Anomalous Floquet topological Anderson skin effect

Sammanfattning

In modern condensed matter physics there exists a plethora of different phases of matter, which interact in a myriad of ways, and in this project we seek to understand the intersection of a few of these through a time-driven two-band model. Specifically, we are interested in investigating the interplay between Ander- son transitions and topological phases in a Floquet system, and in this pursuit we find a one dimensional topological skin effect on the boundary of a two dimensional system.The Rudner-Lidner-Berg-Levin model is a Floquet Topological insulator which functions through a simple and clever reconstruction of the quintessential aspect of a Chern insulator(the edge current) using Floquet engineering. By periodically activating and deactivating the vertices of the lattice it is able to create currents which travel around the edge of the system while leaving the bulk insulating, leading to a Chern insulating phase. Moreover, as a result of the time/energy-periodicity of a Floquet system the energy has a fundamental domain from -pi to pi and there exists an additional gap between the two bands of the system, through the -pi/pi periodic boundary, which allows for an additional kind of edge-mode which contributes inversely to the Chern number, leading to a Floquet specific topological phase; the Anomalous Floquet topological insulator(AFTI). Further complicating this patchwork of phases is the introduction of strong onsite-disorder inducing An- derson transitions, which has the effect of condensing the two topological phases of this model into a single topological phase(Anomalous Floquet Anderson Insulating(AFAI) phase), as well as disrupting the shape of the phase landscape into that of an Anderson insulator by overpowering the onsite potential in the Hamiltonian. Within the RLBL model it is also found that when an edge site is removed from the floquet operator all the states pile up around the defect similarly to the skin-effect in the Hatano-Nelson model(a non-hermitian equivalent of the Su-Schrieffer-Heeger(SSH) model), producing a one dimensional non-hermitian skin effect on the edge of this two dimensional model. When mapping this effect we find that corresponds strongly to the AFTI phase(though it exists also in the Chern insulating(CI) phase), and that under disorder it persists within the AFAI phase. In this project an array of different methods have been used to map and understand aspects of the model: momentum-space winding of bands and gaps has been used to produce a picture of the non-disordered sys- tem state and to validate the model, a real space topological invariant is used to identify the topology both with and without disorder, and direct study of the relevant observables further validates those findings. Additionally the magnetic response of the energy spectra was studied to find that it is possible to wind the AFAI and AFTI edge-energies around the spectrum, something which could possibly be used similarly to a momentum-winding invariant in disordered systems. All of these findings come together to produce a conclusive picture of the mixed order topology in unitary systems.