  The phase diagram of the two-dimensional Nambu-Jona-Lasinio (or chiral
Gross-Neveu) model is characterized by an order parameter in the form of a
chiral spiral. Its radius vanishes at a critical temperature, its period
depends only on the chemical potential. We generalize these findings to
chirally imbalanced systems by including a chiral chemical potential $\mu_5$.
The relationship between the present, static approach and a previous, time
dependent one is traced back to a half-local symmetry which the NJL$_2$ model
shares with massless Dirac fermions, but which has been neglected so far. The
structure of chiral spiral matter is further elucidated by computing fermion
and antifermion momentum distribution functions, using a Bogoliubov
transformation.
