  We predict that below T_c a regime of negative differential conductivity
(NDC) can be reached. The superconductor should be supercooled to T<T_c in the
normal phase under DC voltage. In such a nonequilibrium situation the NDC of
the superconductor is created by the excess conductivity of the fluctuation
Cooper pairs. We propose NDC of supercooled superconductors to be used as an
active medium for generation of electric oscillations. Such generators can be
used in the superconducting electronics as a new type THz source of radiation.
Oscillations can be modulated by the change of the bias voltage, electrostatic
doping by a gate electrode when the superconductor is the channel of a field
effect transistor, or by light. When small amplitude oscillations are
stabilized near the critical temperature T_c the generator can be used as a
bolometer. The essential for the applications NDC is predicted by the solution
of the Boltzmann kinetic equation for the metastable in the normal phase Cooper
pairs. Boltzmann equation for fluctuation Cooper pairs is a result of
state-of-the-art application of the microscopic theory of superconductivity.
Our theoretical conclusions are based on some approximations like time
dependent Ginzburg-Landau theory, but nevertheless can reliably predict
appearance of NDC. The maximal frequency at which superconductors can operate
as generators is determined by the critical temperature \hbar omega_max ~ k_B
T_c. For high-T_c superconductors this maximal frequency falls well inside the
terahertz range. Technical conditions to avoid nucleation of the
superconducting phase are briefly discussed. We suggest that nanostructured
high-T_c superconductors patterned in a single chip can give the best technical
performance of the proposed oscillator.
