  Divergent carrier-density fluctuations equivalent to the critical opalescence
of gas-liquid transitions emerge around a metal-insulator critical point at a
finite temperature. In contrast to the gas-liquid transitions, however, the
critical temperature can be lowered to zero, which offers a challenging quantum
phase transition. We present a microscopic description of such quantum critical
phenomena in two dimensions. The conventional scheme of phase transitions by
Ginzburg, Landau and Wilson is violated and an unconventional universality
appears. It offers a clear insight into the criticalities of metal-insulator
transitions associated with Mott or charge-order transitions. Fermi degeneracy
involving the diverging density fluctuations generates emergent phenomena near
the endpoint of the first-order transition and must shed new light on
remarkable phenomena found in correlated metals like unconventional cuprate
superconductors. It indeed accounts for otherwise puzzling criticality of the
Mott transition recently discovered in an organic conductor. We propose to
measure enhanced dielectric fluctuations at small wavenumbers by accurate
probes.
