Direct observation of a surface charge density wave

Charge density waves in two-dimensional transition metal dichalcogenides

Charge density wave (CDW is one of the most ubiquitous electronic orders in quantum materials. While the essential ingredients of CDW order have been extensively studied, a comprehensive microscopic understanding is yet to be reached. Recent research efforts on the CDW phenomena in two-dimensional (2D) materials provide a new pathway toward a deeper understanding of its complexity. This review provides an overview of the CDW orders in 2D with atomically thin transition metal dichalcogenides (TMDCs) as the materials platform. We mainly focus on the electronic structure investigations on the epitaxially grown TMDC samples with angle-resolved photoemission spectroscopy and scanning tunneling microscopy/spectroscopy as complementary experimental tools. We discuss the possible origins of the 2D CDW, novel quantum states coexisting with them, and exotic types of charge orders that can only be realized in the 2D limit.

Ultrafast Internal Exciton Dissociation through Edge States in MoS2 Nanosheets with Diffusion Blocking

Edge states of two-dimensional transition-metal dichalcogenides (TMDCs) are crucial to quantum circuits and optoelectronics. However, their dynamics are pivotal but remain unclear due to the edge states being obscured by their bulk counterparts. Herein, we study the state-resolved transient absorption spectra of ball-milling-produced MoS₂ nanosheets with 10 nm lateral size with highly exposed free edges. Electron energy loss spectroscopy and first-principles calculations confirm that the edge states are located in the range from 1.23 to 1.78 eV. Upon above bandgap excitations, excitons populate and diffuse toward the boundary, where the potential gradient blocks excitons and the edge states are formed through interband transitions within 400 fs. With below bandgap excitations, edge states are slowed down to 1.1 ps due to the weakened valence orbital coupling. These results shed light on the fundamental exciton dissociation processes on the boundary of functionalized TMDCs, enabling the ground work for applications in optoelectronics and light-harvesting.

Computational Methods for Charge Density Waves in 2D Materials

Two-dimensional (2D) materials that exhibit charge density waves (CDWs)—spontaneous reorganization of their electrons into a periodic modulation—have generated many research endeavors in the hopes of employing their exotic properties for various quantum-based technologies. Early investigations surrounding CDWs were mostly focused on bulk materials. However, applications for quantum devices require few-layer materials to fully utilize the emergent phenomena. The CDW field has greatly expanded over the decades, warranting a focus on the computational efforts surrounding them specifically in 2D materials. In this review, we cover ground in the following relevant theory-driven subtopics for TaS₂ and TaSe₂: summary of general computational techniques and methods, resulting atomic structures, the effect of electron–phonon interaction of the Raman scattering modes, the effects of confinement and dimensionality on the CDW, and we end with a future outlook. Through understanding how the computational methods have enabled incredible advancements in quantum materials, one may anticipate the ever-expanding directions available for continued pursuit as the field brings us through the 21st century.

Semiconductor-Metal Phase Transition and Emergent Charge Density Waves in 1T-ZrX2 (X = Se, Te) at the Two-Dimensional Limit

A charge density wave (CDW) is a collective quantum phenomenon in metals and features a wavelike modulation of the conduction electron density. A microscopic understanding and experimental control of this many-body electronic state in atomically thin materials remain hot topics in materials physics. By means of material engineering, we realized a dimensionality and Zr intercalation induced semiconductor-metal phase transition in 1T-ZrX₂ (X = Se, Te) ultrathin films, accompanied by a commensurate 2 × 2 CDW order. Furthermore, we observed a CDW energy gap of up to 22 meV around the Fermi level. Fourier-transformed scanning tunneling microscopy and angle-resolved photoemission spectroscopy reveal that 1T-ZrX₂ films exhibit the simplest Fermi surface among the known CDW materials in TMDCs, consisting only of a Zr 4d derived elliptical electron conduction band at the corners of the Brillouin zone.

