Tuning the Quantum Stability and Superconductivity of Ultrathin Metal Alloys

Thickness-Dependent Superconductivity in a Layered Electride on Silicon

Layered materials exhibit a plethora of fascinating properties. The challenge is to make the materials into epitaxial films, preferably integrated with mature technological platforms to facilitate their potential applications. Progress in this direction can establish the film thickness as a valuable parameter to control various phenomena, superconductivity in particular. Here, a synthetic route to epitaxial films of SrAlSi, a layered superconducting electride, on silicon is designed. A set of films ranging in thickness is synthesized employing a silicene-based template. Their structure and superconductivity are explored by a combination of techniques. Two regimes of TC dependence on the film thickness are identified, the coherence length being the crossover parameter. The results can be extended to syntheses of other honeycomb-lattice ternary compounds on Si or Ge exhibiting superconducting, magnetic, and other properties.

Realizing a Superconducting Square-Lattice Bismuth Monolayer

Interplay of crystal symmetry, strong spin-orbit coupling (SOC), and many-body interactions in low-dimensional materials provides a fertile ground for the discovery of unconventional electronic and magnetic properties and versatile functionalities. Two-dimensional (2D) allotropes of group 15 elements are appealing due to their structures and controllability over symmetries and topology under strong SOC. Here, we report the heteroepitaxial growth of a proximity-induced superconducting 2D square-lattice bismuth monolayer on superconducting Pb films. The square lattice of monolayer bismuth films in a C₄ symmetry together with a stripey moiré structure is clearly resolved by our scanning tunneling microscopy, and its atomic structure is revealed by density functional theory (DFT) calculations. A Rashba-type spin-split Dirac band is predicted by DFT calculations to exist at the Fermi level and becomes superconducting through the proximity effect from the Pb substrate. We suggest the possibility of a topological superconducting state in this system with magnetic dopants/field. This work introduces an intriguing material platform with 2D Dirac bands, strong SOC, topological superconductivity, and the moiré superstructure.

Equally Spaced Quantum States in van der Waals Epitaxy-Grown Nanoislands

Pursuing the confinement of linearly dispersive relativistic Fermions is of interest in both fundamental physics and potential applications. Here, we report strong STM evidence for the equally spaced, strikingly sharp, and densely distributed quantum well states (QWSs) near Fermi energy in Pb(111) nanoislands, van der Waals epitaxially grown on graphitized 6H-SiC(0001). The observations can be explained as the quantized energies of confined linearly dispersive [111] electrons, which essentially "simulate" the out-of-plane relativistic quasiparticles. The equally spaced QWSs with an origin of confined relativistic electrons are supported by phenomenological simulations and Fabry-Pérot fittings based on the relativistic Fermions. First-principles calculations further reveal that the spin-orbit coupling strengthens the relativistic nature of electrons near Fermi energy. Our finding uncovers the unique equally spaced quantum states in electronic systems beyond Landau levels and may inspire future studies on confined relativistic quasiparticles in flourishing topological materials and applications in structurally simpler quantum cascade laser.

Measuring the Electron–Phonon Interaction in Two-Dimensional Superconductors with He-Atom Scattering

Helium-atom scattering (HAS) spectroscopy from conducting surfaces has been shown to provide direct information on the electron–phonon interaction, more specifically the mass-enhancement factor λ from the temperature dependence of the Debye–Waller exponent, and the mode-selected electron–phonon coupling constants λQν from the inelastic HAS intensities from individual surface phonons. The recent applications of the method to superconducting ultra-thin films, quasi-1D high-index surfaces, and layered transition-metal and topological pnictogen chalcogenides are briefly reviewed.

Superconductivity in undoped BaFe2As2 by tetrahedral geometry design

Fe-based superconductors exhibit a diverse interplay between charge, orbital, and magnetic ordering. Variations in atomic geometry affect electron hopping between Fe atoms and the Fermi surface topology, influencing magnetic frustration and the pairing strength through changes of orbital overlap and occupancies. Here, we experimentally demonstrate a systematic approach to realize superconductivity without chemical doping in BaFe₂As₂, employing geometric design within an epitaxial heterostructure. We control both tetragonality and orthorhombicity in BaFe₂As₂ through superlattice engineering, which we experimentally find to induce superconductivity when the As-Fe-As bond angle approaches that in a regular tetrahedron. This approach to superlattice design could lead to insights into low-dimensional superconductivity in Fe-based superconductors.

