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Register a new userCharge density wave in single-layer Pb/Ge(111) driven by Pb-substrate exchange interaction
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Single layer Pb on top of (111) surfaces of group IV semiconductors hosts charge density wave and superconductivity depending on the coverage and on the substrate. These systems are normally considered to be experimental realizations of single band Hubbard models and their properties are mostly investigated using lattice models with frozen structural degrees of freedom, although the reliability of this approximation is unclear. Here, we consider the case of Pb/Ge(111) at 1/3 coverage, for which surface X-ray diffraction and ARPES data are available. By performing first principles calculations, we demonstrate that the non-local exchange between Pb and the substrate drives the system into a $3times 3$ charge density wave. The electronic structure of this charge ordered phase is mainly determined by two effects: the magnitude of the Pb distortion and the large spin-orbit coupling. Finally, we show that the effect applies also to the $3times 3$ phase of Pb/Si(111) where the Pb-substrate exchange interaction increases the bandwidth by more than a factor 1.5 with respect to DFT+U, in better agreement with STS data. The delicate interplay between substrate, structural and electronic degrees of freedom invalidates the widespread interpretation available in literature considering these compounds as physical realizations of single band Hubbard models.
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We investigate the 1/3 monolayer $alpha$-Pb/Si(111) surface by scanning tunneling spectroscopy (STS) and fully relativistic first-principles calculations. We study both the high-temperature $sqrt{3}timessqrt{3}$ and low-temperature $3times 3$ 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 $3times3$ periodicity. By comparing the Fourier transform of STS conductance maps at the Fermi level with calculated quasiparticle interference from non-magnetic impurities, we demonstrate the occurrence of two large hexagonal Fermi sheets with in-plane spin polarizations and opposite helicities.
The electronic structure of epitaxial single-layer MoS$_2$ on Au(111) is investigated by angle-resolved photoemission spectroscopy, scanning tunnelling spectroscopy, and first principles calculations. While the band dispersion of the supported single-layer is close to a free-standing layer in the vicinity of the valence band maximum at $bar{K}$ and the calculated electronic band gap on Au(111) is similar to that calculated for the free-standing layer, significant modifications to the band structure are observed at other points of the two-dimensional Brillouin zone: At $bar{Gamma}$, the valence band maximum has a significantly higher binding energy than in the free MoS$_2$ layer and the expected spin-degeneracy of the uppermost valence band at the $bar{M}$ point cannot be observed. These band structure changes are reproduced by the calculations and can be explained by the detailed interaction of the out-of-plane MoS$_2$ orbitals with the substrate.
The electronic properties of thin metallic films deviate from the corresponding bulk ones when the film thickness is comparable with the wavelength of the electrons at the Fermi level due to quantum size effects (QSE). QSE are expected to affect the film morphology and structure leading to the low temperature (LT) ``electronic growth of metals on semiconductors. In particular, layer-by-layer growth of Pb(111) films has been reported for deposition on Ge(001) below 130 K. An extremely flat morphology is preserved throughout deposition from four up to a dozen of monolayers. These flat films are shown to be metastable and to reorganize into large clusters uncovering the first Pb layer, pseudomorphic to the substrate, already at room temperature. Indications of QSE induced structural variations of the growing films have been reported for Pb growth on Ge(001), where the apparent height of the Pb(111) monatomic step was shown to change in an oscillatory fashion by He atom scattering (HAS) during layer-by-layer growth. The extent of the structural QSE has been obtained by a comparison of the HAS data with X-ray diffraction (XRD) and reflectivity experiments. Whereas step height variations as large as 20 % have been measured by HAS reflectivity, the displacement of the atomic planes from their bulk position, as measured by XRD, has been found to mainly affect the topmost Pb layer, but with a lower extent, i.e. the QSE observed by HAS are mainly due to a perpendicular displacement of the topmost layer charge density. The effect of the variable surface relaxation on the surface vibration has been studied by inelastic HAS to measure the acoustic dispersion of the low energy phonons.
We analyze the transformation from insulator to metal induced by thermal fluctuations within the Falicov-Kimball model. Using the Dynamic Mean Field Theory (DMFT) formalism on the Bethe lattice we find rigorously the temperature dependent Density of States ($DOS$) at half filling in the limit of high dimensions. At zero temperature (T=0) the system is ordered to form the checkerboard pattern and the $DOS$ has the gap $Delta$ at the Fermi level $varepsilon_F=0$, which is proportional to the interaction constant $U$. With an increase of $T$ the $DOS$ evolves in various ways that depend on $U$. For $U>U_{cr}$ the gap persists for any $T$ (then $Delta >0$), so the system is always an insulator. However, if $U < U_{cr}$, two additional subbands develop inside the gap. They become wider with increasing $T$ and at a certain $U$-dependent temperature $T_{MI}$ they join with each other at $varepsilon_F$. Since above $T_{MI}$ the $DOS$ is positive at $varepsilon_F$, we interpret $T_{MI}$ as the transformation temperature from insulator to metal. It appears, that $T_{MI}$ approaches the order-disorder phase transition temperature $T_{O-DO}$ when $U$ is close to 0 or $ U_{cr}$, but $T_{MI}$ is substantially lower than $T_{O-DO}$ for intermediate values of $U$. Having calculated the temperature dependent $DOS$ we study thermodynamic properties of the system starting from its free energy $F$. Then we find how the order parameter $d$ and the gap $Delta $ change with $T$ and we construct the phase diagram in the variables $T$ and $U$, where we display regions of stability of four different phases: ordered insulator, ordered metal, disordered insulator and disordered metal. Finally, we use a low temperature expansion to demonstrate the existence of a nonzero DOS at a characteristic value of U on a general bipartite lattice.
Substrate engineering provides an opportunity to modulate the physical properties of quantum materials in thin film form. Here we report that TiSe$_2$ thin films grown on TiO$_2$ have unexpectedly large electron doping that suppresses the charge density wave (CDW) order. This is dramatically different from either bulk single crystal TiSe$_2$ or TiSe$_2$ thin films on graphene. The epitaxial TiSe$_2$ thin films can be prepared on TiO$_2$ via molecular beam epitaxy (MBE) in two ways: by conventional co-deposition using selenium and titanium sources, and by evaporating only selenium on reconstructed TiO$_2$ surfaces. Both growth methods yield atomically flat thin films with similar physical properties. The electron doping and subsequent suppression of CDW order can be explained by selenium vacancies in the TiSe$_2$ film, which naturally occur when TiO$_2$ substrates are used. This is due to the stronger interfacial bonding that changes the ideal growth conditions. Our finding provides a way to tune the chemical potential of chalcogenide thin films via substrate selection and engineering.
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