Detectors of high-frequency radiation based on high-electron-mobility transistors benefit from low noise, room-temperature operation, and the possibility to perform radiation spectroscopy using gate-tunable plasmon resonance. Despite successful proof-of-concept demonstrations, the responsivity of transistor-based detectors of THz radiation, at present, remains fairly poor. To resolve this problem, we propose a class of devices supporting singular plasmon modes, i.e. modes with strong electric fields near keen electrodes. A large plasmon-enhanced electric field results in amplified non-linearities, and thus efficient ac-to-dc conversion. We analyze sub-terahertz detectors based on a two-dimensional electron system (2DES) in the Corbino geometry as a prototypical and exactly solvable model and show that the responsivity scales as $1/r_0^{2}$ with the radius of the inner contact $r_0$. This enables responsivities exceeding 10 kV/W at sub-THz frequencies for nanometer-scale contacts readily accessible by modern nanofabrication techniques.
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