  The shear viscosity plays an important role in studies of transport phenomena
in ultracold Fermi gases and serves as a diagnostic of various microscopic
theories. Due to the complicated phase structures of population-imbalanced
Fermi gases, past works mainly focus on unpolarized Fermi gases. Here we
investigate the shear viscosity of homogeneous, population-imbalanced Fermi
gases with tunable attractive interactions at finite temperatures by using a
pairing fluctuation theory for thermodynamical quantities and a gauge-invariant
linear response theory for transport coefficients. In the unitary and BEC
regimes, the shear viscosity increases with the polarization because the excess
majority fermions cause gapless excitations acting like a normal fluid. In the
weak BEC regime the excess fermions also suppress the noncondensed pairs at low
polarization, and we found a minimum in the ratio of shear viscosity and
relaxation time. To help constrain the relaxation time from linear response
theory, we derive an exact relation connecting some thermodynamic quantities
and transport coefficients at the mean-field level for unitary Fermi
superfluids with population imbalance. An approximate relation beyond
mean-field theory is proposed and only exhibits mild deviations from numerical
results.
