  It is expected that the color superconductivity (CSC) phase appears in QCD at
low temperature and high density. On the basis of the lattice perturbation
theory, a possible parameter region in which the CSC occurs has been predicted.
In this work, we perform complex Langevin simulation on an $8^3\times 128$
lattice using four-flavor staggered fermions. We find, in particular, that the
quark number has plateaux with respect to the chemical potential similar to our
previous study, indicating the formation of the Fermi sphere. A
diquark-antidiquark operator, which is an order parameter of color
superconductivity, is formulated on the lattice using the U(1) noise. Our
result for this operator is found to fluctuate violently when the Fermi surface
coincides with the energy levels of quarks. We also discuss partial restoration
of the chiral symmetry at high density.
