Electron correlation and many-body effects at interfaces on semiconducting substrates



Low dimensional systems are characterized by at least one spatial dimension of only some atoms. Such size reduction has often important consequences for physical properties. Electronic correlation and electron–phonon coupling can originate Mott insulators or charge density waves (CDWs), both phenomena enhanced by dimensionality reduction. Interfaces offer a natural way of reducing the dimensionality. Among all the surfaces, semiconducting surfaces are particularly well adapted for electronic correlation studies. In them, correlation is enhanced because of the low dimension, the electronic localization in dangling bonds and the large inter-orbital distances in reconstructions. Despite these factors favoring correlation, eventually stronger than in bulk systems, the field is by far much less developed. We review here the discovery of correlated surfaces, while studying the Schottky barrier of alkalis on Si or GaAs, and coetaneous studies on SiC. We summarize then the studies on K/Si(111):B, whose equation image was considered a surface Mott insulator with an important electron-phonon coupling. The recent discovery of a equation image symmetry has been first interpreted as evidence of a bipolaronic insulator, but new findings have finally proven it to be a band insulator. We will then focus on the model system Sn/Ge(111). The last unclear issue about the (3 × 3) reconstruction at 150 K was related to the Sn 4d core level. High-resolution photoemission has clarified the core level deconvolution while refining the structural model. This metallic reconstruction is sensitive to electronic correlations which trigger a phase transition to a Mott phase below 30 K.

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 equation image reconstruction (equation image 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 equation image low energy electron diffraction (LEED) pattern (equation image 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 Tc 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 equation image, 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.

Figure 1.

Phase diagram for (3 × 3) reconstructions with a band structure similar to that of Sn/Si(111) and vanishing electron–phonon coupling. (a) Phases allowing spin non-collinearity and (b) strictly collinear phases. IM – incommensurate metallic spin density wave (SDW)/CDW, PM – paramagnetic metal, INS – insulating, A(A′) – spiral (collinear) SDW insulating phase, C(C′) – semimetallic versions of A(A′), E – metallic and magnetic phase 12.

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 Ca1.9Sr0.1RuO4 bulk Mott insulator 25 exhibits also another one. K/Si(111):B has been revisited and a new equation image reconstruction has been observed 26. Together with other evidences, it has been concluded the bipolaronic nature for the equation image interface. We will review in the following the physics of the main interfaces at semiconducting substrates with electronic correlation or many-body effects.

2 Alkalis on GaAs(110): Mott and bipolaronic insulators

Cs on GaAs(110) has been studied in detail because Cs atoms do not diffuse into GaAs, so that well-defined metal/semiconductor interfaces and Schottky barriers can be grown. Below 0.5 ML, STM shows the presence of a zig-zag chain reconstruction along the equation image direction with a local coverage of 0.5 ML 28. For coverages up to the saturation of the work function, this phase coexists with a strained phase of 0.9 ML local coverage, that covers the whole surface for saturation coverage 29. Both the zig-zag and the strained phases should be metallic, according to simple electron counting arguments. Alkali deposition fills the empty Ga surface state of the GaAs(110) surface up to 1 ML, when the system becomes ideally insulating. Ab initio calculations considering the precise structure support the metallic behavior predicted in the previous intuitive consideration 30, 31. However, photoemission and inverse photoemission show states near the valence and the conduction band 32–35, away from the Fermi level. The nonmetallicity is further confirmed by STM 28, 36, and EELS 1, 37. Figure 2 shows how the 1.40 eV substrate gap becomes slightly smaller below 0.5 ML, and above this coverage two energy losses at 0.42 and 1.04 eV appear 1. These results can be explained by observing that, according to theoretical calculations, bulk Cs (5.3 Å of interatomic distance) is near the Mott state 38. In Cs/GaAs(110), the Cs[BOND]Cs interatomic distance is even larger and so the system has been interpreted as a Mott insulator 1, 39, 40.

Figure 2.

(a) EELS series at RT as a function of coverage. (b) Structure for 0.9 ML Cs on GaAs 1, 27. Schematic picture of orbitals, charge excitation, and energy loss spectrum.

