Surface structure, band structure and electrical conductance of Au and Na coadsorbed Si(111)root 3x root 3 reconstruction have been studied in situ with low-energy electron diffraction, scanning tunneling microscopy, angle-resolved photoelectron spectroscopy and four-point probe technique. The Si(111)-h-root 3x root 3-(Au, Na) homogeneous structure has been detected after adsorption of 0.08-0.09 ML of sodium onto the Si(111)-alpha-root 3x root 3-Au reconstructed surface at 350 degrees C. Photoemission spectra show the details of the filling the surface state bands demonstrating the two-dimensional electron gas occurrence. Surface conductivity measurements reveal correlations with electron density changes in surface state bands and its dispersion.