Charged pion condensation under parallel electromagnetic fields

The formation of charged pion condensate under parallel electromagnetic fields is studied within the two-flavor Nambu--Jona-Lasinio model. The technique of Schwinger proper time method is extended to explore the quantity locating in the off-diagonal flavor space, i.e., charged pion. We obtain the associated effective potential as a function of the strength of the electromagnetic fields and find out that it contains a sextic term which possibly induce weakly first order phase transition. Dependence of pion condensation on model parameters is investigated.