Pseudogap mediated by quantum-size effects in lead islands

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.

Scanning tunneling microscopic observation of enhanced superconductivity in epitaxial Sn islands grown on SrTiO3 substrate

Recent experimental and theoretical studies of single-layer FeSe film grown on SrTiO₃ have revealed interface enhanced superconductivity, which opens up a pathway to promote the superconducting transition temperature. Here, to investigate the role of SrTiO₃ substrate in epitaxial superconducting film, we grew a conventional superconductor β-Sn (bulk T_c ∼ 3.72 K) onto SrTiO₃ substrate by molecular beam epitaxy. By employing scanning tunneling microscope and spectroscopic measurements, an enhanced T_c of 8.2 K is found for epitaxial β-Sn islands, deduced by fitting the temperature dependence of the gap values using the BCS formula. The observed interfacial charge injection and enhanced electron-phonon coupling are responsible for this T_c enhancement. Moreover, the critical field of 8.3 T exhibits a tremendous increase due to the suppression of the vortex formation. Therefore, the coexistence of enhanced superconductivity and high critical field of Sn islands demonstrates a feasible and effective route to improve the superconductivity by growing the islands of conventional superconductors on perovskite-type titanium oxide substrates.

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.

Tuning the Proximity Effect through Interface Engineering in a Pb/Graphene/Pt Trilayer System

The fate of superconductivity of a nanoscale superconducting film/island relies on the environment; for example, the proximity effect from the substrate plays a crucial role when the film thicknesses is much less than the coherent length. Here, we demonstrate that atomic-scale tuning of the proximity effects can be achieved by one atomically thin graphene layer inserted between the nanoscale Pb islands and the supporting Pt(111) substrate. By using scanning tunneling microscopy and spectroscopy, we show that the coupling between the electron in a normal metal and the Cooper pair in an adjacent superconductor is dampened by 1 order of magnitude via transmission through a single-atom-thick graphene. More interestingly, the superconductivity of the Pb islands is greatly affected by the moiré patterns of graphene, showing the intriguing influence of the graphene-substrate coupling on the superconducting properties of the overlayer.

Local measurement of the Eliashberg function of Pb islands: enhancement of electron-phonon coupling by quantum well states

Inelastic tunneling spectroscopy of Pb islands on Cu(111) obtained by scanning tunneling microscopy below 1 K provides a direct access to the local Eliashberg function of the islands with high energy resolution. The Eliashberg function describes the electron-phonon interaction causing conventional superconductivity. The measured Eliashberg function strongly depends on the local thickness of the Pb nanostructures and shows a sharp maximum when quantum well states of the Pb islands come close to the Fermi energy. Ab initio calculations reveal that this is related to enhanced electron-phonon coupling at these thicknesses.

A review of finite size effects in quasi-zero dimensional superconductors

Quantum confinement and surface effects (SEs) dramatically modify most solid state phenomena as one approaches the nanometer scale, and superconductivity is no exception. Though we may expect significant modifications from bulk superconducting properties when the system dimensions become smaller than the characteristic length scales for bulk superconductors-such as the coherence length or the penetration depth-it is now established that there is a third length scale which ultimately determines the critical size at which Cooper pairing is destroyed. In quasi-zero-dimensional (0D) superconductors (e.g. nanocrystalline materials, isolated or embedded nanoparticles), one may define a critical particle diameter below which the mean energy level spacing arising from quantum confinement becomes equal to the bulk superconducting energy gap. The so-called Anderson criterion provides a remarkably accurate estimate of the limiting size for the destabilization of superconductivity in nanosystems. This review of size effects in quasi-0D superconductors is organized as follows. A general summary of size effects in nanostructured superconductors (section 1) is followed by a brief overview of their synthesis (section 2) and characterization using a variety of techniques (section 3). Section 4 reviews the size-evolution of important superconducting parameters-the transition temperature, critical fields and critical current-as the Anderson limit is approached from above. We then discuss the effect of thermodynamic fluctuations (section 5), which become significant in confined systems. Improvements in fabrication methods and the increasing feasibility of addressing individual nanoparticles using scanning probe techniques have lately opened up new directions in the study of nanoscale superconductivity. Section 6 reviews both experimental and theoretical aspects of the recently discovered phenomena of 'parity effect' and 'shell effect' that lead to a strong, non-monotonic size dependence of the superconducting energy gap and associated properties. Finally, we discuss in section 7 the properties of ordered heterostructures (bilayers and multilayers of alternating superconducting and normal phases) and disordered heterostructures (nanocomposites consisting of superconducting and normal phases), which are primarily controlled by the proximity effect.

