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At low temperature and high density, quark matter is expected to be a color superconductor(CSC). In a recent study based on lattice perturbation theory, we have found that the CSC occurs even on a lattice with a small spatial length. According to our previous study (JHEP10(2020)144), the complex Langevin method is expected to work on such a lattice without suffering from the excursion and singular drift problems. Here we perform complex Langevin simulation on an $8^3\times 128$ lattice using 4-flavor staggered fermions. We find, in particular, that the quark number has plateaux with respect to the chemical potential similarly to our previous study, indicating the formation of the Fermi sphere. Furthermore, we found that the Polyakov loop is enhanced when the Fermi surface passes through discrete points in the momentum space, as observed in two-color QCD and QCD on $S^1 \times S^3$ by Hands. et. al.. We also present some preliminary results on CSC using a diquark-antidiquark operator, which seems to agree with the prediction of lattice perturbation theory.
