  Single crystals of Ba$_{1-x}$Na$_x$Fe$_2$As$_2$ with $x$ = 0, 0.25, 0.35, 0.4
were grown using a self-flux high temperature solution growth technique. The
superconducting and normal state properties were studied by temperature
dependent magnetic susceptibility, electrical resistivity and specific heat
revealing that the magnetic and structural transition is rapidly suppressed
upon Na-substitution at the Ba-site in BaFe$_2$As$_2$, giving rise to
superconductivity. A superconducting transition as high as 34 K is reached for
a Na-content of $x$=0.4. The positive Hall coefficient confirms that the
substitution of Ba by Na results in hole-doping similarly to the substitution
of Ba by K. Angle resolved photoemission spectroscopy was performed on all
Ba$_{1-x}$Na$_x$Fe$_2$As$_2$ crystals. The Fermi surface of hole-doped
Ba$_{1-x}$Na$_x$Fe$_2$As$_2$ is to high extent the same as the Fermi surface
found for the K-doped sister compounds, suggesting a similar impact of the
substitution of Ba by either K or Na on the electronic band dispersion at the
Fermi level