√7 × √3 surface with a double layer of In on Si(1 1 1) exhibiting both hexagonal and rectangular features

Using a scanning tunneling microscope (STM), we demonstrate that the In-induced hexagonal (√7  ×  √3-hex) and rectangular (√7  ×  √3-rect)  √7  ×  √3 phases on Si(111) are from the same surface with a double layer of In. The double-layer In thickness was derived from observations that a  √7  ×  √3-hex island was formed on the  √7  ×  √3-'striped' phase, which is believed to have a single layer of In atoms. Bias-dependent STM images were obtained from the same  √7  ×  √3 domain and exhibited both  √7  ×  √3-hex and  √7  ×  √3-rect features, which led to the conclusion that both  √7  ×  √3 STM features originate from the same structure. These findings are in stark contrast to the prevailing idea that there are two  √7  ×  √3 surfaces with different structures and In coverage. We also observed a long-range Moiré-like superstructure in the  √7  ×  √3 surface and attribute it to the mismatch of the lattices of the surface layer of In and the Si(1 1 1) substrate.

Geometric quenching of orbital pair breaking in a single crystalline superconducting nanomesh network

In a superconductor Cooper pairs condense into a single state and in so doing support dissipation free charge flow and perfect diamagnetism. In a magnetic field the minimum kinetic energy of the Cooper pairs increases, producing an orbital pair breaking effect. We show that it is possible to significantly quench the orbital pair breaking effect for both parallel and perpendicular magnetic fields in a thin film superconductor with lateral nanostructure on a length scale smaller than the magnetic length. By growing an ultra-thin (2 nm thick) single crystalline Pb nanowire network, we establish nm scale lateral structure without introducing weak links. Our network suppresses orbital pair breaking for both perpendicular and in-plane fields with a negligible reduction in zero-field resistive critical temperatures. Our study opens a frontier in nanoscale superconductivity by providing a strategy for maintaining pairing in strong field environments in all directions with important technological implications.

Fulde-Ferrell state in superconducting core/shell nanowires: role of the orbital effect

The orbital effect on the Fulde-Ferrell (FF) phase is investigated in superconducting core/shell nanowires subjected to the axial magnetic field. Confinement in the radial direction results in quantization of the electron motion with energies determined by the radial j and orbital m quantum numbers. In the external magnetic field, the twofold degeneracy with respect to the orbital magnetic quantum number m is lifted which leads to the Fermi wave vector mismatch between the paired electrons, [Formula: see text]. This mismatch is transferred to the nonzero total momentum of the Cooper pairs, which results in a formation of the FF phase occurring sequentially with increasing magnetic field. By changing the nanowire radius R and the superconducting shell thickness d, we discuss the role of the orbital effect in the FF phase formation in both the nanowire-like ([Formula: see text]) and nanofilm-like ([Formula: see text]) regime. We have found that the irregular pattern of the FF phase which appears for the case of the nanowire-like regime, for the nanofilm-like geometry evolves towards the regular distribution in which the FF phase stability regions emerge periodically between the BCS states. The transition between these two different phase diagrams is explained as resulting from the orbital effect and the multigap character of superconductivity in the core/shell nanowires.

Routes to probe Bismuth induced strong-coupling superconductivity in bimetallic BiIn alloys

We report the observation of strong electron-phonon coupling in intergranular linked BiIn superconductors over an infinite range mediated by low-lying phonons. An enhanced superconducting transition temperature was observed from the magnetization, revealing a main diamagnetic Meissner state below T_C(0) = 5.86(1) K and a critical field H_C(0) = 1355(15) Oe with an In₂Bi phase of the composite sample. The electron-phonon coupling to low lying phonons is found to be the leading mechanism for observed strong-coupling superconductivity in the BiIn system. Our findings suggest that In₂Bi is in the strong-coupling region with T_C(0) = 5.62(1) K, λ_ep = 1.45, ω_ln = 45.92 K and α = 2.23. The estimated upper critical field can be well-described by a power law with α value higher than 2, consistent with the strong electron-phonon coupling.

