovered superconductivity in cuprate materials at such high temperatures where theoretically it shouldn't be possible within the known mechanisms. Up to now the microscopic origin of superconductivity in cuprates is still under debate whereas the materials easily entered into application due to the high transition temperatures above 100K. In 2008 Kamihara and collaborators reported superconductivity in doped iron pnictide materials which added another class of materials that are superconducting at high temperatures up to 55 K. Recently, active research has been carried out in this field because the materials show a rich phase diagram that contains an interplay between superconductivity, magnetism and crystal structure. Among the many known materials there are three compounds which are particularly interesting because they don't fit into the standard paradigm: LiFeAs, KFe2-ySe2 and FeSe (under pressure).
The main questions that we address here are the symmetry of the order parameter and how parameters make a superconductor gaped or gapless. Starting point is the so-called spin fluctuation theory of pairing where the glue of the Cooper pairs is mediated by quantum fluctuations of the electron spins.

Impurities in superconductors
Figure: spectra close to strong impurity
Spatial evolution of the spectra close to a strong impurity in the material NaCCOC
(Choubey, et al., Phys. Rev. B 96, 174523 (2017))
Impurities are often an unwanted property of crystalline systems because they destroy the strict discrete translation symmetry of a crystal. In the case of superconductors, they can however be used to probe the properties of the system. Impurities can be introduced in a controlled way by exposing the crystal to electron irradiation such that the properties of the superconducting order parameter changes as a function of impurity concentration. Another way to observe the implications on impurities is to grow crystals of iron-based superconductors in presence of small concentrations of atoms that substitute for iron atoms and then observe this on the atomic scale with the scanning tunneling microscopy technique.
Superconductivity is a phenomenon that emerges due to the quantum mechanical properties of the electrons which are described by a wavefunction. Within a interference experiment of these waves, one can reveal the structure of this state. Impurities can be used as scattering centers for these waves and the resulting interference phenomena can be observed on the microscopic scale. This method called quasiparticle interference (QPI) delivers information about the electronic system in the normal (non-superconducting) state and the superconducting state with high energetic resolution.

Investigations of the gap structure
Figure: pairing glue with orbital selective mechanism
Modification of the pairing interactions (colored arrows) within the orbital selective pairing.
(Kreisel, et al., Phys. Rev. B 95, 174504 (2017))
Proposals for the pairing mechanism that leads to superconductivity, i.e. the glue that binds together electrons to form the Cooper pairs, need to be tested towards expected structures of the order parameter. Theoretically, one starts from a microscopic model for the pairing interaction and calculates for example the excitation gap in the superconducting state. This can be measured directly with spectroscopic probes, or has imprints on thermodynamic quantities as for example specific heat. Comparison to experimental results finally can decide whether the theoretical proposal is compatible with the observations or has to be rejected.

Theory for STM
Figure: tunneling conductange close to Zn impurity
Theoretically expected tunneling conductance close to a strong impurity in Cuprates within different approximations compared to experimental observations
(Kreisel, et al., Phys. Rev. Lett. 114, 217002 (2015))
The experimental tool of scanning tunneling microscopy delivers spectacular images of conducting surfaces on the atomic scale. It has been used to examine the normal state and the superconducting state of high-Tc materials. However, these materials are layered such that the tunneling out of the surface needs to take into account the wave function of the electronic state when calculating tunneling with sub-atomic resolution.

Dissertation: Spin-wave calculations for Heisenberg magnets with reduced symmetry

