Triangular Mott-Hubbard insulator phases of Sn/Si(111) and Sn/Ge(111) surfaces

Superconductivity in a Hole-Doped Mott-Insulating Triangular Adatom Layer on a Silicon Surface

Adsorption of one-third monolayer of Sn on an atomically clean Si(111) substrate produces a two-dimensional triangular adatom lattice with one unpaired electron per site. This dilute adatom reconstruction is an antiferromagnetic Mott insulator; however, the system can be modulation doped and metallized using heavily doped p-type Si(111) substrates. Here, we show that the hole-doped dilute adatom layer on a degenerately doped p-type Si(111) wafer is superconducting with a critical temperature of 4.7±0.3  K. While a phonon-mediated coupling scenario would be consistent with the observed T_{c}, Mott correlations in the Sn-derived dangling-bond surface state could suppress the s-wave pairing channel. The latter suggests that the superconductivity in this triangular adatom lattice may be unconventional.

Correlation-Driven Charge Order in a Frustrated Two-Dimensional Atom Lattice

We thoroughly examine the ground state of the triangular lattice of Pb on Si(111) using scanning tunneling microscopy and spectroscopy. We detect electronic charge order, and disentangle this contribution from the atomic configuration which we find to be 1-down-2-up, contrary to previous predictions from density functional theory. Applying an extended variational cluster approach we map out the phase diagram as a function of local and nonlocal Coulomb interactions. Comparing the experimental data with the theoretical modeling leads us to conclude that electron correlations are the driving force of the charge-ordered state in Pb/Si(111). These results resolve the discussion about the origin of the well-known 3×3 reconstruction. By exploiting the tunability of correlation strength, hopping parameters, and band filling, this material class represents a promising platform to search for exotic states of matter, in particular, for chiral topological superconductivity.

Observation of the nesting and defect-driven 1D incommensurate charge density waves phase in the 2D system

We report on the low-temperature scanning tunneling microscopy/spectroscopy (STM/STS) study of the (Bi, Na)/Si(1 1 1)[Formula: see text] reconstruction that is known to possess Fermi surface with apparently good nesting. We found that defects on this surface produce a one-dimensional-like pattern with the periodicity of 8.2 [Formula: see text] 0.4 [Formula: see text] that is incommensurate with the [Formula: see text] lattice period. The [Formula: see text] mapping analysis reveals an occurrence of the k-dependent branch associated with quasi-particle interference and the k-independent branch associated with the nesting vector connecting the parallel segments of the (Bi,Na)/Si(1 1 1)[Formula: see text] Fermi surface, the fingerprint of the charge-density-wave (CDW) phase. The STS data demonstrates that development of the CDW phase leads to reducing electron density of states at the Fermi level.

Chiral Spin Texture in the Charge-Density-Wave Phase of the Correlated Metallic Pb/Si(111) Monolayer

We investigate the 1/3 monolayer α-Pb/Si(111) surface by scanning tunneling spectroscopy (STS) and fully relativistic first-principles calculations. We study both the high-temperature sqrt[3]×sqrt[3] and low-temperature 3×3 reconstructions and show that, in both phases, the spin-orbit interaction leads to an energy splitting as large as 25% of the valence-band bandwidth. Relativistic effects, electronic correlations, and Pb-substrate interaction cooperate to stabilize a correlated low-temperature paramagnetic phase with well-developed lower and upper Hubbard bands coexisting with 3×3 periodicity. By comparing the Fourier transform of STS conductance maps at the Fermi level with calculated quasiparticle interference from nonmagnetic impurities, we demonstrate the occurrence of two large hexagonal Fermi sheets with in-plane spin polarizations and opposite helicities.