Let us consider now Na/GaAs(110). STM images show chains with two inequivalent Ga sites, giving rise to a splitted Ga surface state. With one alkali atom per two Ga dangling bonds, the lowest band is partially filled and the surface is metallic. Again, photoemission and HREELS experiments show a gap between 0.3 and 0.9 ML of Na 9, 35. In contrast to Cs/GaAs(110) there are no clearly distinct energy loses. Na/GaAs(110) has thus been explained through a surface relaxation triggered by the accumulation of two electrons within one site, despite the Coulomb repulsion 2, i.e., the manifestation of a bipolaronic insulator 9.

Cs/GaAs(110) and Na/GaAs(110) differ in their ionic radius. Na is smaller and stabilizes closer to the substrate, polarizing more the Ga atoms and increasing the electron–phonon coupling. Even if the interaction strength were insufficient to induce a bipolaronic state, it could favor electron localization and trigger a Mott transition afterwards. In such a situation, every second Na will host two electrons while the adjacent will remain empty. Na atoms may then be arranged in zig-zag chains like in Cs/GaAs(110), but only half of the Na atoms will be visible. This interpretation explains the observations in Na/GaAs(110), in particular the STM images that show linear chains further apart than in the Cs case 36.

3 SiC(0001) and electronic correlation

Coetaneously to previous studies on alkalis on GaAs, equation image and (3 × 3) reconstructions of SiC(0001) have been proposed as Mott insulators. The generally accepted structural model for the equation image reconstruction corresponds to 1/3 ML Si atoms in T4 position, i.e., above Si atoms of the last SiC bilayer. Such structure is compatible with STM images 43 and it is calculated to be the most stable 44, 45. The band structure predicts a half-filled surface state corresponding to a metallic surface (Fig. 3), but photoemission and inverse photoemission show an empty and a filled state separated by 2.0 eV with a weak bandwidth of 0.25–0.35 eV 10, 11, 46–49. STM shows that these two states have the same spatial location 50. These results have promoted the interpretation of a Mott insulator surface and calculations within the Hubbard model have been performed for U between 1.5 and 2.1 eV 41, 51–53.

The (3 × 3) reconstruction may appear either on the 3C or the 6H polytype of SiC, since both are identical up to the fourth layer. The structural model consists of Si trimers bonded to the last Si layer of the substrate and to a fourth Si adatom above, the latter being separated laterally by 9.19 Å. Photoemission and inverse photoemission show two bands separated by around 1 eV (Fig. 3) 42, which have been interpreted as the Hubbard bands of a Mott insulator. Surprisingly, Ueff is 1 eV on the (3 × 3) reconstruction while it is 2 eV on the equation image, whereas (3 × 3) surface states are less dispersive. Furthmüller et al. explained this behavior by the richer Si composition of the (3 × 3) reconstruction. Si favors a more efficient screening as dielectric constants for SiC and Si are ∼6.5 and 12, respectively 41.

4 Mott/bipolaronic insulators on K/Si(111):B

Another historic Mott insulator is K/Si(111):B surface at 1/3 ML. K is evaporated on a equation image reconstruction of Si(111) that appears when B atoms acting as bulk dopant migrate to the surface 54. We describe first the substrate in order to understand the charge transfer upon alkali adsorption.

4.1 The Si(111):B substrate

B dopant atoms migrate to the surface upon annealing and they can reach 1/3 ML on the surface, a very high concentration for bulk Si (the most highly doped substrates have a concentration of 2 × 1019 cm−3, corresponding to 0.0094 ML). The same equation image reconstruction of the substrate appears also when Si(111)-(7 × 7) is exposed to decaborane (B10H14) and annealed afterwards at 900–1000 °C to desorb hydrogen 4, 55. These two preparation methods end up with a equation image reconstruction.

The equation image reconstruction is common on Si(111) when adsorbing 1/3 ML of a group III element. Al, Ga, and In occupy T4 sites and fill the surface dangling bonds. B was expected to behave similarly, but its smaller radius would strain the neighboring Si atoms due to the small bonding distance. The high overlap of the electronic states would also induce an electronic instability. On the other hand, B decreases the strain when it is in sub-surface position by substituting one Si atom every three in the second layer (in the site known as S5), while the replaced Si occupies an adatom position directly above the B. Si transfers its electron to B and empties its dangling bond, passivating the surface, and reaching a band-insulator surface (Fig. 5) that is even more stable than the (7 × 7) reconstruction 56.

