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Hole-doping in BaFe$_2$As$_2$: The case of Ba$_{1-x}$Na$_x$Fe$_2$As$_2$ single crystals

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