Growth, phase transition, and island motion of Au on Ge(111)

Using low energy electron microscopy, Au on Ge(111) is determined to follow a Stranski-Krastanov growth mode consisting of a single layer up to one monolayer (ML), followed by three-dimensional Au-Ge alloy droplets. Near 600 °C, we report the first observation of a reversible first-order phase transition that occurs from the (3 × 3)R30° phase to a (1 × 1) phase, which has a coverage of 0.367 ML. The transition gradually occurs through a coexistence region with a temperature range of about 2 °C and weakly depends on coverage, varying from 640 °C at 1 ML down to 580 °C at 0.8 ML. The phase transition is accompanied by phase fluctuations of small domains or the fluctuations of phase boundaries of large domains. At coverage >1 ML and above 250 °C, the 3D droplets move with stick-slip hopping behavior that has previously been explained by dissolution of Ge at step edges into the alloy droplet, which then comes to concentration and thermal equilibrium via the island motion.

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.

Two-Dimensional Molecular Charge Density Waves in Single-Layer-Thick Islands of a Dirac Fermion System

Charge density waves have been intensely studied in inorganic materials such as transition metal dichalcogenides; however their counterpart in organic materials has yet to be explored in detail. Here we report the finding of robust two-dimensional charge density waves in molecular layers formed by α-(BEDT-TTF)₂-I₃ on a Ag(111) surface. Low-temperature scanning tunneling microscopy images of a multilayer thick α-(BEDT-TTF)₂-I₃ on a Ag(111) substrate reveal the coexistence of 5a₀ × 5a₀ and 31a0×31a0 R9° charge density wave patterns commensurate with the underlying molecular lattice at 80 K. Both charge density wave patterns remain in nanosize molecular islands with just a single constituent molecular-layer thickness at 80 and 5 K. Local tunneling spectroscopy measurements reveal the variation of the gap from 244 to 288 meV between the maximum and minimum charge density wave locations. Density functional theory calculations further confirm a vertical positioning of BEDT-TTF molecules in the molecular layer. While the observed charge density wave patterns are stable for the defect sites, they can be reversibly switched for one molecular lattice site by means of inelastic tunneling electron energy transfer with the electron energies exceeding 400 meV using a scanning tunneling microscope manipulation scheme.

Coupled Sublattice Melting and Charge-Order Transition in Two Dimensions

Two-dimensional melting is one of the most fascinating and poorly understood phase transitions in nature. Theoretical investigations often point to a two-step melting scenario involving unbinding of topological defects at two distinct temperatures. Here, we report on a novel melting transition of a charge-ordered K-Sn alloy monolayer on a silicon substrate. Melting starts with short-range positional fluctuations in the K sublattice while maintaining long-range order, followed by longer-range K diffusion over small domains, and ultimately resulting in a molten sublattice. Concomitantly, the charge order of the Sn host lattice collapses in a multistep process with both displacive and order-disorder transition characteristics. Our combined experimental and theoretical analysis provides a rare insight into the atomistic processes of a multistep melting transition of a two-dimensional materials system.

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.

Bias-Voltage Driven Switching of the Charge-Density-Wave and Normal Metallic Phases in 1T-TaS2 Thin-Film Devices

We report on switching among three charge-density-wave phases, commensurate, nearly commensurate, incommensurate, and the high-temperature normal metallic phase in thin-film 1T-TaS₂ devices induced by application of an in-plane bias voltage. The switching among all phases has been achieved over a wide temperature range, from 77 to 400 K. The low-frequency electronic noise spectroscopy has been used as an effective tool for monitoring the transitions, particularly the switching from the incommensurate charge-density-wave phase to the normal metal phase. The noise spectral density exhibits sharp increases at the phase transition points, which correspond to the step-like changes in resistivity. Assignment of the phases is consistent with low-field resistivity measurements over the temperature range from 77 to 600 K. Analysis of the experimental data and calculations of heat dissipation indicate that Joule heating plays a dominant role in the voltage induced transitions in the 1T-TaS₂ devices on Si/SiO₂ substrates, contrary to some recent claims. The possibility of the bias-voltage switching among four different phases of 1T-TaS₂ is a promising step toward nanoscale device applications. The results also demonstrate the potential of noise spectroscopy for investigating and identifying phase transitions in the materials.

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.