4.2 equation image and equation image reconstructions on K/Si(111):B

When K is evaporated on the equation image substrate reconstruction, the saturated surface shows a equation image LEED pattern 5, 6, 54. Such a symmetry indicates only a minor reorganization of the surface. Core level analysis supports also a small surface modification, because when K atoms are desorbed at 500 K, B 1s core level recovers its initial line shape 54. Another strong evidence comes from the valence band. The equation image reconstruction maintains the surface states associated with the Si adatom px, py backbonds with the B atom 4. K atoms should thus be adsorbed without any considerable modification of the surface at the most favorable site, which is in between two adatom dangling bonds. They are unable to break the highly stable Si[BOND]B bond, but the K 4s orbital interacts with the empty Si dangling bond and gives rise to a significant charge transfer. As the coverage of adatoms is 1/3 ML and there is no backbond modification, the alkali coverage should thus be 1/3 ML 5, which is also the coverage that minimizes the work function calculations 57.

Figure 3.

Electronic structure of the (3 × 3) reconstruction of SiC. (a) DFT-LDA calculations on 3C-SiC(111). Bulk band projection is indicated in gray. Point size is proportional to the surface localization 41. (b) Experimental dispersion for 6H-SiC(0001) 42.

One third of monolayer consists of one K atom that contributes with one electron per equation image unit cell. The surface should thus be metallic, as predicted by band theory (Fig. 4). However, neither photoemission nor inverse photoemission find states at the Fermi level (Fig. 5) 3–5. On the other hand, there are weakly dispersive occupied and unoccupied states around 600–700 meV away from the Fermi level 3, 58, 59. The unexpected gap could either appear in a Mott insulator or in a bipolaronic insulator as Na/GaAs 2, 9. Polarons may play a role in this system, because spectral features in the valence band are very broad (0.7–0.8 eV), even wider than the bandwidth. Weitering et al. evoked the Franck–Condon model to explain qualitatively the experimental width. The spectral line shape is the envelope of vibrational excitations 4, due to the strength of the electron–phonon coupling in this surface, as predicted 2, 7, 8. However, the bipolaronic state was ruled out on the first experiments because of the unobserved equation image symmetry, where every second site is empty or filled by two electrons. It was concluded that K/Si(111)-equation image was in a Mott phase 57, 58, 60, with localized electrons (and spins) on a triangular lattice. The system can thus be well adapted for studying frustration as well as exotic magnetic phases.

Figure 4.

Calculated electronic structure of (a) Si(111):B-equation image. Filled triangles, diamonds and dots correspond to theoretical surface states. Empty shapes are experimental data 56 and (b) K/Si(111):B-equation image. Band structure for K in H3 site, Si adatom in T4 and B in S5. Shadowed regions display the bulk band structure projection. Dot size is proportional to the K contribution to the total state charge 58.

However, more recently, K/Si(111):B has been revisited by Cárdenas et al. They found that a equation image structure is compatible with photoemission band foldings, and it has been explicitly observed by LEED and STM 26. A equation image also appears in other alkali adsorbed reconstructions on Si(111):B 61, where a (3 × 3) reconstruction is also present at lower coverage. The observation of the new equation image periodicity associated to the importance of electron–phonon coupling has lead to the bipolaronic nature of the reconstruction 26. In this picture, the electron–phonon coupling compensates the Coulomb repulsion and allows the double occupancy of dangling bonds. A perfect alternative of empty and double-occupied dangling bonds will thus render the system insulating. A bipolaronic insulator will thus appear on this system.

4.3 Coverage of K/Si(111):B-equation image

After the discovery of the equation image reconstruction, its atomic structure has been studied in more detail. It was a surprise not to confirm the expected 1/3 ML coverage. Moreover, a different coverage could have important consequences for the nature of the ground state, as we describe below.

Coverage calibration in surface reconstructions is always a difficult but important issue, because structure fully determines the properties of the system. One example has been the controverse on K/Si(001)-(2 × 1). STM observed chains compatible with 0.5 ML 62, whereas photoemission or photoelectron diffraction suggested 1 ML 63, 64. The difference was later explained from the difficulty in obtaining clean alkali layers, which can modify the saturation and promote another growth mode 65–67.

