  We investigate heat transport between two thermal reservoirs that are coupled
via a large spin composed of N identical two level systems. One coupling
implements the dissipative Dicke super- radiance. The other coupling is locally
of the pure-dephasing type and requires to go beyond the standard weak-coupling
limit by employing a Bogoliubov mapping in the corresponding reservoir. After
the mapping, the large spin is coupled to a collective mode with the original
pure-dephasing interaction, but the collective mode is dissipatively coupled to
the residual oscillators. Treating the large spin and the collective mode as
the system, a standard master equation approach is now able to capture the
energy transfer between the two reservoirs. Assuming fast relaxation of the
collective mode, we derive a coarse-grained rate equation for the large spin
only and discuss how the original Dicke superradiance is affected by the
presence of the additional reservoir. Our main finding is a cooperatively
enhanced rectification effect due to the interplay of supertransmittant heat
currents (scaling quadratically with $N$) and the asymmetric coupling to both
reservoirs. For large $N$, the system can thus significantly amplify current
asymmetries under bias reversal, functioning as a heat diode. We also briefly
discuss the case when the couplings of the collective spin are locally
dissipative, showing that the heat-diode effect is still present.

Mesoscale and Nanoscale Physics;Statistical Mechanics;Quantum Physics