Realization of a Hole-Doped Mott Insulator on a Triangular Silicon Lattice

The physics of doped Mott insulators is at the heart of some of the most exotic physical phenomena in materials research including insulator-metal transitions, colossal magnetoresistance, and high-temperature superconductivity in layered perovskite compounds. Advances in this field would greatly benefit from the availability of new material systems with a similar richness of physical phenomena but with fewer chemical and structural complications in comparison to oxides. Using scanning tunneling microscopy and spectroscopy, we show that such a system can be realized on a silicon platform. The adsorption of one-third monolayer of Sn atoms on a Si(111) surface produces a triangular surface lattice with half filled dangling bond orbitals. Modulation hole doping of these dangling bonds unveils clear hallmarks of Mott physics, such as spectral weight transfer and the formation of quasiparticle states at the Fermi level, well-defined Fermi contour segments, and a sharp singularity in the density of states. These observations are remarkably similar to those made in complex oxide materials, including high-temperature superconductors, but highly extraordinary within the realm of conventional sp-bonded semiconductor materials. It suggests that exotic quantum matter phases can be realized and engineered on silicon-based materials platforms.

Hidden phase in a two-dimensional Sn layer stabilized by modulation hole doping

Semiconductor surfaces and ultrathin interfaces exhibit an interesting variety of two-dimensional quantum matter phases, such as charge density waves, spin density waves and superconducting condensates. Yet, the electronic properties of these broken symmetry phases are extremely difficult to control due to the inherent difficulty of doping a strictly two-dimensional material without introducing chemical disorder. Here we successfully exploit a modulation doping scheme to uncover, in conjunction with a scanning tunnelling microscope tip-assist, a hidden equilibrium phase in a hole-doped bilayer of Sn on Si(111). This new phase is intrinsically phase separated into insulating domains with polar and nonpolar symmetries. Its formation involves a spontaneous symmetry breaking process that appears to be electronically driven, notwithstanding the lack of metallicity in this system. This modulation doping approach allows access to novel phases of matter, promising new avenues for exploring competing quantum matter phases on a silicon platform.

Broken symmetry phases may occur in 2D materials upon doping, yet introducing doping without inducing chemical disorder remains a challenge. Here, the authors use a modulation doping approach that unveils a hidden equilibrium phase involving spontaneous symmetry breaking in a hole-doped Sn bilayer.

Nature of the Insulating Ground State of the Two-Dimensional Sn Atom Lattice on SiC(0001)

Semiconductor surfaces with narrow surface bands provide unique playgrounds to search for Mott-insulating state. Recently, a combined experimental and theoretical study of the two-dimensional (2D) Sn atom lattice on a wide-gap SiC(0001) substrate proposed a Mott-type insulator driven by strong on-site Coulomb repulsion U within a single-band Hubbard model. However, our systematic density-functional theory (DFT) study with local, semilocal, and hybrid exchange-correlation functionals shows that the Sn dangling-bond state largely hybridizes with the substrate Si 3p and C 2p states to split into three surface bands due to the crystal field. Such a hybridization gives rise to the stabilization of the antiferromagnetic order via superexchange interactions. The band gap and the density of states predicted by the hybrid DFT calculation agree well with photoemission data. Our findings not only suggest that the Sn/SiC(0001) system can be represented as a Slater-type insulator driven by long-range magnetism, but also have an implication that taking into account long-range interactions beyond the on-site interaction would be of importance for properly describing the insulating nature of Sn/SiC(0001).

Uncertainty principle for experimental measurements: Fast versus slow probes

The result of a physical measurement depends on the time scale of the experimental probe. In solid-state systems, this simple quantum mechanical principle has far-reaching consequences: the interplay of several degrees of freedom close to charge, spin or orbital instabilities combined with the disparity of the time scales associated to their fluctuations can lead to seemingly contradictory experimental findings. A particularly striking example is provided by systems of adatoms adsorbed on semiconductor surfaces where different experiments--angle-resolved photoemission, scanning tunneling microscopy and core-level spectroscopy--suggest different ordering phenomena. Using most recent first principles many-body techniques, we resolve this puzzle by invoking the time scales of fluctuations when approaching the different instabilities. These findings suggest a re-interpretation of ordering phenomena and their fluctuations in a wide class of solid-state systems ranging from organic materials to high-temperature superconducting cuprates.

