Electron correlation effects in transport and tunneling spectroscopy of the Si(111)-$7\times 7$ surface

Electronic properties of the Si(111)-$7\times 7$ surface are studied using four- and two-probe conductivity measurements and tunneling spectroscopy. We demonstrate that the temperature dependence of the surface conductivity corresponds to the Efros-Shklovskii law at least in $10-100$~K temperature range. The energy gap at the Fermi level observed in tunneling spectroscopy measurements at $T\ge 5$~K vanishes by thermal fluctuations at $T\approx 30$~K, without any sign of the metal-insulator transition. We show that the low-temperature energy gap observed by the tunneling spectroscopy technique is actually the consequence of the Coulomb blockade effect.