Disregarding contamination effects, the determination of an alkali coverage is often a difficult task. First, the sticking coefficient varies strongly near room temperature. Second, if the sample is slightly hot during the evaporation, the saturation coverage may also change 69. Alternatively, if the sample has been cooled down below RT, a second layer may even grow. An additional problem is the difficulty in estimating the coverage by STM. Imaging is difficult because alkalis induce a bonding with a W tip stronger than to Si atoms 70, 71, which easily induces tip modifications 65, 72. Moreover, alkali atoms can be invisible in STM due to their high mobility 73, 74. For instance, Na on Si(111)-(7 × 7) hops 7 × 1010 times/s at 300 K and diffuses easily 75. Na is the less mobile of alkalis and the tip can sometimes detect its movement and give rise to noisy images. On the other hand, K or Cs on Si(111)-(7 × 7) are only distinguished by a contrast change, except if they form trimers. They become then visible because their bonding changes from ionic to covalent.

Figure 5.

Angle-resolved photoemission along the equation image direction on (a) K/Si(111)-equation image and (b) the substrate Si(111)-equation image:B 4.

With all these considerations in mind, the necessity to study the K/Si(111):B-equation image coverage was evident. The well-known K/Si(111)-(3 × 1) reconstruction can be used as a reference to determine the absolute coverage of the equation image reconstruction 68. A comparative LEED and XPS study of K/Si(111):B-equation image and K/Si(111)-(3 × 1) was then performed. From the saturation on K/Si(111):B-equation image and on K/Si(111)-(3 × 1), the equation image coverage can be determined. The K 2p intensity ratio in both reconstructions is near 3/2 (Fig. 6), which indicates a 0.5 ± 20% ML coverage for the equation image, i.e., 6 ± 1 atoms per unit cell. It is puzzling why other studies on this system obtained a coverage of 0.33 ML for saturation 4. One explanation may be a difference in saturation for the work function 3, 54, 58, 59, 76 and for the core level 68, because it is known that the work function may saturate before core levels 77. However, Weitering et al. 58 found a simultaneous saturation of work function and core levels. Another possibility may be a different concentration of boron vacancies 78 or different substrate temperatures during the evaporation. Independently of the reasons of the disagreement in the saturation coverage, the equation image coverage has been determined and its structure can be understood, together with its ground state.

Figure 6.

(online color at: www.pss-a.com) K 2p in saturated surfaces of K/Si(111):B-equation image and K/Si(111)-(3 × 1). The inset shows the equation image LEED pattern 68. These data can be used to determine the coverage 68.

4.4 equation image: A band insulator

The equation image reconstruction has 6 atoms per unit cell. There are two different sites in the unit cell, as B 1s displays two components in 1:3 ratio (Fig. 7). Calculations show that the optimal structure consists of K trimers that give rise to a considerable atomic relaxation of Si adatoms 79. Two of the Si adatoms are further apart from alkalis than the others. The electronic density in these two adatoms is smaller and they maintain the substrate Si[BOND]B distance (2.16 Å). The electronic density in the other four Si adatoms is higher and they display a large vertical distortion, which explains the experimental chemical shift.

Figure 7.

(online color at: www.pss-a.com) (a) B 1s core level at  = 230 eV for 0.5 ML K/Si(111):B-equation image (top) and for Si:B (bottom). (b) Model structure for the equation image reconstruction 79.

This model predicts a band insulator as shown by photoemission and scanning tunneling spectroscopy experiments (Fig. 8). The calculations do not take into account electronic correlation, so the Mott insulator nature can be ruled out for the equation image reconstruction. The bipolaronic insulator nature would be, in principle, possible. However, the charge difference between both types of Si[BOND]B environment is only of 0.3e, far from the expected 2e for a bipolaronic insulator. The insulating nature of the K/Si(111)-equation image reconstruction has its origin in a large surface distortion opening a band gap well described in a band insulator model 79.

Figure 8.

(online color at: www.pss-a.com) (a) Theoretical density of states of K/Si(111):B-equation image projected on the different atoms. (b) Scanning tunneling spectroscopy (77 K) and photoemission spectra (equation image point, 55 K) 79.