Superconducting nanofilms: molecule-like pairing induced by quantum confinement

Quantum confinement of the perpendicular motion of electrons in single-crystalline metallic superconducting nanofilms splits the conduction band into a series of single-electron subbands. A distinctive feature of such a nanoscale multi-band superconductor is that the energetic position of each subband can vary significantly with changing nanofilm thickness, substrate material, protective cover and other details of the fabrication process. It can occur that the bottom of one of the available subbands is situated in the vicinity of the Fermi level. We demonstrate that the character of the superconducting pairing in such a subband changes dramatically and exhibits a clear molecule-like trend, which is very similar to the well-known crossover from the Bardeen-Cooper-Schrieffer regime to Bose-Einstein condensation (BCS-BEC) observed in trapped ultracold fermions. For Pb nanofilms with thicknesses of 4 and 5 monolayers (MLs) this will lead to a spectacular scenario: up to half of all the Cooper pairs nearly collapse, shrinking in the lateral size (parallel to the nanofilm) down to a few nanometers. As a result, the superconducting condensate will be a coherent mixture of almost molecule-like fermionic pairs with ordinary, extended Cooper pairs.

Dynamical Coulomb blockade observed in nanosized electrical contacts

Electrical contacts between nanoengineered systems are expected to constitute the basic building blocks of future nanoscale electronics. However, the accurate characterization and understanding of electrical contacts at the nanoscale is an experimentally challenging task. Here, we employ low-temperature scanning tunneling spectroscopy to investigate the conductance of individual nanocontacts formed between flat Pb islands and their supporting substrates. We observe a suppression of the differential tunnel conductance at small bias voltages due to dynamical Coulomb blockade effects. The differential conductance spectra allow us to determine the capacitances and resistances of the electrical contacts which depend systematically on the island-substrate contact area. Calculations based on the theory of environmentally assisted tunneling agree well with the measurements.

Interface effects on the quantum well states of Pb thin films

Using scanning tunneling spectroscopy, we have studied the interface effect on quantum well states of Pb thin films grown on various metal-terminated (Pb, Ag, and Au) n-type Si(111) surfaces and on two different p-type Si(111) surfaces. The dispersion relation E(k) of the electrons of the Pb film and the phase shift at the substrate interface were determined by applying the quantization rule to the measured energy positions of the quantum well states. Characteristic features in the phase shift versus energy curves were identified and were correlated to the directional conduction band of the silicon substrate and to the Schottky barrier formed between the metal film and the semiconductor. A model involving the band structure of the substrate, the Schottky barrier, and the effective thickness of the interface was introduced to qualitatively but comprehensively explain all the observed features of the phase shift at the substrate interface. Our physical understanding of the phase shift is critically important for using interface modification to control the quantum well states.

Size-dependent superconducting state of individual nanosized Pb islands grown on Si(111) by tunneling spectroscopy

By measuring the temperature-dependent tunneling spectroscopy of a set of flat-top Pb islands from 3.2 to 15 K, the limiting size of a nine-monolayer-thick Pb island with superconductivity above 3.2 K was determined to be ∼ 30 nm(2), in good agreement with the Anderson criterion. Further analysis indicates that the zero-temperature energy gap decreases significantly faster than the transition temperature when the Pb island size approaches this limit. This leads to a decrease of 2Δ(0)/k(B)T(C) from 4.5 to 3.3, thus showing that the Pb island superconductors undergo a change from strong to weak electron-phonon coupling.

Vortex properties of two-dimensional superconducting Pb films

Using low temperature scanning tunnelling microscopy/spectroscopy (STM/STS) we have investigated the vortex behaviours of two-dimensional superconducting Pb films at different thicknesses. STS at the vortex core shows an evolution of electronic states with film thickness. Transition from the clean limit to the dirty limit of superconductivity is identified, which can be ascribed to the decreased electronic mean free path induced by stronger scattering from the disordered interface at smaller thicknesses. A magnetic field dependent vortex core size is observed even for such a low- κ superconductor. The weak pinning induced by surface defects leads to the formation of a distorted hexagonal vortex lattice.

Reduction of the superconducting gap of ultrathin Pb islands grown on Si(111)

The energy gap Delta of superconducting Pb islands grown on Si(111) was probed in situ between 5 and 60 monolayers by low-temperature scanning tunneling spectroscopy. Delta was found to decrease from its bulk value as a function of inverse island thickness. Corresponding T_{c} values, estimated using bulk gap-to-T_{c} ratio, are in quantitative agreement with ex situ magnetic susceptibility measurements, however, in strong contrast to previous scanning probe results. Layer-dependent ab initio density functional calculations for freestanding Pb films show that the electron-phonon coupling constant, determining T_{c}, decreases with diminishing film thickness.