  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.
