The main areas of research performed in our Emmy Noether group are concentrated around three distinct topics: effective field theories of quantum phases of matter, the physics of Weyl nodal surfaces and universality in few-body quantum physics. For more information you can visit our group web-page here.

Effective theories in condensed matter physics

Although microscopically condensed matter physics is about interaction between electrons, protons, neutrons and light, often the many-body nature of the problem gives rise to emergence of new degrees of freedom with intriguing collective behavior at low energies. These degrees of freedom constitute the building blocks of effective field theories that in addition are constrained by symmetries of the problem. This set-up provides a reliable micro-independent framework for non-perturbative understanding of strongly interacting quantum systems. In our group we are especially interested in the interplay of topology, symmetries and geometry in quantum phases of matter. We develop and apply effective theories to various topological quantum fluids and solids.

Selected Publications:

  • Effective field theory of a vortex lattice in a bosonic superfluid, arXiv:1803.10934
  • Topological order, symmetry, and Hall response of two-dimensional spin-singlet superconductors, Phys. Rev. B 95, 014508 (2017)
  • Effective theory of chiral two-dimensional superfluids, Phys. Rev. B 89, 174507 (2014)

Weyl nodal surfaces

The advent of topological insulators in the last decade deepened our understanding of interplay of topology and symmetries in band insulators. This work culminated in the development of the ten-fold way classification of non-interacting gapped topological phases and the emergence of new symmetry protected topological phases of matter. In last years the main interest in the field shifted towards systems with band degeneracies. In three dimensions the simplest and most well-studied are Weyl (semi)metals which are distinguished by isolated pointlike two-band degeneracies in the Brillouin zone. In our group we are interested in Weyl nodal surfaces where two bands touch each other on two-dimensional surfaces in the Brillouin zone. This is a theoretical frontier of research of nodal structures in band theory with a lot of exciting unanswered questions.

  • -Weyl nodal surfaces, Phys. Rev. B 97, 075120 (2018)
  •  Coulomb-induced instabilities of nodal surfaces, arXiv:1807.09170

Universality in few-body quantum physics

In quantum mechanics three identical bosons in three dimensions interacting resonantly via a short-range two-body potential form an infinite tower of bound states, whose energy spectrum organizes itself into a geometric series accumulating at zero energy. This was discovered theoretically by Vitaly Efimov in 1970 and is known today as the Efimov effect. This effect is a beautiful example of few-body universality since it is independent of the detailed form of the interaction potential provided it is tuned to the resonance. Last decade saw a wave of interest in few-body Efimov physics which was fueled by its experimental verification in cold atom experiments. Although originally predicted to occur only in three dimensional systems with short-range resonant interactions, the Efimov physics is more general. In our group we are pushing forward the theoretical frontier of the Efimov physics focusing mainly to lower-dimensional systems.

Selected Publications:

  • Super Efimov effect of resonantly interacting fermions in two dimensions, Phys. Rev. Lett. 110, 235301 (2013)
  • Generalized Efimov effect in one dimension, Phys. Rev. Lett. 115, 180406 (2015)