  The research of geoneutrino is a new interdisciplinary subject of particle
experiments and geo-science. Potassium-40 ($^\text{40}$K) decays contribute
roughly 1/3 of the radiogenic heat of the Earth, but it is still missing from
the experimental observation. Solar neutrino experiments with liquid
scintillators have observed uranium and thorium geoneutrinos and are the most
promising in the low-background neutrino detection. In this article, we present
the new concept of using liquid-scintillator Cherenkov detectors to detect the
neutrino-electron elastic scattering process of $^\text{40}$K geoneutrinos.
Liquid-scintillator Cherenkov detectors using a slow liquid scintillator can
achieve this goal with both energy and direction measurements for charged
particles. Given the directionality, we can significantly suppress the dominant
intrinsic background originating from solar neutrinos in conventional
liquid-scintillator detectors. We simulated the solar- and geo-neutrino
scatterings in the slow liquid scintillator detector, and implemented energy
and directional reconstructions for the recoiling electrons. We found that
$^\text{40}$K geoneutrinos can be detected with three standard deviation
accuracy in a kiloton-scale detector.
