Paper detail

Floquet topological systems in the vicinity of band crossings: Reservoir induced coherence and steady-state entropy production

Results are presented for an open Floquet topological system represented by Dirac fermions coupled to a circularly polarized laser and an external reservoir. It is shown that when the separation between quasi-energy bands becomes small, and comparable to the coupling strength to the reservoir, the reduced density matrix in the Floquet basis, even at steady-state, has non-zero off-diagonal elements, with the magnitude of the off-diagonal elements increasing with the strength of the coupling to the reservoir. In contrast, the coupling to the reservoir only weakly affects the diagonal elements, hence inducing an effective coherence. The steady-state reduced density matrix synchronizes with the periodic drive, and a Fourier analysis allows the extraction of the occupation probabilities of the Floquet quasi-energy levels. The lack of detailed balance at steady-state is quantified in terms of an entropy production rate, and it is shown that this equals the heat current flowing out of the system, and into the reservoir. It is also shown that the entropy production rate mainly depends on the off-diagonal components of the Floquet density matrix. Thus a stronger coupling to the reservoir leads to an enhanced entropy production rate, implying a more efficient removal of heat from the system, which in turn helps the system maintain coherence. Analytic expressions in the vicinity of the Dirac point are derived which highlights these results, and also indicates how the reservoir may be engineered to enhance the coherence of the system.