We construct a hadron-quark two-phase model based on the Walecka-quantum hadrodynamics and the improved Polyakov-Nambu--Jona-Lasinio model with an explicit chemical potential dependence of Polyakov-loop potential ($mu$PNJL model). With respect to the original PNJL model, the confined-deconfined phase transition is largely affected at low temperature and large chemical potential. Using the two-phase model, we investigate the equilibrium transition between hadronic and quark matter at finite chemical potentials and temperatures. The numerical results show that the transition boundaries from nuclear to quark matter move towards smaller chemical potential (lower density) when the $mu$-dependent Polyakov loop potential is taken. In particular, for charge asymmetric matter, we compute the local asymmetry of $u, d$ quarks in the hadron-quark coexisting phase, and analyse the isospin-relevant observables possibly measurable in heavy-ion collision (HIC) experiments. In general new HIC data on the location and properties of the mixed phase would bring relevant information on the expected chemical potential dependence of the Polyakov Loop contribution.
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