Berry-phase-induced heat pumping and its impact on the fluctuation theorem

Applying adiabatic, cyclic two-parameter modulations we investigate quantum heat transfer across an anharmonic molecular junction contacted with two heat baths. We demonstrate that the pumped heat typically exhibits a Berry-phase effect in providing an additional geometric contribution to heat flux. Remarkably, a robust fractional quantized geometric phonon response is identified as well. The presence of this geometric phase contribution in turn causes a breakdown of the fluctuation theorem of the Gallavotti-Cohen type for quantum heat transfer. This can be restored only if (i) the geometric phase contribution vanishes and if (ii) the cyclic protocol preserves the detailed balance symmetry.