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.