  In the present paper, we return to the problem on a spontaneous generation of
the $A_0$-background field in QCD at finite temperature and include in addition
a quark chemical potential, $\mu$. We reproduce the known expressions in terms
of Bernoulli's polynomials for the gluons and quarks using the same formalism.
Then we calculate the $\mu$-dependence, both for small $\mu$ as expansion, and
numerically for finite $\mu$.
  One result is that the chemical potential only weakly changes the values of
the condensed field, but quite strongly deepens the minima of the effective
potential. The gauge dependence of the condensation is discussed in terms of
Nielsen's identity. It also is expressed in terms of Polyakov's loop. Both
these representations guarantee gauge invariance of the condensation
phenomenon. Also, we discuss the dependence of the Polyakov loop in the minimum
of the effective potential on the chemical potential.