Ultrafast Atomic Diffusion Inducing a Reversible (2sqrt[3]×2sqrt[3])R30°↔(sqrt[3]×sqrt[3])R30° Transition on Sn/Si(111)∶B

Dynamical phase transitions are a challenge to identify experimentally and describe theoretically. Here, we study a new reconstruction of Sn on silicon and observe a reversible transition where the surface unit cell divides its area by a factor of 4 at 250 °C. This phase transition is explained by the 24-fold degeneracy of the ground state and a novel diffusive mechanism, where four Sn atoms arranged in a snakelike cluster wiggle at the surface exploring collectively the different quantum mechanical ground states.

Dynamical screening effects in correlated electron materials-a progress report on combined many-body perturbation and dynamical mean field theory: 'GW + DMFT'

We give a summary of recent progress in the field of electronic structure calculations for materials with strong electronic Coulomb correlations. The discussion focuses on developments beyond the by now well established combination of density functional and dynamical mean field theory dubbed 'LDA + DMFT'. It is organized around the description of dynamical screening effects in the solid. Indeed, screening in the solid gives rise to dynamical local Coulomb interactions U(ω) (Aryasetiawan et al 2004 Phys. Rev. B 70 195104), and this frequency dependence leads to effects that cannot be neglected in a truly first principles description. We review the recently introduced extension of LDA + DMFT to dynamical local Coulomb interactions 'LDA + U(ω) + DMFT' (Casula et al 2012 Phys. Rev. B 85 035115, Werner et al 2012 Nature Phys. 1745-2481). A reliable description of dynamical screening effects is also a central ingredient of the 'GW + DMFT' scheme (Biermann et al 2003 Phys. Rev. Lett. 90 086402), a combination of many-body perturbation theory in Hedin's GW approximation and dynamical mean field theory. Recently, the first GW + DMFT calculations including dynamical screening effects for real materials have been achieved, with applications to SrV O3 (Tomczak et al 2012 Europhys. Lett. 100 67001, Tomczak et al Phys. Rev. B submitted (available electronically as arXiv:1312.7546)) and adatom systems on surfaces (Hansmann et al 2013 Phys. Rev. Lett. 110 166401). We review these and comment on further perspectives in the field. This review is an attempt to put elements of the original works into the broad perspective of the development of truly first principles techniques for correlated electron materials.

Ferrimagnetic Slater insulator phase of the Sn/Ge(111) surface

We perform semilocal and hybrid density-functional theory (DFT) studies of the Sn/Ge(111) surface to identify the origin of the observed insulating sqrt[3]×sqrt[3] phase below ∼30  K. In contrast with the semilocal DFT calculation predicting a metallic 3×3 ground state, the hybrid DFT calculation including van der Waals interactions shows that the insulating ferrimagnetic structure with a sqrt[3]×sqrt[3] structural symmetry is energetically favored over the metallic 3×3 structure. It is revealed that the correction of the self-interaction error with a hybrid exchange-correlation functional gives rise to a band gap opening induced by a ferrimagnetic order. The results show that the observed insulating phase is attributed to the Slater mechanism via itinerant magnetic order rather than the hitherto accepted Mott-Hubbard mechanism via electron correlations.

Long-range Coulomb interactions in surface systems: a first-principles description within self-consistently combined GW and dynamical mean-field theory

Systems of adatoms on semiconductor surfaces display competing ground states and exotic spectral properties typical of two-dimensional correlated electron materials which are dominated by a complex interplay of spin and charge degrees of freedom. We report a fully ab initio derivation of low-energy Hamiltonians for the adatom systems Si(111):X, with X=Sn, Si, C, Pb, that we solve within self-consistently combined GW and dynamical mean-field theory. Calculated photoemission spectra are in agreement with available experimental data. We rationalize experimentally observed trends from Mott physics toward charge ordering along the series as resulting from substantial long-range interactions.

Understanding the insulating nature of alkali-metal/Si(111):B interfaces

We have recently revisited the phase diagram of alkali-metal/Si(111):B semiconducting interfaces previously suggested as the possible realization of a Mott-Hubbard insulator on a triangular lattice. The insulating character of the 2√[3] × 2√[3]R30 surface reconstruction observed at the saturation coverage, i.e. 0.5 ML, has been shown to find its origin in a giant alkali-metal-induced vertical distortion. Low energy electron diffraction, photoemission spectroscopy and scanning tunneling microscopy and spectroscopy experiments coupled with linear augmented plane-wave density functional theory calculations allow a full understanding of the k-resolved band structure, explaining both the inhomogeneous charge transfers into an Si-B hybridized surface state and the opening of a band gap larger than 1 eV. Moreover, √[3] × √[3]R30, 3 × 3 and 2√[3] × 2√[3]R30 surface reconstructions observed as a function of coverage may reveal a filling-controlled transition from a half-filled correlated magnetic material to a strongly distorted band insulator at saturation.