MOF catalysts in biomass upgrading towards value-added fine chemicals

The development of new synthetic routes from biomass sources towards already existing molecules, which are then called bio-based molecules, or the transformation of biomass into new building blocks and materials will be of great impact. This review presents a critical comparison between MOFs and other catalysts (e.g. zeolites) for biomass transformation.

Dimensionality and Valency Dependent Quantum Growth of Metallic Nanostructures: A Unified Perspective

Quantum growth refers to the phenomena in which the quantum mechanically confined motion of electrons in metallic wires, islands, and films determines their overall structural stability as well as their physical and chemical properties. Yet to date, there has been a lack of a unified understanding of quantum growth with respect to the dimensionality of the nanostructures as well as the valency of the constituent atoms. Based on a first-principles approach, we investigate the stability of nanowires, nanoislands, and ultrathin films of prototypical metal elements. We reveal that the Friedel oscillations generated at the edges (or surfaces) of the nanostructures cause corresponding oscillatory behaviors in their stability, leading to the existence of highly preferred lengths (or thicknesses). Such magic lengths of the nanowires are further found to depend on both the number of valence electrons and the radial size, with the oscillation period monotonously increasing for alkali and group IB metals, and monotonously decreasing for transition and group IIIA-VA metals. When the radial size of the nanowires increases to reach ∼10 Å, the systems equivalently become nanosize islands, and the oscillation period saturates to that of the corresponding ultrathin films. These findings offer a generic perspective of quantum growth of different classes of metallic nanostructures.

Ultrathin two-dimensional superconductivity with strong spin-orbit coupling

We report on a study of epitaxially grown ultrathin Pb films that are only a few atoms thick and have parallel critical magnetic fields much higher than the expected limit set by the interaction of electron spins with a magnetic field, that is, the Clogston-Chandrasekhar limit. The epitaxial thin films are classified as dirty-limit superconductors because their mean-free paths, which are limited by surface scattering, are smaller than their superconducting coherence lengths. The uniformity of superconductivity in these thin films is established by comparing scanning tunneling spectroscopy, scanning superconducting quantum interference device (SQUID) magnetometry, double-coil mutual inductance, and magneto-transport, data that provide average superfluid rigidity on length scales covering the range from microscopic to macroscopic. We argue that the survival of superconductivity at Zeeman energies much larger than the superconducting gap can be understood only as the consequence of strong spin-orbit coupling that, together with substrate-induced inversion-symmetry breaking, produces spin splitting in the normal-state energy bands that is much larger than the superconductor's energy gap.

Compact low temperature scanning tunneling microscope with in-situ sample preparation capability

We report on the design of a compact low temperature scanning tunneling microscope (STM) having in-situ sample preparation capability. The in-situ sample preparation chamber was designed to be compact allowing quick transfer of samples to the STM stage, which is ideal for preparing temperature sensitive samples such as ultra-thin metal films on semiconductor substrates. Conventional spring suspensions on the STM head often cause mechanical issues. To address this problem, we developed a simple vibration damper consisting of welded metal bellows and rubber pads. In addition, we developed a novel technique to ensure an ultra-high-vacuum (UHV) seal between the copper and stainless steel, which provides excellent reliability for cryostats operating in UHV. The performance of the STM was tested from 2 K to 77 K by using epitaxial thin Pb films on Si. Very high mechanical stability was achieved with clear atomic resolution even when using cryostats operating at 77 K. At 2 K, a clean superconducting gap was observed, and the spectrum was easily fit using the BCS density of states with negligible broadening.

Quantum size effect on the paramagnetic critical field in free-standing superconducting nanofilms

The quantum size effect on the in-plane paramagnetic critical field in Pb(1 1 1) free-standing nanofilms is investigated with the use of the spin-generalized Bogoliubov-de Gennes equations. It is shown that the critical field oscillates as a function of the nanofilm thickness with the period ∼ 2 ML (even-odd oscillations), modulated by the beating effect. The calculated values of the critical field for different nanofilm thicknesses are analyzed in the context of the Clogston-Chandrasekhar limit. It is found that the critical field for superconducting nanofilms differs from this limit. This phenomena is explained in terms of quantization of the electron energy caused by the confinement of electron motion in a direction perpendicular to the film. The thermal effect and thickness-dependence of electron-phonon coupling on the value of the critical magnetic field are also studied.