Modeling of networks and globules of charged domain walls observed in pump and pulse induced states

Experiments on optical and STM injection of carriers in layered MX₂ materials revealed the formation of nanoscale patterns with networks and globules of domain walls. This is thought to be responsible for the metallization transition of the Mott insulator and for stabilization of a “hidden” state. In response, here we present studies of the classical charged lattice gas model emulating the superlattice of polarons ubiquitous to the material of choice 1T − TaS₂. The injection pulse was simulated by introducing a small random concentration of voids which subsequent evolution was followed by means of Monte Carlo cooling. Below the detected phase transition, the voids gradually coalesce into domain walls forming locally connected globules and then the global network leading to a mosaic fragmentation into domains with different degenerate ground states. The obtained patterns closely resemble the experimental STM visualizations. The surprising aggregation of charged voids is understood by fractionalization of their charges across the walls’ lines.

Design and performance of an ultra-high vacuum spin-polarized scanning tunneling microscope operating at 30 mK and in a vector magnetic field

We describe the design and performance of a scanning tunneling microscope (STM) that operates at a base temperature of 30 mK in a vector magnetic field. The cryogenics is based on an ultra-high vacuum (UHV) top-loading wet dilution refrigerator that contains a vector magnet allowing for fields up to 9 T perpendicular and 4 T parallel to the sample. The STM is placed in a multi-chamber UHV system, which allows in situ preparation and exchange of samples and tips. The entire system rests on a 150-ton concrete block suspended by pneumatic isolators, which is housed in an acoustically isolated and electromagnetically shielded laboratory optimized for extremely low noise scanning probe measurements. We demonstrate the overall performance by illustrating atomic resolution and quasiparticle interference imaging and detail the vibrational noise of both the laboratory and microscope. We also determine the electron temperature via measurement of the superconducting gap of Re(0001) and illustrate magnetic field-dependent measurements of the spin excitations of individual Fe atoms on Pt(111). Finally, we demonstrate spin resolution by imaging the magnetic structure of the Fe double layer on W(110).

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.

Nanoscale electrodynamics of strongly correlated quantum materials

Electronic, magnetic, and structural phase inhomogeneities are ubiquitous in strongly correlated quantum materials. The characteristic length scales of the phase inhomogeneities can range from atomic to mesoscopic, depending on their microscopic origins as well as various sample dependent factors. Therefore, progress with the understanding of correlated phenomena critically depends on the experimental techniques suitable to provide appropriate spatial resolution. This requirement is difficult to meet for some of the most informative methods in condensed matter physics, including infrared and optical spectroscopy. Yet, recent developments in near-field optics and imaging enabled a detailed characterization of the electromagnetic response with a spatial resolution down to 10 nm. Thus it is now feasible to exploit at the nanoscale well-established capabilities of optical methods for characterization of electronic processes and lattice dynamics in diverse classes of correlated quantum systems. This review offers a concise description of the state-of-the-art near-field techniques applied to prototypical correlated quantum materials. We also discuss complementary microscopic and spectroscopic methods which reveal important mesoscopic dynamics of quantum materials at different energy scales.

Quasi-One-Dimensional Metal-Insulator Transitions in Compound Semiconductor Surfaces

Existing examples of Peierls-type 1D systems on surfaces involve depositing metallic overlayers on semiconducting substrates, in particular, at step edges. Here we propose a new class of Peierls system on the (101[over ¯]0) surface of metal-anion wurtzite semiconductors. When the anions are bonded to hydrogen or lithium atoms, we obtain rows of threefold coordinated metal atoms that act as one-atom-wide metallic structures. First-principles calculations show that the surface is metallic, and below a certain critical temperature the surface will condense to a semiconducting state. The idea of surface scaffolding is introduced in which the rows are constrained to move along simple up-down and/or sideways displacements, mirroring the paradigm envisioned in Peierls's description. We predict that this type of insulating state should be visible in the partially hydrogenated (101[over ¯]0) surface of many wurtzite compounds.

STM study of PTCDA on Sn/Si(111)-2√3×2√3

The electronic structures of perylene tetracarboxylic dianhydride on Sn/Si(111)-2√3×2√3 have been studied by scanning tunneling microscopy and spectroscopy. Individual molecules have been investigated at 0.15 ML, while at 0.3 ML molecules formed short rods. At 0.6 ML, the molecular rods interacted with each other, coupling with the substrate and forming a new 4√3×2√3 super structure. At 0.9 ML, the surface was further reconstructed and consisted of strips with two and three rods of molecules. We found that these surface structures are strongly modified by the molecule/substrate and the intermolecular interactions. As a result, the HOMO-LUMO gaps of these molecules change with respect to the phases and the thickness. For a single molecular layer of the 4√3×2√3 phase, the HOMO-LUMO levels were split with a gap of approximately 2.1 eV, which is caused by charge transfer from the substrate to the molecules.

