Occupation of topological Floquet bands in open systems

Floquet topological insulators are noninteracting quantum systems that, when driven by a time-periodic field, are described by effective Hamiltonians whose bands carry nontrivial topological invariants. A longstanding question concerns the possibility of selectively populating one of these effective bands, thereby maximizing the system's resemblance to a static topological insulator. We study such Floquet systems coupled to a zero-temperature thermal reservoir that provides dissipation. We find that the resulting electronic steady states are generically characterized by a finite density of excitations above the effective ground state, even when the driving has a small amplitude and/or large frequency. We discuss the role of reservoir engineering in mitigating this problem.

Figure 1

Ambiguity in the ordering of quasienergy bands. For two quasienergy bands falling within a given strip of size $\omega$, as in (a), a gauge transformation of the form (1.3) can be used to shift the window and invert the ordering, as in (b).

Figure 2

Closed loop in a graphical representation of the state space defined by the Floquet states and the rates $R_{i\to j}$ connecting them. Blue circles represent Floquet states, and a directed arrow pointing from state $i$ to state $j$ represents the rate $R_{i\to j}$. If the condition (2.31) is satisfied around all closed loops in the graph, then the extra factors of $m_{ij}\omega$ on the links can be removed by a gauge transformation of the form (2.6), yielding a thermal quasienergy distribution.

Figure 3

Suppressing unwanted transitions between Floquet states by design of the function $g\left(E\right)$. Depleting the density of states in the neighborhood of such a transition ensures that there is no corresponding transition in the bath to compensate, essentially forbidding it.