5 Sn and Pb on Si(111) and Ge(111)

5.1 From the CDW to dynamical fluctuations

We have seen that correlated surfaces were discovered accidentally by studying Schottky barriers in alkali/semiconductor interfaces. Other abrupt surfaces that served as a model for Schottky barrier studies were Pb/Ge(111) and Pb/Si(111). 1/3 ML of Pb (or Sn) on Ge(111) or Si(111) forms a equation image reconstruction. Such a reconstruction is very common in metal/semiconductor interfaces because of the substrate symmetry. It minimizes the number of Ge dangling bonds: one adatom per unit cell reduces the number of dangling bonds by three when it is positioned in T4 position (i.e., on the threefold sites directly above second layer Ge atoms).

Surprisingly, while lowering the temperature under 100 K, a equation image symmetry change was observed on Pb/Ge(111) 21, 80. STM images showed that the equivalent Sn atoms at room temperature became inequivalent at 100 K (LT). Two different sites appeared, and the LT images of filled and empty states seemed complementary. Such observation was interpreted as indication of a weak structural modification and evidence of a charge redistribution. The system was considered as the first realization of a surface CDW on the basis of HREELS experiments, showing non-metallicity, and of ab initio calculations, where nesting seemed to be important 21. The equation image phase at RT was metallic and the (3 × 3) would be a CDW phase. The CDW was triggered by nesting followed by a gap opening induced by electronic correlation 21. A similar transition was observed at 210 K on Sn/Ge(111) 80, where physical properties are similar but the quality of the interface is better 80–82. On Sn/Ge(111), density functional theory (DFT) calculations found a negligible nesting, confirmed also by Fermi surface measurements 83, 84. The CDW was unexplained by a Peierls mechanism 80 and it was necessary to evoke correlation effects 80 and the role of defects 85–88. Defects are mainly Ge atoms substituting Sn atoms, which induce the formation of small (3 × 3) regions around them 85. Their concentration on Sn/Ge(111) is 2–5% depending on the preparation procedure 89. However, several evidences indicate that defects are not responsible of the transition. First, calculations show that defect–defect interaction is extremely localized 90, and it cannot justify an eventual defect ordering at low temperature. Second, STM studies on Pb/Si(111) have conclusively demonstrated that the transition appears also in undefected areas 91.

Other experiments showed that the RT phase with equation image symmetry and the (3 × 3) phase at 150 K have the same metallic character 22, 83, 93, 94. The strong similarity of both band structures highlighted the same atomic structure, which was also observed on the Sn 4d core level (Fig. 9). The line shape was the same for the two phases and two components were observed 22, 92, 93, 95. Two components reflect two inequivalent Sn sites 22, 92, 93, in contradiction to a flat equation image phase. Photoelectron diffraction showed also that the equation image reconstruction at RT and the (3 × 3) had the same structure 96.

Figure 9.

Pb/Ge(111): (a) Photoemission spectra along equation image for the equation image at room temperature and for the (3 × 3) at 100 K. S′ has Pb px py character whereas S1 and S2 are associated with Pb pz83. (b) Sn 4d core level for the equation image phase at room temperature and for the metallic (3 × 3) phase (0.35 ML of Sn). The lines show the three components, the fit and the residual 92.

The origin of the transition was elucidated by ab initio molecular dynamics calculations 22 and the analysis of phonon dynamics as a function of the temperature 97. At low temperature, the three Sn atoms per unit cell have two different heights. When temperature increases, the highest atoms exchange their positions with the lowest atoms while maintaining locally the (3 × 3) structure (Fig. 10). At intermediate temperatures, the oscillation is moderate, but at RT the fluctuation is so important that destroys the long-range (3 × 3) symmetry. An experimental evidence of vertical fluctuations comes from the temporal dependence of the tunnel current above Sn atoms 98. This picture is called “the dynamical fluctuations model”, similar to the dimer oscillation in Si(100) 99. At this surface, the vibration freezing explains the transition from a (2 × 1) phase at RT toward a equation image at LT 100–103. Similarly to this case, the transition on Sn/Ge(111) is due to the freezing of the soft phonon associated with the vertical vibration of Sn adatoms 104, as observed experimentally 97. Such a soft phonon is however not associated to a Peierls mechanism, as the transition is of order–disorder nature. The RT fluctuations explain STM images and LEED patterns, as these techniques observe the average position of fluctuating atoms. On the other hand, photoemission is a femtosecond sensitive technique and it observes the (3 × 3) symmetry even at RT 22, 97. Finally, it was determined that the model of the (3 × 3) phase consists of one atom of the unit cell (“up”) higher than the other two (“down”). This configuration is often called the “1U2D” model.