What about U on surfaces? Extended Hubbard models for adatom systems from first principles

Electronic correlations together with dimensional constraints lead to some of the most fascinating properties known in condensed matter physics. As possible candidates where these conditions are realized, semiconductor (111) surfaces and adatom systems on surfaces have been under investigation for quite some time. However, state-of-the-art theoretical studies on these materials that include many-body effects beyond the band picture are rare. First principles estimates of inter-electronic Coulomb interactions for the correlated states are missing entirely, and usually these interactions are treated as adjustable parameters. In this work, we report on calculations of the interaction parameters for the group IV surface-adatom systems in the α-phase series of Si(111):C, Si, Sn, Pb. For all systems investigated, the inter-electronic Coulomb interactions are indeed large compared to the kinetic energies of the states in question. Moreover, our study reveals that intersite interactions cannot be disregarded. We explicitly construct an extended Hubbard model for the series of group IV surface-adatom systems on silicon, which can be used for further many-body calculations.

Giant alkali-metal-induced lattice relaxation as the driving force of the insulating phase of alkali-metal/Si(111):B

Ab initio density-functional theory calculations, photoemission spectroscopy (PES), scanning tunneling microscopy, and spectroscopy (STM, STS) have been used to solve the 2sqrt[3]×2sqrt[3]R30 surface reconstruction observed previously by LEED on 0.5 ML K/Si:B. A large K-induced vertical lattice relaxation occurring only for 3/4 of Si adatoms is shown to quantitatively explain both the chemical shift of 1.14 eV and the ratio 1/3 measured on the two distinct B 1s core levels. A gap is observed between valence and conduction surface bands by ARPES and STS which is shown to have mainly a Si-B character. Finally, the calculated STM images agree with our experimental results. This work solves the controversy about the origin of the insulating ground state of alkali-metal/Si(111):B semiconducting interfaces which were believed previously to be related to many-body effects.

Detecting and localizing surface dynamics with STM: a study of the Sn/Ge(111) and Sn/Si(111) α-phase surfaces

After almost three decades since the invention of the scanning tunnelling microscope (STM) its application to the study of dynamic processes at surfaces is attracting a great deal of interest due to its unique capacity to observe such processes at the atomic level. The α-phase of group IV adatoms on Ge(111) and Si(111) is the ideal playground for the analysis of critical phenomena and represents a prototype of a two-dimensional electron system exhibiting thermally activated peculiar Sn adatom dynamics. This paper will relate the study of adatom dynamics at the α-Sn/Ge(111) and α-Sn/Si(111) surfaces, discussing in detail the methods we used for such kinds of time-resolved measurements. The microscope tip was used to record the tunnelling current on top of an oscillating Sn adatom, keeping the feedback loop turned off. The dynamics of the adatoms is detected as telegraph noise present in the tunnelling versus time curves. With this method it is possible to increase the acquisition rate to the actual limit of the instrument electronics, excluding piezo movement and feedback circuitry response time. We put emphasis on the statistical data analysis which allows the localization of the sample areas that are involved in dynamical processes.

Surface-state bipolaron formation on a triangular lattice in the sp-type alkali-metal/Si(111) Mott insulator

We report on new low-energy electron diffraction, scanning tunneling microscopy, and angle-resolved photoemission spectroscopy studies of alkali-metal/Si(111) previously established as having a Mott-insulating ground state at surface. The observation of a strong temperature dependent Franck-Condon broadening of the surface band together with the novel sqrt[3] x sqrt[3] --> 2(sqrt[3] x sqrt[3]) charge and lattice ordering below 270 K evidence a surface charge density wave in the strong electron-phonon coupling limit (g approximately 8). Both the adiabatic ratio variant Planck's over 2piomega_{0}/t approximately 0.8 and the effective pairing energy V_{eff} = U - 2gvariant Planck's over 2piomega_{0} approximately -800 meV are consistent with the possible formation of a bipolaronic insulating phase consisting of alternating doubly occupied and unoccupied dangling bonds as expected in the Holstein-Hubbard model.