Superconductivity of lanthanum revisited: enhanced critical temperature in the clean limit

The thickness dependence of the superconducting energy gap ΔLa of double hexagonally close packed (dhcp) lanthanum islands grown on W(110) is studied by scanning tunneling spectroscopy, from the bulk to the thin-film limit. Superconductivity is suppressed by the boundary conditions for the superconducting wavefunction on the surface and W/La interface, leading to a linear decrease of the critical temperature Tc as a function of the inverse film thickness. For the thick, bulk-like films, ΔLa and Tc are 40% larger compared to the literature values of dhcp La as measured by other techniques. This finding is reconciled by examining the effects of surface contamination as probed by modifications of the surface state, suggesting that the large Tc originates in the superior purity of the samples investigated here.

Unveiling mode-selected electron-phonon interactions in metal films by helium atom scattering

The quasi two-dimensional electron gas on a metal film can transmit to the surface even minute mechanical disturbances occurring in the depth, thus allowing the gentlest of all surface probes, helium atoms, to perceive the vibrations of the deepest atoms via the induced surface-charge density oscillations. A density functional perturbation theory (DFPT) and a helium atom scattering study of the phonon dispersion curves in lead films of up to 7 mono-layers on a copper substrate show that: (a) the electron-phonon interaction is responsible for the coupling of He atoms to in-depth phonon modes; and (b) the inelastic HAS intensity from a given phonon mode is proportional to its electron-phonon coupling. The direct determination of mode-selected electron-phonon coupling strengths has great relevance for understanding superconductivity in thin films and two-dimensional systems.

Growth morphology of thin films on metallic and oxide surfaces

In this work we briefly review recent investigations concerning the growth morphology of thin metallic films on the Mo(110) and Ni3Al(111) surfaces, and Fe and copper phthalocyanine (C32H16N8Cu) on the Al2O3/Ni3Al(111) surface. Comparison of Ag, Au, Sn, and Pb growth on the Mo(110) surface has shown a number of similarities between these adsorption systems, except that surface alloy formation has only been observed in the case of Sn and Au. In the Pb/Mo(110) and Pb/Ni3Al(111) adsorption systems selective formation of uniform Pb island heights during metal thin film growth has been observed and interpreted in terms of quantum size effects. Furthermore, our studies showed that Al2O3 on Ni3Al(111) exhibits a large superstructure in which the unit cell has a commensurate relation with the substrate lattice. In addition, copper phthalocyanine chemisorbed weakly onto an ultra-thin Al2O3 film on Ni3Al(111) and showed a poor template effect of the Al2O3/Ni3Al(111) system. In the case of iron cluster growth on Al2O3/Ni3Al(111) the nucleation sites were independent of deposition temperature, yet the cluster shape showed a dependence. In this system, Fe clusters formed a regular hexagonal lattice on the Al2O3/Ni3Al(111).

Macroscopic superconducting current through a silicon surface reconstruction with indium adatoms: Si(111)-(√7 × √3)-In

Macroscopic and robust supercurrents are observed by direct electron transport measurements on a silicon surface reconstruction with In adatoms [Si(111)-(√7 × √3)-In]. The superconducting transition manifests itself as an emergence of the zero resistance state below 2.8 K. I-V characteristics exhibit sharp and hysteretic switching between superconducting and normal states with well-defined critical and retrapping currents. The two-dimensional (2D) critical current density J(2D,c) is estimated to be as high as 1.8 A/m at 1.8 K. The temperature dependence of J(2D,c) indicates that the surface atomic steps play the role of strongly coupled Josephson junctions.