Figure 10.

(online color at: www.pss-a.com) Molecular dynamics simulations on Sn/Ge(111). Temporal evolution of the z coordinate (perpendicular to the surface) of the three Sn atoms of the unit cell (blue, red, and black lines) of the (3 × 3) phase at T = 125, 250, and 500 K 22.

5.2 The metallic (3 × 3) phase of Sn/Ge(111)

The 1U2D model explains the Sn 4d line shape in a non straightforward manner as we will describe below. The height difference between Sn atoms promotes a charge transfer from the “down” to the “up” atoms. The component associated with the “up” atom should thus appear at lower binding energy. On the contrary, the lower binding component comes from the two “down” atoms, with higher intensity. So, in order to explain the binding energies of the components within the 1U2D model it was necessary to introduce final state effects in the photoemission process 22, 92, 105. However, doping and X-ray standing wave experiments concluded that the low binding energy component corresponds to an electron acceptor, which should be the up atoms 106–108. As the low binding energy component of the core level is the most intense, the (3 × 3) phase should correspond to a 2U1D structure. These results were in contradiction with the established 1U2D model. However, a complementary analysis of the Fermi surface, the Sn 4d core level measured at high resolution and STM have allowed reaching a comprehensive understanding of all the observations.

The charge distribution in 1U2D and 2U1D models is very different, so the expected electronic structure is modified accordingly 109. The 1U2D structure gives rise to a filled band localized on the up atom (S1) and a half-filled band localized on the down atoms (S2) 90, 110, 111. The energetic separation between S1 and S2 depends on their height difference. When the dangling bonds of down atoms are filled, the Ge[BOND]Ge bond along (111) is reinforced while the Sn[BOND]Ge bond is weakened, so the atom rises. Simultaneously, the two other Sn atoms go down by the natural depopulation of their orbitals. The resulting bands are rather narrow (∼0.2 eV) and because of the intrasite coulomb repulsion (∼0.55 eV), correlation effects may be relevant 112. The main differences in the electronic structure of 1U2D and 2U1D models appear at the equation image point of the (3 × 3) reciprocal space 111, 113. In the 1U2D model, there is a surface state of 0.3–0.5 eV binding energy, whereas in the 2U1D model the state is empty. Moreover, only the 2U1D model shows spectral weight around equation image at the Fermi level, in contradiction with experimental observations (Fig. 11). These results support thus the 1U2D structure.

Figure 11.

(online color at: www.pss-a.com) Isoenergetic contours at the Fermi level and at 150 meV binding energy: 1U2D model (top), 2U1D model (middle), and experimental results (bottom). White (gray) points correspond to S2 (S1) surface states 84.

Figure 12 shows the Sn 4d core level. The high resolution shows that the line shape cannot be explained with the admitted number of components, i.e., a component for the “up” atoms and another for the “down” atoms. An additional component is necessary. The physical meaning of the new component becomes clearer by observing that the main three components C1, C2, and C3 have the same intensity, because they correspond to each Sn site in the unit cell. C2 and C3 are similar but different from C1. C1 is thus associated with up atoms while C2 and C3 should correspond to two inequivalent down atoms, which had never been observed previously. In this new decomposition there is therefore a component associated to each atom in the unit cell. Figure 12 shows a representative STM image indicating the two inequivalent down atoms. The introduction of the third component is therefore fully justified. This deconvolution allows to explain the apparent inconsistencies of previous results. First, it explains the core level line shape within the 1U2D model, because the low binding energy component is that of the acceptor 106, 108. Second, as the height difference between the “down” atoms is much smaller than their average difference with the “up” atom, the 1U2D description remains valid, in agreement with the previous Fermi surface analysis. So the structure of this surface is a (3 × 3) reconstruction within the 1U2D, with a fine structure of the down atoms. We have called this structure the Inequivalent Down Atoms-(3 × 3) model: IDA-(3 × 3).

