Non-equilibrium dynamics of topological insulatorsUlčakar, Lara (Avtor) Rejec, Tomaž (Mentor) Mravlje, Jernej (Komentor) topological insulatorquantum phase transitiontime-reversal symmetryquenchKibble-Zurek mechanismLandau-Zener modelHall effectedge statetopological invariantlocal Chern markercritical exponentTopological insulators are band insulators with a non-trivial band topology that leads to the presence of in-gap edge states at the boundaries and the associated dissipationless transport. The thesis is focused on non-equilibrium behaviour that arises when a topological insulator is slowly quenched, i.e. is smoothly driven across a topological phase transition. We study a Chern insulator, represented by the Qi-Wu-Zhang model, and a time-reversal symmetric topological insulator, described by the Bernevig-Hughes-Zhang model, and find similar non-equilibrium transport. For slow quenches, the (spin) Hall conductivity approaches that of the final ground state. The deviations from this value diminish as a power-law as the quench becomes slow, which is consistent with the Kibble-Zurek prediction. Conversely, the behaviour of topological invariants differs. The Chern number is conserved under a unitary evolution, while the classification of time-reversal symmetric phases breaks down since the time evolution dynamically breaks the time-reversal symmetry. We also investigate a Chern insulator in ribbon geometry and show that after the system is driven from a trivial to a topological phase, the in-gap states emerge and are populated with electrons. As the Chern invariant remains unchanged, the bulk-boundary correspondence is broken. In order to explore the critical properties and the non-equilibrium dynamics in real space, we introduce a weak disorder to a Chern insulator. In the ground state, the local Chern marker exhibits a critical length scale in its inhomogeneous profile that behaves consistently with the one extracted from the width of the peak in the Berry curvature. During the quench, the length scale grows and saturates to a value that increases with the quench time, as predicted by the Kibble-Zurek mechanism.20202020-12-02 08:15:09Doktorsko delo/naloga122256sl