# Friday 06 Jun 2014: Colloquium: Topological states in condensed matter and optical lattices

### Prof. Cristiane de Morais Smith - Utrecht University, Netherlands

**Newman Red** 12:00-13:00

Condensed-matter physics in the 19th century was concerned with the description of classical states of matter, like gas, liquid, or solid, and their phase transitions. In the 20th century, more exotic states of matter were discovered: superfluids and superconductors, Bose-Einstein condensates, and quantum Hall fluids. These systems are characterized by more complex order parameters and a dissipation-less flow of matter.

Here, I will discuss some properties of quantum Hall fluids, more specifically the so-called topological insulators, which exhibit a dissipation-less quantized spin-current. The current is generated by a coupling between the spin and the momentum of the electrons (spin-orbit interaction) and is protected by a topological invariant, i.e., it depends only on the topology of the material and not on its microscopic details. This quantized Hall spin-current is analogous to the quantized charge current that occurs in semiconductors, in the quantum Hall regime [1].

The recent realization of "synthetic graphene" by the self-assembling of semiconducting nano-crystals into a honeycomb lattice has opened new perspectives into the realization of topological materials in condensed matter [2]. By choosing the chemical elements in the nanocrystal, the spin-orbit coupling can be tuned to a great extent, thus allowing us to engineer new materials that could be useful for technological applications.

Topological states of matter are being studied not only in condensed matter, but also in quantum optics. By loading ultracold fermions or bosons into optical lattices, it is possible to simulate cond-mat systems, thus custom tailoring model Hamiltonians which are supposed to describe complex quantum systems. The recent experimental realization of a $p_x + i p_y$ Bose-Einstein condensate of Rb in a 2D optical lattice, for which time-reversal symmetry is spontaneously broken, is a fascinating example of the numerous possibilities to be explored with those systems [3].

[1] N. Goldman, W. Beugeling, and C. Morais Smith, EPL 97, 23003 (2012).

[2] E. Kalesaki, C. Delerue, C. Morais Smith, W. Beugeling, G. Allen, and D. Vanmaekelbergh, PRX 4, 011010 (2014).

[3] M. Ölschläger, T. Kock, G. Wirth, A. Ewerbeck, C. Morais Smith and A Hemmerich, New Journal Phys.15, 083041 (2013).