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.

Colloidal particles driven across periodic optical-potential-energy landscapes

We study the motion of colloidal particles driven by a constant force over a periodic optical potential energy landscape. First, the average particle velocity is found as a function of the driving velocity and the wavelength of the optical potential energy landscape. The relationship between average particle velocity and driving velocity is found to be well described by a theoretical model treating the landscape as sinusoidal, but only at small trap spacings. At larger trap spacings, a nonsinusoidal model for the landscape must be used. Subsequently, the critical velocity required for a particle to move across the landscape is determined as a function of the wavelength of the landscape. Finally, the velocity of a particle driven at a velocity far exceeding the critical driving velocity is examined. Both of these results are again well described by the two theoretical routes for small and large trap spacings, respectively. Brownian motion is found to have a significant effect on the critical driving velocity but a negligible effect when the driving velocity is high.

Microscopic dynamics of synchronization in driven colloids

Synchronization of coupled oscillators has been scrutinized for over three centuries, from Huygens' pendulum clocks to physiological rhythms. One such synchronization phenomenon, dynamic mode locking, occurs when naturally oscillating processes are driven by an externally imposed modulation. Typically only averaged or integrated properties are accessible, leaving underlying mechanisms unseen. Here, we visualize the microscopic dynamics underlying mode locking in a colloidal model system, by using particle trajectories to produce phase portraits. Furthermore, we use this approach to examine the enhancement of mode locking in a flexible chain of magnetically coupled particles, which we ascribe to breathing modes caused by mode-locked density waves. Finally, we demonstrate that an emergent density wave in a static colloidal chain mode locks as a quasi-particle, with microscopic dynamics analogous to those seen for a single particle. Our results indicate that understanding the intricate link between emergent behaviour and microscopic dynamics is key to controlling synchronization.

Synchronization may occur when naturally oscillating systems are driven by an external modulation, for example, in charge density waves. Here, Juniper et al. visualize the locked modes of synchronization at a microscopic level using a colloidal system.

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.

Stabilization and manipulation of electronically phase-separated ground states in defective indium atom wires on silicon

Exploration and manipulation of electronic states in low-dimensional systems are of great importance in the fundamental and practical aspects of nanomaterial and nanotechnology. Here, we demonstrate that the incorporation of vacancy defects into monatomic indium wires on n-type Si(111) can stabilize electronically phase-separated ground states where the insulating 8×2 and metallic 4×1 phases coexist. Furthermore, the areal ratio of the two phases in the phase-separated states can be tuned reversibly by electric field or charge doping, and such tunabilities can be quantitatively captured by first principles-based modeling and simulations. The present results extend the realm of electronic phase separation from strongly correlated d-electron materials typically in bulk form to weakly interacting sp-electron systems in reduced dimensionality.

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.

Double-layer in structural model for the In/Si(111)-√7×√3 surface

We demonstrate by using density functional calculations that the In/Si(111)-√7×√3 surface consists of an In double layer, contrary to the prevailing idea that the In overlayer on this surface is just one atom thick and thus can be used to represent the ultimate 2D limit of metal overlayer properties. The double-layer In structure is sound energetically and microscopically and, above all, well reproduces the measured photoemission band structure that could not be fairly compared with any single-layer In model. The present double-layer model urges a reconsideration on the recent experimental claims that the In overlayer properties were pushed to a single-layer limit in this surface.

Structure determination of Pb/Ge(111)-β-(√3 × √3)R30° by dynamical low-energy electron diffraction analysis and first-principles calculation

We have determined the atomic structure of the Pb/Ge(111)-β-(√3 × √3)R30° surface, which was shown to exhibit a large Rashba spin splitting in a metallic surface state by dynamical low-energy electron diffraction analysis. The Pb coverage for the optimized atomic structure is 4/3 with one Pb atom located at every third H(3) site of the bulk-truncated Ge(111) surface and the other three near the T(1) sites but slightly displaced towards the T(4) sites. The determined atomic structure agrees well with the energetically optimized one obtained from the first-principles calculation. The calculation also revealed that the potential for the Pb atoms on the H(3) sites is very soft along the surface normal, suggesting that their vertical position is distributed within a range of about 0.2-0.3 Å. The previously proposed phase transition associated with the surface melting is discussed.

