Dirac clouds around dilatonic black holes

Dirac cloud is in absence in general relativity since the superradiance mechanism fails to work for Dirac fields. For the first time we find a mechanism to support Dirac clouds in modified gravity. We study quasi bound states of Dirac particles around a charged spherical black hole in dilatonic gravity. We find that the quasi bound states become real bound states when the central black hole becomes extremal. We make an intensive study of the energy spectrum of the stationary clouds for different fine structure constant $mu M$, and reveal the existence condition of these clouds. Our result strongly implies that extreme dilatonic black holes behave as elementary particles.