Surface alloy formation of noble adatoms adsorbed on Si(111)-√3 × √3-Pb surface: a first-principles study

The geometric structures, stability and electronic properties of initial stages of surface alloy formation for noble atoms adsorbed on Si(111)-)-√3 × √3-Pb surfaces have been comparatively and extensively studied by using first-principles calculations within density functional theory. Our results revealed that an Au trimer rather than a tetramer adsorption induces a surface alloy by combining with Pb atoms in covalent bonds, exhibiting semiconducting characteristics due to the localization of surface states. The stability of the two-dimensional (2D) surface alloy obeys the Hume-Rothery rule. The electronic structures of the 2D surface alloy are sensitive to the number of Au adatoms and can be modulated by the quantity of Au adatoms. Unlike the Au atoms, our further calculations indicated that adsorption of Ag or Cu atoms on the surface cannot form a surface alloy with Pb atoms in the surface layer due to a weaker interaction or smaller radius.

Freestanding palladium nanosheets with plasmonic and catalytic properties

Ultrathin metal films can exhibit quantum size and surface effects that give rise to unique physical and chemical properties. Metal films containing just a few layers of atoms can be fabricated on substrates using deposition techniques, but the production of freestanding ultrathin structures remains a significant challenge. Here we report the facile synthesis of freestanding hexagonal palladium nanosheets that are less than 10 atomic layers thick, using carbon monoxide as a surface confining agent. The as-prepared nanosheets are blue in colour and exhibit a well-defined but tunable surface plasmon resonance peak in the near-infrared region. The combination of photothermal stability and biocompatibility makes palladium nanosheets promising candidates for photothermal therapy. The nanosheets also exhibit electrocatalytic activity for the oxidation of formic acid that is 2.5 times greater than that of commercial palladium black catalyst.

Strong quantum size effects in Pb(111) thin films mediated by anomalous Friedel oscillations

Using first-principles calculations within density functional theory, we study Friedel oscillations (FOs) in the electron density at different metal surfaces and their influence on the lattice relaxation and stability of ultrathin metal films. We show that the FOs at the Pb(111) surface decay as 1/x with the distance x from the surface, different from the conventional 1/x(2) power law at other metal surfaces. The underlying physical reason for this striking difference is tied to the strong nesting of the two different Fermi sheets along the Pb(111) direction. The interference of the strong FOs emanating from the two surfaces of a Pb(111) film, in turn, not only results in superoscillatory interlayer relaxations around the center of the film, but also determines its stability in the quantum regime. As a simple and generic picture, the present findings also explain why quantum size effects are exceptionally robust in Pb(111) films.

Quantum size effects on the work function of metallic thin film nanostructures

In this paper, we present the direct observation of quantum size effects (QSE) on the work function in ultrathin Pb films. By using scanning tunneling microscopy and spectroscopy, we show that the very existence of quantum well states (QWS) in these ultrathin films profoundly affects the measured tunneling decay constant kappa, resulting in a very rich phenomenon of "quantum oscillations" in kappa as a function of thickness, L, and bias voltage, V(s). More specifically, we find that the phase of the quantum oscillations in kappa vs. L depends sensitively upon the bias voltage, which often results in a total phase reversal at different biases. On the other hand, at very low sample bias (|V(s)| < 0.03 V) the measurement of kappa vs. L accurately reflects the quantum size effect on the work function. In particular, the minima in the quantum oscillations of kappa vs. L occur at the locations where QWS cross the Fermi energy, thus directly unraveling the QSE on the work function in ultrathin films, which was predicted more than three decades ago. This further clarifies several contradictions regarding the relationship between the QWS locations and the work function.

Superconductivity in just four pairs of (BETS)2GaCl4 molecules

How small can a sample of superconducting material be and still display superconductivity? This question is relevant to our fundamental understanding of superconductivity, and also to applications in nanoscale electronics, because Joule heating of interconnecting wires is a major problem in nanoscale devices. It has been shown that ultrathin layers of metal can display superconductivity, but any limits on the size of superconducting systems remain a mystery. (BETS)2GaCl4, where BETS is bis(ethylenedithio)tetraselenafulvalene, is an organic superconductor, and in bulk it has a superconducting transition temperature Tc of approximately 8 K and a two-dimensional layered structure that is reminiscent of the high-Tc cuprate superconductors. Here, we use scanning tunnelling spectroscopy to show that a single layer of (BETS)2GaCl4 molecules on an Ag(111) surface displays a superconducting gap that increases exponentially with the length of the molecular chain. Moreover, we show that a superconducting gap can still be detected for just four pairs of (BETS)2GaCl4 molecules. Real-space spectroscopic images directly visualize the chains of BETS molecules as the origin of the superconductivity.

