  We demonstrate that the complex Langevin method (CLM) enables calculations in
QCD at finite density in a parameter regime in which conventional methods, such
as the density of states method and the Taylor expansion method, are not
applicable due to the severe sign problem. Here we use the plaquette gauge
action with $\beta = 5.7$ and four-flavor staggered fermions with degenerate
quark mass $m a = 0.01$ and nonzero quark chemical potential $\mu$. We confirm
that a sufficient condition for correct convergence is satisfied for $\mu /T =
5.2 - 7.2$ on a $8^3 \times 16$ lattice and $\mu /T = 1.6 - 9.6$ on a $16^3
\times 32$ lattice. In particular, the expectation value of the quark number is
found to have a plateau with respect to $\mu$ with the height of 24 for both
lattices. This plateau can be understood from the Fermi distribution of quarks,
and its height coincides with the degrees of freedom of a single quark with
zero momentum, which is 3 (color) $\times$ 4 (flavor) $\times$ 2 (spin) $=24$.
Our results may be viewed as the first step towards the formation of the Fermi
sphere, which plays a crucial role in color superconductivity conjectured from
effective theories.