Figure 12.

(online color at: www.pss-a.com) (a) Experimental Sn 4d core level (circles), as well as the fit and the four doublets of the decomposition (solid lines). (b) Empty state STM image for the (3 × 3) phase at 77 K. (c) Profiles along the directions shown in (b), showing two inequivalent down atoms 114.

5.3 Existence of a Mott transition

A new phase transition has been observed on Pb/Ge(111) around 76 K, where an ordered (3 × 3) phase changed to a disordered “glass-like” phase at LT 115. The transition has been initially explained from the competition between different interactions in a strongly correlated system. However, STM experiments have ruled out the “glasslike” transition solely observed in the occupied states, because the unoccupied states always show the (3 × 3) symmetry 91.

Correlation effects appear explicitly on Sn/Ge(111), where a reversible phase transition has been observed at ∼25 K (Fig. 13). LEED and STM show that when decreasing the temperature the (3 × 3) symmetry disappears in favor of a equation image one with equivalent Sn atoms. Concomitantly with this structural transition, a gap opens in the whole reciprocal space (Fig. 14), while LDA calculations for a equation image flat structure predict a metallic surface. On the basis of these observations, together with the importance of electronic correlation in this system, the structural and electronic changes have been interpreted as a Mott phase transition 23, 116.

Figure 13.

(online color at: www.pss-a.com) LEED patterns at 94 eV of (a) the (3 × 3) metallic phase and (b) the equation image LT phase. Circles show the (1 × 1) (green), (3 × 3) (blue), and equation image spots (red). (c) 18 × 11 nm2 STM image of the equation image phase (V = −1.4 V, I = 1.0 nA, T = 5 K). (d) 7 × 5 nm2 STM image of the (3 × 3) phase (V = −1.0 V, I = 1.0 nA, T = 112 K) and the equation image phase (V = −1.4 V, I = 1.0 nA, T = 5 K). (e) Profiles of images in (d) 23.

Figure 14.

(online color at: www.pss-a.com) Mott transition. (a) Electronic states (energy symmetrized) along equation image for (3 × 3) (left) and equation image (right). Symmetry points are those of the (3 × 3) Brillouin zone. Brighter colors correspond to more intensity 23. (b) Scheme of the Fermi surface compensation when energy is symmetrized to compare two different temperatures.

After the discovery of the first surface Mott transition, another metal-insulator transition has been observed by tunnel spectroscopy on Sn/Si(111) at 150 K 24, where the tunnel conductance dI/dV decreases at the Fermi level with the temperature lowering (Fig. 15). The system is similar to Sn/Ge, but keeps its equation image symmetry down to at least 6 K 117. Transport measurements with a four tip STM on Sn/Si have also conclusively shown that resistivity increases when temperature lowers 118 and calculations have described the phase transitions in Sn/Si and Sn/Ge as Mott transitions 119.

Figure 15.

(online color at: www.pss-a.com) (Top) Scanning tunneling spectroscopy on Sn/Si(111). The normalized differential conductance shows a gap opening as a function of temperature 24. (Bottom) STS on Sn/Ge(111) 120.

Other groups studied the Mott transition on Sn/Ge(111) and found evidences of a metallicity reduction. Morikawa et al. did not observe a equation image phase but they found a bad metal at low temperature 121. Colonna et al. performed an STS study and concluded that Sn/Ge is still metallic at LT 120. They attributed the observed equation image structure below 30 K to a tip-induced surface modification 120. However, Morikawa and Yeom did not observe such measuring artifacts 122 and Colonna et al. results show the same conductivity reduction at 5 K as the one observed in Sn/Si (Fig. 15). Another study casted doubts on the equation image phase observation because its LEED experiment contaminated the (3 × 3) surface and a equation image symmetry appeared afterwards 123. All these studies show the interest about surface Mott transitions, and how the studies on clean surfaces coincide on showing the metallicity reduction on Sn/Ge. We will explain below where are the subtle differences between the experiments.

