Geometric Phase Effect in Heat Transport

Nonlinear molecular heat-pumping devices, which operate via explicitly modulating at least two parameters, are crucial for energy control in low dimensional nano-scale systems. We have applied slow two-parameter modulations on such a molecular junctions and consequently uncovered an intrinsic heat flux contribution, additional to the known, usual dynamical heat flux (from hot to cold). This additional heat flux derives from a nontrivial geometric origin that relates to a non-vanishing, so termed finite Berry phase. It provides a free lunch for the pumped heat and even can direct heat flux against the temperature bias. In addition we are able to show that this so pumped energy exhibits a novel robust fractional quantization phenomenon. Interestingly, this additional geometric heat pump mechanism is also shown to cause a breakdown of the heat-flux fluctuation theorem, which holds true for the non-driving, stationary heat flux transfer. The validity of this theorem is guaranteed whenever (i) the geometric phase contribution vanishes and (ii) the cyclic protocol preserves the detailed balance symmetry.