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We propose and analyze a new way of using $\pi$ stacking to design molecularjunctions that either enhance or suppress a phononic heat current, but at thesame time remain conductors for an electric current. Such functionality ishighly desirable in thermoelectric energy converters, as well as in otherelectronic components where heat dissipation should be minimized or maximized.We suggest a molecular design consisting of two masses coupled to each otherwith one mass coupled to each lead. By having a small coupling (springconstant) between the masses, it is possible to either reduce, or perhaps moresurprisingly enhance the phonon conductance. We investigate a simple modelsystem to identify optimal parameter regimes and then use first principlecalculations to extract model parameters for a number of specific molecularrealizations, confirming that our proposal can indeed be realized usingstandard molecular building blocks.

Designing $\pi$-stacked molecular structures to control heat transport through molecular junctions