  We study theoretically proximity-induced superconductivity and its inverse
effect in dice lattice flat band model by considering Josephson junction with
an s-wave pairing in the superconducting leads. Using self-consistent
tight-binding Bogoliubov-de Gennes method, we show that there is a critical
value for chemical potential of the superconductors depending on paring
interaction strength over which for undoped normal region the proximity effect
is enhanced. Whereas if the superconductor chemical potential is less than the
critical one the proximity effect decreases regardless of normal region doping
and in the meanwhile, the pairing amplitude of superconducting region increases
significantly. Furthermore, we unveil that the supercurrent passing through the
junction is large (vanishingly small) when the superconductor chemical
potential is smaller (larger) than the critical value which increases as a
function of normal region chemical potential.
