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We introduce a new thermal transport phenomenon, a unidirectionalselection-rule blockade, and show how it produces unprecedented rectificationof bosonic heat flow through molecular or mesoscopic quantum systems.Rectification arises from the quantization of energy levels of the conductionelement and selection rules of reservoir coupling operators. The simplestsystem exhibiting the selection-rule blockade is an appropriately coupledthree-level system, providing a candidate for a high-performance heat diode. Wepresent an analytical treatment of the transport problem and discuss how thephenomenon generalizes to multilevel systems.

Selection-rule blockade and rectification in quantum heat transport