Topological energy pumping in a quasiperiodically driven four-level system
Phys. Rev. B 113, 184312 – Published 11 May, 2026
DOI: https://doi.org/10.1103/prg5-3srn
Abstract
We investigate a quasiperiodically driven four-level system that serves as a temporal analog of topological phenomena found in four-band models with intertwined spin and orbital degrees of freedom. Under a two-tone drive in the strong-driving regime, the system realizes a two-dimensional synthetic Floquet lattice, thus facilitating the realization of topological energy pumping. For a temporal quantum spin Hall insulator, we find that the rates of emission and absorption of energy between the two drives are not exactly opposite for a given band. However, when contributions from two chiral symmetric partner bands are added, they become exactly opposite. This quantized rate of energy exchange is a direct consequence of propagating edge modes in the real-space model, which we further characterize by computing the spin-Chern number. Interestingly, our analysis yields a zero rate of exchange of energy between the drives for a temporally higher-order topological insulator, suggesting the presence of localized corner modes that we characterize by the mid-gap Wannier spectra. Our findings uncover the role of chiral, particle-hole, and time reversal symmetries on the energy dynamics in temporal quantum spin Hall and higher-order topological insulators. Finally, we demonstrate that the perfect (imperfect) nature of the fidelity during the time evolution of the system serves as a characteristic signature of a topological (trivial) phase.
