## 1 Discovery of correlated surfaces

Correlated surfaces were discovered in the 1980s during studies on metal/semiconductor interfaces aimed at understanding the microscopic details of the Schottky barrier. Alkali metals induce a considerable work function reduction and their sole s electron should in principle simplify calculations. It was therefore natural to study the Schottky barrier on GaAs(110) because its direct gap favored optical applications. DiNardo et al. deposited Cs over GaAs(110) and they found an inconsistency between the predicted metallicity and the observed insulating character. They therefore concluded that the system was a surface Mott insulator 1. Some years later, Pankratov and Scheffler studied theoretically the alkali adsorption on GaAs and they pointed out that the electronic localization in this system might come from the electronic correlation or from a strong electron–lattice interaction with bipolaron formation 2.

Concomitantly with these studies, other researches focused on Si and on SiC. Boron is a usual dopant in Si that induces a reconstruction ( in the following) on the (111) face when it migrates to the surface in the correct concentration. Such a reconstruction involves only one adatom, simplifying the analysis of metal/semiconductor interfaces with respect to the complex Si(111)-(7 × 7) reconstruction. In one of these studies, Grehk et al. observed that K/Si(111):B was insulating with a localized state at 0.7 eV from the Fermi level 3. Weitering et al. interpreted afterwards this system as a Mott insulator 4–6. Moreover, from the large spectral width of the surface state they stated the non-negligible electron–phonon coupling, *i.e*., the importance of polarons. Such a coupling had already been proposed theoretically for Si 7, 8 and it seems to stabilize a bipolaronic insulator in the polar surface of Na/GaAs(110) 2, 9. Although a bipolaronic ground state was evoked, it was excluded because of the absence of a low energy electron diffraction (LEED) pattern ( in the following) up to the saturation coverage. Similar studies on SiC found that some SiC reconstructions that according to theoretical models should be metallic, were indeed insulating 10, 11.

Most known Mott insulators at that time where d electron systems, as NiO or the parent compounds of high *T*_{c} superconductors. Correlated surfaces were at their earliest stages, though as it could have been foreseen, correlation effects play an important role at surfaces. The effective Coulomb repulsion can be ∼1 eV for an ideal Si(111) surface 13, 14 whereas the bandwidth is often less than 1 eV. Several factors in semiconducting surfaces increase the electronic localization and reduce the bandwidth: the dimensionality reduction that lowers the number of neighbors, and surface reconstructions, which promote longer distances between adatoms. Interestingly, the hopping constant *t* varies as , where *D* is the distance between adatoms 13, so it may be possible to induce Mott transitions as a function of the coverage when it controls the adatom–adatom distance. Surface Mott transitions remained however unobserved, probably because all observed correlated surfaces were stable Mott insulators where temperature increasing destroys the surface reconstruction.

Theoretical studies on electronic correlations and possible Mott phases have been performed on the famous (7 × 7) reconstruction of Si(111) 15, 16, where correlations are almost strong enough to favor a Mott transition. Some experiments have found traces of such an insulating behavior by tunnel spectroscopy 17, photoemission 18, and four-tip STM 19. Correlation effects have also been predicted in Pb/Ge(111), Sn/Ge(111), or Sn/Si(111) 20. These systems have deserved a particular attention since the discovery of a transition around 150 K interpreted as the first realization of a surface charge density wave (CDW) 21. Even if the transition has revealed to be of order–disorder nature 22, correlation effects had been highlighted. The calculated phase diagram in these systems is particularly complex. Figure 1 shows the variety of fundamental states of Sn/Si(111) as a function of intrasite (*U*) and intersite (*V*) electronic correlation. Depending on *U* and *V*, metallic, insulating, magnetic, and non-magnetic phases may appear.

More recently, several studies have renewed the interest in these systems. Sn/Ge(111) has allowed observing the first surface Mott transition 23, and soon after, Sn/Si(111) has shown another 24. The surface of Ca_{1.9}Sr_{0.1}RuO_{4} bulk Mott insulator 25 exhibits also another one. K/Si(111):B has been revisited and a new reconstruction has been observed 26. Together with other evidences, it has been concluded the bipolaronic nature for the interface. We will review in the following the physics of the main interfaces at semiconducting substrates with electronic correlation or many-body effects.