5.4 Transition toward the Mott phase

The LT equation image phase cannot be an STM artifact or an LEED contaminated surface because we have observed its reversibility by LEED (Fig. 13) and by core level spectroscopy. The reversibility is also observed by STM for a constant current of 1 nA, where the surface recovers its initial state only by varying the temperature 124.

Figure 16 compares our STM images at 50 K with those of Morikawa et al. at 5 K. The green rectangle shows a (3 × 3) region similar to that of Morikawa et al. coexisting along the same scan line with a equation image phase indicated by the red rectangle, further indicating that the equation image phase is not a measuring artifact. While we observe these new phase at 50 K, Morikawa et al. observe it at 5 K, maybe because of a different defect concentration in the two preparations. It is known that defects play no active role in the transition but they act as nucleation centers for the (3 × 3) phases 125, so surfaces with more defects will have lower equation image transition temperatures. These images suggest that the process of the phase transition toward the Mott phase could be more complex than expected 124, which may explain the controversial results mentioned above.

Figure 16.

(online color at: www.pss-a.com) Comparison of filled states STM images of (a) Morikawa et al. (4 K) 121 and (b) our data (50 K, V = −1.0 V, I = 1.0 nA).

6 Conclusions

All the above examples show the interest of semiconducting substrates in the study of correlation effects. Many evidences demonstrate that the narrow bands associated with widely spaced dangling bonds increase the electronic localization and may drive metal[BOND]insulator transitions. The localization can be tuned by studying similar reconstructions with different lattice parameter or different adsorbate species. Doping experiments with standard surface science techniques allows further tailoring the systems and eventually relate the Mott insulators with two-dimensional superconductors 119, just as high Tc superconductors are coupled to their parent compounds. Interestingly, electronic localization is obviously related to spin localization, which may promote exotic magnetic phases, especially in triangular lattice systems prone to magnetic frustration. This allows envisioning a promising future to the research on electronic correlation and many-body effects at surfaces.


We are extremely grateful to a number of close collaborators: J. Lobo-Checa, A. Taleb-Ibrahimi, P. Le Févre, and F. Bertran for synchrotron measurements, C. Didiot and B. Kierren for STM experiments, L. Cárdenas and C. Tournier-Colletta for both photoemission and STM experiments, and L. Chaput, D.G. Trabada, J. Ortega, F. Flores and J. Merino for theoretical calculations. This work was funded by MICINN (FIS2007-64982, FIS2008-00399), SurMott ANR and CNRS PICS.

Biographical Information

Antonio Tejeda is a researcher at CNRS, the main French Research Center. He received his PhD at Autonoma University in Madrid in 2003. He worked at Denis Diderot University in Paris under a Marie Curie Fellowship, and obtained a tenure position at CNRS in 2004. Since 2008 he has been working at Lorraine University (France), where he obtained his habilitation in 2011. Moreover, he is an associated scientist to the CASSIOPEE beam line of SOLEIL synchrotron. His area of expertise are low dimensional systems, often combining structural techniques and electronic spectroscopies.

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Biographical Information

Yannick Fagot-Révurat is an assistant professor at Lorraine University (Nancy, France). He received his PhD in Physics at Joseph Fourier University (Grenoble) and was then granted by the Alexander von Humboldt foundation to study many body physics in low dimensional materials at Physikalisches Institut (Stuttgart). He joined then the Surfaces and Spectroscopies group of the Institut Jean Lamour (Nancy). His fields of interest are now structural and electronic properties of surfaces and interfaces by combining Scanning Tunneling Microscopy/Spectroscopy with Angle-Resolved Photoemission Spectroscopy including synchrotron radiation facilities.

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Biographical Information

Arantzazu Mascaraque is a professor at the Department of Material Physics at the Complutense University in Madrid (Spain). She received her PhD at the Autonoma University in Madrid in 1999 and worked at the French Synchrotron LURE in Orsay and the Technical University in Munich. In 2003 she obtained a “Ramon y Cajal” tenure contract. Her primary research interests are the study of the electronic structure of low dimensional systems in metal and oxide surfaces including Fermi Surface analysis. She is an expert in two-dimensional phase transitions using experimental techniques sensitive to both reciprocal and real space.

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