Topological Floquet Anderson Insulators (TFAIs) are systems in which an interplay of topology, driving, and static disorder stabilizes a unique form of topological quantum matter. Here, the authors present a first-principles theory, describing the topological phases and quantum criticality of the two-dimensional TFAIs in symmetry class A. Within this framework, they demonstrate how disorder is key to the formation of topological quantization, and that its critical behavior is in the quantum Hall universality class.
Topological Anderson insulators (TAIs) provide a mechanism for topological phase transitions in disordered systems and have implications for quantum material design. In this work, we investigate the emergence of multiple TAIs in a one-dimensional spin-orbit coupled (SOC) chain subject to Fibonacci modulation, which transforms a trivial band structure into a sequence of topologically nontrivial phases. This behavior is characterized by the appearance of zero-energy modes and changes in the Z2 topological quantum number. As the SOC amplitude decreases, the number of TAI phases increases, a feature that is closely related to the fractal structure of the energy spectrum induced by Fibonacci modulation. In contrast to conventional TAI phases with fully localized eigenstates, the wave functions in the Fibonacci-modulated TAI phases display multifractal properties. This model can be experimentally realized using a Bose-Einstein condensate in a momentum-space lattice, where its topological transitions and multifractal features can be explored through quench dynamics. Topological Anderson insulators are quantum phases that can arise in disordered systems and are of interest for both fundamental research and future materials. Here, the authors show that applying Fibonacci modulation to a 1D spin-orbit coupled chain generates multiple topological Anderson insulator phases with multifractal wave functions, which may be observed experimentally in cold atom setups
We present an analytic theory of quantum criticality in the quasi-one-dimensional topological Anderson insulators of class AIII and BDI. We describe the systems in terms of two parameters (
g, $\ensuremath{\chi}$) representing localization and topological properties, respectively. Surfaces of half-integer valued $\ensuremath{\chi}$ define phase boundaries between distinct topological sectors. Upon increasing system size, the two parameters exhibit flow similar to the celebrated two-parameter flow describing the class
A quantum Hall insulator. However, unlike the quantum Hall system, an exact analytical description of the entire phase diagram can be given. We check the quantitative validity of our theory by comparison to numerical transfer matrix computations.