Symmetry-induced even/odd parity in charge and heat pumping

It is shown that the presence of discrete symmetries in Floquet systems connected to metallic reservoirs imprints a definite parity on the charge and heat pumping as a function of the reservoir's chemical potential, $\mu$. In particular, when particle-hole symmetry (PHS) holds, the pumping of charge (heat) is an odd (even) function of $\mu$. Whereas, if only the product of PHS and parity symmetry is present, pumping of charge (heat) is even (odd) in $\mu$. Our results also extend to the presence of other unitary symmetries and provide a simple criterion for reversing (or maintaining) the direction of the flow. We illustrate our findings using two variants of the Su-Schrieffer-Heeger model under a time-periodic perturbation.