Symmetry-Induced Even/Odd Parity In Charge And Heat Pumping

We study the effect of discrete symmetries on charge and heat pumping through noninteracting Floquet systems when spatial symmetry (SS) is broken. Particle-hole symmetry (PHS) implies that the pumping of charge (heat) is an odd (even) function of the chemical potential. If PHS is broken, the product of PHS and SS produces even (odd) charge (heat) pumping. Simultaneous breaking of PHS and SS can be due to the coupling to the leads, even if the latter is spatially symmetric. This provides a very simple criterion for reversing (or maintaining) the direction of the flow. We illustrate these results by considering two variants of the Su-Schrieffer-Heeger model under a time-periodic perturbation.