Giant kink in electron dispersion of strongly coupled lead nanowires

Our photoelectron spectroscopy study shows a giant kink in the electron dispersion, a sign of high-energy manybody interactions of electrons, in a well-ordered Pb nanowire array self-assembled on a silicon substrate. We show that the unique electronic band structure due to the strong lateral coupling and the atomic structure of the nanowires drives an enhanced manybody interaction for kinked electron dispersion. The major giant kink mechanisms discussed previously, the magnetic and plasmonic excitations, are not relevant in the present system, supporting the recent kink theory based purely on electron-electron correlation. This suggests that tailored electronic band structures in nano array systems can provide unprecedented ways to study manybody interactions of electrons.

Surface-sensitive conductance measurements

Several approaches for surface-sensitive conductance measurements are reviewed. Particular emphasis is placed on nanoscale multi-point probe techniques. The results for two model systems, which have given rise to some dispute, are discussed in detail: Si(111)(7 × 7) and ([Formula: see text])Ag-Si(111). Other recent examples are also given, such as phase transitions in quasi-one-dimensional structures on semiconductor surfaces and the surface sheet conductivity of Bi(111), the surface of a semimetal.

Metallic nature of the alpha-Sn/Ge(111) surface down to 2.5 K

Low temperature (down to 2.5 K) scanning tunneling microscopy (STM) and spectroscopy (STS) measurements are presented to assess the nature of the alpha-Sn/Ge(111) surface. Bias-dependent STM and STS measurements have been used to demonstrate that such a surface preserves a metallic 3 x 3 reconstruction at very low temperature. A tip-surface interaction mechanism becomes active below about 20 K at the alpha-Sn/Ge(111) surface, resulting in an apparent unbuckled (sqrt[3] x sqrt[3]) reconstruction when filled states STM images are acquired with tunneling currents higher than 0.2 nA.

Structural origin of the Sn 4d core level line shape in Sn/Ge(111)-(3x3)

High-resolution photoemission of the Sn 4d core level of Sn/Ge(111)-(3x3) resolves three main components in the line shape, which are assigned to each of the three Sn atoms that form the unit cell. The line shape found is in agreement with an initial state picture and supports that the two down atoms are inequivalent. In full agreement with these results, scanning tunnel microscopy images directly show that the two down atoms are at slightly different heights in most of the surface, giving rise to an inequivalent-down-atoms (3x3) structure. These results solve a long-standing controversy on the interpretation of the Sn 4d core-level line shape and the structure of Sn/Ge(111)-(3x3).

Evidence of Sn adatoms quantum tunneling at the alpha-Sn/Si(111) surface

We present a low-temperature scanning tunneling microscopy study of the alpha-Sn/Si(111) surface that demonstrates the fluctuating behavior of the Sn adatoms. The dynamical fluctuation model, successfully applied in describing the alpha-Sn/Ge(111) surface, is proposed for the related alpha-Sn/Si(111) surface too, although with a much lower transition temperature. In addition, a new phenomenon appears responsible for the unexpected evidence that the average oscillation frequency remains constant at temperatures lower than 15 K, in contradiction to the Arrhenius law. We explain this phenomenon as quantum tunneling of Sn adatoms.

Insulating ground state of Sn/Si(111)-(square root 3 x square root 3)R30 degrees

The Sn/Si(111)-(square root 3 x square root 3)R30 degrees surface was so far believed to be metallic according to the electron counting argument. We show, by using tunneling spectroscopy, scanning tunneling microscopy, photoemission, and photoelectron diffraction, that below 70 K this surface has a very low density of states at the Fermi level and is not appreciably distorted. The experimental results are compatible with the insulating Mott-Hubbard ground state predicted by LSDA+U calculations [G. Profeta and E. Tosatti, Phys. Rev. Lett. 98, 086401 (2007)].