  The Berezinskii-Kosterlitz-Thouless (BKT) mechanism describes the breakdown
of superfluidity in a two-dimensional Bose gas or a two-dimensional gas of
paired fermions. In the latter case, a population imbalance between the two
pairing partners in the Fermi mixture is known to influence pairing
characteristics. Here, we investigate the effects of imbalance on the
two-dimensional BKT superfluid transition, and show that superfluidity is even
more sensitive to imbalance than for three dimensional systems.
Finite-temperature phase diagrams are derived using the functional integral
formalism in combination with a hydrodynamic action functional for the phase
fluctuations. This allow to identify a phase separation region and tricritical
points due to imbalance. In contrast to superfluidity in the three-dimensional
case, the effect of imbalance is also pronounced in the strong-coupling regime.
