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  1. Free, publicly-accessible full text available March 18, 2023
  2. Abstract We study a Morita-equivalent version of the Zariski cancellation problem.
  3. Light emission from biased tunnel junctions has recently gained much attention owing to its unique potential to create ultracompact optical sources with terahertz modulation bandwidth1,2,3,4,5. The emission originates from an inelastic electron tunnelling process in which electronic energy is transferred to surface plasmon polaritons and subsequently converted to radiation photons by an optical antenna. Because most of the electrons tunnel elastically, the emission efficiency is typically about 10−5–10−4. Here, we demonstrate efficient light generation from enhanced inelastic tunnelling using nanocrystals assembled into metal–insulator–metal junctions. The colour of the emitted light is determined by the optical antenna and thus can be tuned by the geometry of the junction structures. The efficiency of far-field free-space light generation reaches ~2%, showing an improvement of two orders of magnitude over previous work3,4. This brings on-chip ultrafast and ultracompact light sources one step closer to reality.