Quantum-well-induced giant spin-orbit splitting

We report on the observation of a giant spin-orbit splitting of quantum-well states in the unoccupied electronic structure of a Bi monolayer on Cu(111). Up to now, Rashba-type splittings of this size have been reported exclusively for surface states in a partial band gap. With these quantum-well states we have experimentally identified a second class of states that show a huge spin-orbit splitting. First-principles electronic structure calculations show that the origin of the spin-orbit splitting is due to the perpendicular potential at the surface and interface of the ultrathin Bi film. This finding allows for the direct possibility to tailor spin-orbit splitting by means of thin-film nanofabrication.

Quantum-well states in a double-well system: an example of Cu/Co(Ni)/Cu

The quantum-well (QW) states in the Cu/Co double-well system are studied by first-principles calculations. We have shown that the monolayer Ni or Co as a heterogeneous spacer in Cu QW can not only disturb the QW states extending into the whole structure, but also create new QW states because of the interfaces introduced, resulting in sub-well-confining electrons. If the QW state energy in two sub-wells is close to each other, these two sub-well QW states can couple together. We have also demonstrated that monolayer Co and Ni spacers play different roles for modulating QW states at different energy levels, which also result in a complicated distribution of QW states. The obtained results are in good agreement with experiment data.

Superconducting nanowires: quantum confinement and spatially dependent Hartree-Fock potential

It is well known that, in bulk, the solution of the Bogoliubov-de Gennes equations is the same whether or not the Hartree-Fock term is included. Here the Hartree-Fock potential is position independent and so gives the same contribution to both the single-electron energies and the Fermi level (the chemical potential). Thus, the single-electron energies measured from the Fermi level (they control the solution) stay the same. This is not the case for nanostructured superconductors, where quantum confinement breaks the translational symmetry and results in a position-dependent Hartree-Fock potential. In this case its contribution to the single-electron energies depends on the relevant quantum numbers. We numerically solved the Bogoliubov-de Gennes equations with the Hartree-Fock term for a clean superconducting nanocylinder and found a shift of the curve representing the thickness-dependent oscillations of the critical superconducting temperature to larger diameters.

Quantum oscillations in coupled two-dimensional electron systems

Quantum oscillations of the electron-phonon coupling of a Shockley surface state induced by the coupling to a metallic quantum well are observed experimentally as the thickness of the quantum well is increased. Microscopic calculations allow us to assign these oscillations to changes in the Eliashberg function, caused by a modulation in the electronic density overlap between the 2D surface state band and the 2D electron system of the quantum well and by the gradient of the one-electron potential in combination with the localized character of the Shockley-type surface state wave function. The findings are important in the context of the control of surface processes such as film growth and surface chemical reactions.

Phase relations associated with one-dimensional shell effects in thin metal films

The physical and chemical properties of thin metal films show damped oscillations as a function of film thickness (one-dimensional shell effects). While the oscillation period, determined by subband crossings of the Fermi level, is the same for all properties, the phases can be different. Specifically, oscillations in the work function and surface energy are offset by 1/4 of a period. For Pb(111) films, this offset is approximately 0.18 monolayers, a seemingly very small effect. However, aliasing caused by the discrete atomic layer structure leads to striking out-of-phase beating patterns displayed by these two quantities.

Size effects in the nonlinear resistance and flux creep in a virtual Berezinskii-Kosterlitz-Thouless state of superconducting films

We show that the size effects radically affect the electric-field-current (E-I) relation of superconducting films. We calculate E(J) due to thermally activated hopping of single vortices driven by a current I across the film in a magnetic field H, taking into account the interaction of free vortices with their antivortex images and peaks in the Meissner currents at the film edges. The unbinding of the virtual vortex-antivortex pairs not only mimics the transport uniform Berezinskii-Kosterlitz-Thouless behavior, it can also dominate the observed E(J) and result in the field-dependent Ohmic resistance at small I. We show that E(I) can be tuned by changing the film geometry and propose experimental tests of this theory.