Figure: Feynman diagrams
Corrections to the self energy in second order of the 3-point magnon vertices of the Goldstone magnon
(Dissertation)
Figure: dispersion of quasiparticles
Kinematics determines the possibility of quasiparticle decay: stable quasi particles (left), unstable quasiparticles (right) upon inclusion of 3 magnon scattering
(Dissertation)
The phenomenon of magnetism is a pure quantum effect and has been studied since the beginning of civilization. The practical use of magnetic materials for technical purposes was well established in the 19th century; still nowadays there is no lack of new high-tech applications based on magnetism for example in information technology to store and process data.
Figure: YIG crystal structure
Crystal structure of YIG
(Dissertation)
Figure: dispersion of magnons
Spin-wave dispersion of the lowest magnon mode in a YIG film: A Bose condensate evolves at the minimum of the dispersion and imposes additional condensates at odd multiples of the momentum at the minimum
(Dissertation)
This thesis does not focus on the development of new applications of magnetism in technology, nor enhancement of known fields of application. Instead, the intention is to use a quantum theory of magnetism for obtaining new insights on physical effects that accompany the phenomenon of magnetism. Therefore three different model systems, each of which are believed to describe a class of real compounds, are considered. Starting from the idea that magnetism can be understood by use of the so-called Heisenberg model that microscopically characterizes the interaction between localized magnetic moments, we restrict ourselves to the case where a long-range magnetic order is present. In order to deduce consequences resulting from this microscopic picture we use the spin-wave theory that is introduced in the first chapter. Central objects of this theory are the magnons which are elementary quantum excitations in ordered magnets.
Figure: magnon dispersion
Measured spectrum in YIG for spinwaves traveling parallel to the external magnetic field
(Dissertation)
An application of these mathematical techniques to a model that describes an antiferromagnet in an external magnetic field is presented in the second chapter. Quantities like the spin-wave velocity and the damping of magnons are calculated using a Hermitian operator approach in the framework of spin-wave theory. A strong renormalization of the magnetic excitations arises because the symmetry of the system is reduced due to the external magnetic field.
Figure: classical ground state
Classical ground state of a frustrated anti-ferromagnet with anisotropy (model for Cesium-Copper-cloride)
(Dissertation)
In the second model system, that describes thin films of a ferromagnet, concepts of classical physics meet quantum physics: The magnetic dipole-dipole interaction that is also known in everyday life from the magnetic forces between magnets and was initially formulated in the theory of electromagnetism, is included in the microscopic model. Having a special compound in mind where the magnetic excitations are directly accessible in experiments, the energy dispersions of magnon modes in thin-film ferromagnets are deduced. Our approach is essentially a basis for further investigations beyond this thesis to describe strong correlations and condensation of magnons. A recent realization of data processing devices with spin waves puts the understanding of physical processes in these ferromagnetic films in the focus of upcoming research.
Figure: sound velocity
Sound velocity and damping in Cesium-Copper-cloride as a function of the external magnetic field
(Dissertation)
Figure: Pulse-echo technique
Measurement of the sound velocity and damping in a crystal using the pulse-echo technique
(Disputation)
The third model system brings in the so-called frustration where the interactions between the spins are such that the total energy cannot be minimized by an appropriate alignment of the magnetic moments in the classical picture. In the simplest case this appears because the antiferromagnetically coupled spins are located on a triangular lattice. This situation will lead to strong quantum fluctuations which make this model system interesting. Finally the overall symmetry is reduced by inclusion of spin anisotropies and an external magnetic field. Instead of focusing on the properties of the magnetic excitations, the effect of the magnetic field on the properties of the lattice vibrations is subject to the investigation. This is interesting because the characteristics of lattice vibrations can be measured experimentally using the supersonic technique.

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Diploma thesis: Spin-wave interactions in quantum antiferromagnets

Figure: spin wave in a ferromagnet
Spin wave in a ferromagnet
(Diploma thesis)
Figure: staggered structure factor
Staggered structure factor of an anti-ferromagnet in arbitrary dimension
(Diploma thesis)
Magnetic properties of materials are well known since the days of antiquity when the Greeks described the ion ore. These materials called ferromagnets are widely used in our everyday life for example in electric apparatus. In ferromagnets the magnetic moments of the atoms involved are aligned in a parallel way. Therefore one can observe an macroscopic magnetization outside the solid.
Figure: spontaneous symmetry breaking
Order parameter emerging at spontaneous symmetry breaking described in Hermitean parametrization
(Diploma thesis)
Figure: self energy
Diagrammatic visualization of the corrections to the self energy in Hermitean parametrization
(Diploma thesis)
In the case of the anti-ferromagnet this is different: An anti parallel alignment leads to a cancellation of the total magnetic moment and it is not possible to directly observe magnetic forces. These materials are nevertheless featuring properties due to the underlying magnetism. I calculated some of these properties in my diploma thesis.
content (German only)
diploma thesis (German only)

Research Stays Abroad


  • 09/2008-10/2008, 10/2009-11/2009 International Center for Condensed Matter Physics - ICCMP at Universidade de Brasília in Brasília, Brazil.
  • 09/2010-10/2010, 12/2011 International Institute of Physics - IIP at Universidade Federal do Rio Grande do Norte in Natal, Brazil.
  • 11/2014 Kavli Institute for Theoretical Physics KITP at University of California Santa Barbara, CA, USA.