The pseudo-critical temperature of the confinement–deconfinement transition and the phase transition surface are investigated by using the complex chemical potential. We can interpret the imaginary chemical potential as the Aharonov–Bohm phase, then the analogy of the topological order suggests that the Roberge–Weiss endpoint would define the pseudo-critical temperature. The behavior of the Roberge–Weiss endpoint at small real quark chemical potential is investigated with the perturbative expansion. The expected QCD phase diagram at complex chemical potential is presented.