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.

Weak dimers and soft phonons on the β-SiC(100) surface

We study the β-SiC(100) [Formula: see text] reversible phase transition, using first-principles molecular dynamics simulations to search for the ground state atomic structure as well as to investigate the dynamics of this surface. We find that this surface consists of weakly bonded asymmetric Si dimers that exhibit a complex atomic motion, associated with a surface soft phonon. This soft phonon is strongly coupled to the electrons in dangling bond states close to the Fermi level, explaining the observed insulator-metal transition. We identify the dynamical processes responsible for the phase transition and predict that this surface should undergo another reversible phase transition at low T.

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.

Vicinal surfaces for functional nanostructures

Vicinal surfaces are currently the focus of research. The regular arrangements of atomic steps on a mesoscopic scale reveal the possibility to functionalize these surfaces for technical applications, e.g. nanowires, catalysts, etc. The steps of the vicinal surface are well-defined defect structures of atomic size for nucleation of low-dimensional nanostructures. The concentration and therefore the coupling between the nanostructures can be tuned over a wide range by simply changing the inclination angle of the substrate. However, the coupling of these nano-objects to the substrate is just as important in controlling their electronic or chemical properties and making a functionality useable. On the basis of stepped insulating films, these aspects are fulfilled and will be considered in the first part of this review. Recent results for the epitaxial growth of wide bandgap insulating films (CaF(2), MgO, NaCl, BaSrO) on metallic and semiconducting vicinal substrates (Si(100), Ge(100), Ag(100)) will be presented. The change of the electronic structure, the adsorption behavior as well as the kinetics and energetics of color centers in the presence of steps is discussed. The successful bridging of the gap between the atomic and mesoscopic world, i.e. the functionalization of vicinal surfaces by nanostructures, is demonstrated in the second part by metal adsorption on semiconducting surfaces. For (sub)monolayer coverage these systems have in common that the surface states do not hybridize with the support, i.e. the semiconducting surfaces are insulating. Here I will focus on the latest results of macroscopic transport measurements on Pb quantum wires grown on vicinal Si(111) showing indeed a one-dimensional transport behavior.

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.

Anisotropic charge ordering on the gallium surface

Low-temperature scanning tunneling microscopy of atomically flat Ga(001) islands revealed the 2D electronic superlattice composed of stripe domains. Tunnel spectroscopy of these surface electrons indicates the formation of a 2D charge-ordered state of Wigner-crystal type driven by competition of short-range and long-range Coulomb energies. At the boundaries of stripe domains the energy spectra exhibit splitting due to charged excitonic states and shift due to charge doping, altogether indicating the self-assembly of 1D hole stripes. The size distribution of stripe domains is broadened around 4a.

Charge-order fluctuations in one-dimensional silicides

Metallic nanowires are of great interest as interconnects in nanoelectronic devices. They also represent important systems for understanding the complexity of electronic interactions and conductivity in one dimension. We have fabricated exceptionally long and uniform YSi(2) nanowires through self-assembly of yttrium atoms on Si(001). The wire widths are quantized in odd multiples of the Si substrate lattice constant. The thinnest wires represent one of the closest realizations of the isolated Peierls chain, exhibiting van Hove type singularities in the one-dimensional density of states and charge-order fluctuations below 150 K. The structure of the wire was determined through a detailed comparison of scanning tunnelling microscopy data and first-principles calculations. Quantized width variations along the thinnest wires produce built-in Schottky junctions, the electronic properties of which are governed by the finite size and temperature scaling of the charge-ordering correlation. This illustrates how a collective phenomenon such as charge ordering might be exploited in nanoelectronic devices.

