Physics (Internal)

Topological order: new states and new probes

This event is part of the Biophysics/Condensed Matter Seminar Series.

Since the identification of quantum Hall states as topological states of matter, the search for new topological states of matter has been a central endeavour. I will present the composite fermion theory of fractional quantum Hall states in the Hofstadter model of interacting particles on a lattice exposed to a (synthetic) magnetic field [1], providing the numerical evidence for Chern insulators [1,2]. In this model, new types of fractional quantum Hall states can be formed due to the presence of higher Chern number bands in the single-particle spectrum [2,3].

Another crucial question remains how to best probe topologically ordered phases in experiment, besides macroscopic properties such as quantised Hall conductance. I will discuss the topological marker [4] as an interesting local probe for topological order, and discuss how to use the marker to probe the critical properties of topological phase transitions, as well as its non-equilibrium dynamics after a quantum quench through the transition [5]. Finally, I will show how the topological marker can be inferred from measurements of the single-particle density matrix [5].

1.Möller, G. & Cooper, N. R. Composite Fermion Theory for Bosonic Quantum Hall States on Lattices. Phys. Rev. Lett. 103, 105303 (2009). 2.Möller, G. & Cooper, N. R. Fractional Chern Insulators in Harper-Hofstadter Bands with Higher Chern Number. Phys. Rev. Lett. 115, 126401 (2015). 3.Andrews, B. & Möller, G. Stability of fractional Chern insulators in the effective continuum limit of Harper-Hofstadter bands with Chern number |C|>1. Phys. Rev. B 97, 035159 (2018). 4.Bianco, R. & Resta, R. Mapping topological order in coordinate space. Phys. Rev. B 84, 241106 (2011). 5.Caio, M. D., Möller, G., Cooper, N. R. & Bhaseen, M. J. Topological Marker Currents in Chern Insulators, Nature Physics 315, 1 (2019).