Harmonic oscillator chains connecting two harmonic reservoirs at different constant temperatures cannot act as thermal diodes, irrespective of structural asymmetry. However, here we prove that perfectly harmonic junctions can rectify heat once the reservoirs (described by white Langevin noise) are placed under temperature gradients, which are asymmetric at the two sides, an effect that we term temperature-gradient harmonic oscillator diodes. This nonlinear diode effect results from the additional constraint -- the imposed thermal gradient at the boundaries. We demonstrate the rectification behavior based on the exact analytical formulation of steady state heat transport in harmonic systems coupled to Langevin baths, which can describe quantum and classical transport, both regimes realizing the diode effect under the involved boundary conditions. Our study shows that asymmetric harmonic systems, such as room-temperature hydrocarbon molecules with varying side groups and end groups, or a linear lattice of trapped ions may rectify heat by going beyond simple boundary conditions.
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