Surface phase transition in H/W(110) induced by tuning the fermi surface nesting vector by hydrogen loading

At a hydrogen coverage of one monolayer, W(110) is known to exhibit a Fermi nesting in its electronic surface states with a nesting vector q{N} of 0.9 A{-1} along [001]. Here we show that additional H adsorption allows a controlled tuning of q{N}. As q{N} approaches the commensurate value of 1.0 A{-1}, its signature in inelastic He-atom scattering becomes more pronounced, finally disappearing as a surface charge density wave (CDW) develops and the surface symmetry changes from c(2 x 2) to a p(8 x 2) superstructure. The gradual change in q{N} is attributed to an energetic shift of the spin-polarized electronic surface states that eventually form the surface CDW.

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.

Local tunneling spectroscopy across a metamagnetic critical point in the bilayer ruthenate Sr3Ru2O7

The local spectroscopic signatures of metamagnetic criticality in Sr(3)Ru(2)O(7) were explored using scanning tunneling microscopy (STM). Singular features in the tunneling spectrum were found close to the Fermi level, as would be expected in a Stoner picture of itinerant electron metamagnetism. These features showed a pronounced magnetic field dependence across the metamagnetic critical point, which cannot be understood in terms of a naive Stoner theory. In addition, a pseudogap structure was observed over several tens of meV, accompanied by a c(2 x 2) superstructure in STM images. This result represents a new electronic ordering at the surface in the absence of any measurable surface reconstruction.

Adatom-adatom interaction mediated by an underlying surface phase transition

Low temperature scanning tunneling microscopy measurements on the adsorption of single Pb adatoms on Si(111)-(square root 3 x square root 3)-Pb surfaces reveal the vertical displacement patterns induced on the substrate by these Pb adatoms as well as a novel adatom-adatom interaction. The origin of both can be traced back to the (square root 3 x square root 3)<-->(3 x 3) phase transition taking place at lower temperatures. A Landau-like approach explains the displacement patterns as due to the corresponding order parameter and shows that the vicinity of a surface phase transition gives rise to a nonmonotonic adatom-adatom interaction.

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)].

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

The ground state of Sn/Si(111) and Sn/Ge(111) surface alpha phases is reexamined theoretically, based on ab initio calculations where correlations are approximately included through the orbital dependence of the Coulomb interaction (in the local density+Hubbard U approximation). The effect of correlations is to destabilize the vertical buckling in Sn/Ge(111) and to make the surface magnetic, with a metal-insulator transition for both systems. This signals the onset of a stable narrow gap Mott-Hubbard insulating state, in agreement with very recent experiments. Antiferromagnetic exchange is proposed to be responsible for the observed Gamma-point photoemission intensity, as well as for the partial metallization observed above 60 K in Sn/Si(111). Extrinsic metallization of Sn/Si(111) by, e.g., alkali doping, could lead to a novel 2D triangular superconducting state of this and similar surfaces.

Soft phonon, dynamical fluctuations, and a reversible phase transition: indium chains on silicon

The In/Si(111)-(4 x 1) surface is a paradigmatic example of a quasi-one-dimensional system showing a reversible structural and electronic (metal-insulator) phase transition when the temperature is lowered. In this work, we use first-principles simulation techniques to uncover the atomic and electronic origin of this controversial transition. Our calculations show that the ground state consists of insulating (4 x 2) indium chains with a weak interchain coupling that induces opposite shear distortions in alternate chains. First-principles molecular dynamics simulations show that the (4 x 1) <--> (8 x 2) phase transition is due to the "dynamical fluctuations" the system undergoes when, at high temperature, it fluctuates chaotically between degenerate ground states. The metallicity of the In/Si(111)-(4 x 1) surface is related to the low energy cost for the shear distortion.

Observation of a Mott insulating ground state for Sn/Ge(111) at low temperature

We report an investigation on the properties of 0.33 ML of Sn on Ge(111) at temperatures down to 5 K. Low-energy electron diffraction and scanning tunneling microscopy show that the (3x3) phase formed at approximately 200 K, reverts to a new ((square root 3)x(square root 3))R30 degrees phase below 30 K. The vertical distortion characteristic of the (3x3) phase is lost across the phase transition, which is fully reversible. Angle-resolved photoemission experiments show that, concomitantly with the structural phase transition, a metal-insulator phase transition takes place. The ((square root 3)x(square root 3))R30 degrees ground state is interpreted as the formation of a Mott insulator for a narrow half-filled band in a two-dimensional triangular lattice.