Experimental observation of thermal fluctuations in single superconducting Pb nanoparticles through tunneling measurements

An important question in the physics of superconducting nanostructures is the role of thermal fluctuations on superconductivity in the zero-dimensional limit. Here, we probe the evolution of superconductivity as a function of temperature and particle size in single, isolated Pb nanoparticles. Accurate determination of the size and shape of each nanoparticle makes our system a good model to quantitatively compare the experimental findings with theoretical predictions. In particular, we study the role of thermal fluctuations (TF) on the tunneling density of states (DOS) and the superconducting energy gap (D) in these nanoparticles. For the smallest particles, h < 13nm, we clearly observe a finite energy gap beyond Tc giving rise to a "critical region". We show explicitly through quantitative theoretical calculations that these deviations from mean-field predictions are caused by TF. Moreover, for T << Tc, where TF are negligible, and typical sizes below 20 nm, we show that D gradually decreases with reduction in particle size. This result is described by a theoretical model that includes finite size effects and zero temperature leading order corrections to the mean field formalism.Comment: Accepted in Physical Review

Image potential states as quantum probe of graphene interfaces

Image potential states (IPSs) are electronic states localized in front of a surface in a potential well formed by the surface projected bulk band gap on one side and the image potential barrier on the other. In the limit of a two-dimensional solid a double Rydberg series of IPSs has been predicted which is in contrast to a single series present in three-dimensional solids. Here, we confirm this prediction experimentally for mono- and bilayer graphene. The IPSs of epitaxial graphene on SiC are measured by scanning tunnelling spectroscopy and the results are compared to ab-initio band structure calculations. Despite the presence of the substrate, both calculations and experimental measurements show that the first pair of the double series of IPSs survives, and eventually evolves into a single series for graphite. Thus, IPSs provide an elegant quantum probe of the interfacial coupling in graphene systems.Comment: Accepted for publication in New Journal of Physic

Observation of shell effects in superconducting nanoparticles of Sn

In a zero-dimensional superconductor, quantum size effects(QSE) not only set the limit to superconductivity, but are also at the heart of new phenomena such as shell effects, which have been predicted to result in large enhancements of the superconducting energy gap. Here, we experimentally demonstrate these QSE through measurements on single, isolated Pb and Sn nanoparticles. In both systems superconductivity is ultimately quenched at sizes governed by the dominance of the quantum fluctuations of the order parameter. However, before the destruction of superconductivity, in Sn nanoparticles we observe giant oscillations in the superconducting energy gap with particle size leading to enhancements as large as 60%. These oscillations are the first experimental proof of coherent shell effects in nanoscale superconductors. Contrarily, we observe no such oscillations in the gap for Pb nanoparticles, which is ascribed to the suppression of shell effects for shorter coherence lengths. Our study paves the way to exploit QSE in boosting superconductivity in low-dimensional systems

Influence of the Rotational Domain in the Growth of Transition Metal Clusters on Graphene

The influence of the relative orientation between graphene monolayers and the underlying substrate on the growth of transition metal clusters over epitaxial graphene on Ir(111) surfaces is investigated by scanning tunneling microscopy (STM) in ultrahigh vacuum (UHV). This experimental study has been carried out for W and Ir clusters and, in both cases, the results revealed the existence of noticeable differences in the size and distribution of the clusters formed over areas where graphene and substrate lattices are aligned with respect to those grown on regions where both lattices present a relative rotation angle. In particular, while over aligned domains, in a consistent way with previous findings, the formation of ordered arrays of monodisperse clusters exhibiting a great structural perfection is observed, on the rotated ones it takes place the formation of larger size isolated clusters scattered around the surface. Moreover, the boundaries between different rotational domains are found to be decorated by these larger clusters. This disparity observed in the growth of clusters is explained in terms of the differences in the graphenesubstrate interaction existing on aligned and rotated domains

Measuring graphene’s Berry phase at B = 0 T

International audienceThe Berry phase of wave functions is a key quantity to understand various low-energy propertiesof matter, among which electric polarisation, orbital magnetism, as well as topological and ultra-relativisticphenomena. Standard approaches to probe the Berry phase in solids rely on the electron dynamics inresponse to electromagnetic forces. In graphene, probing the Berry phase π of the massless relativisticelectrons requires an external magnetic field. Here, we show that the Berry phase also affects the staticresponse of the electrons to a single atomic scatterer, through wavefront dislocations in the surroundingstanding-wave interference. This provides a new experimental method to measure the graphene Berry phasein the absence of any magnetic field and demonstrates that local disorder can be exploited as probe oftopological quantum matter in scanning tunnelling microscopy experiments.Les interférences de quasiparticules observées par microscopie à effet tunnel sont particulièrementutiles pour étudier les propriétés électroniques de matériaux en surfaces. Ces interférences possèdent desinformations sur la surface de Fermi du système et leur résolution en énergie permet, dans certains cas,de reconstruire la relation dispersion. Nous montrons ici que les images d’interférences de quasiparticulespeuvent aussi contenir une information sur la phase de Berry qui caractérise la structure de bande dumatériau. La phase de Berry est une phase géométrique que les fonctions d’onde electroniques acquièrentlors d’une évolution cyclique dans un espace de paramètres. Elle est quantifiée lorsque la trajectoire del’évolution enserre une singularité des fonctions d’onde. Il s’agit alors d’une propriété topologique de lastructure de bande. La phase de Berry dans les solides est traditionnellement mesurée en appliquant deschamps électromagnétiques pour forcer les particules à former de trajectoires fermées. L’utilisation de lafigure d’interférence de quasiparticules permet de s’extraire de ce paradigme car la phase de Berry peutaffecter la réponse statique des électrons au désordre en l’absence de champ électromagnétique

Friedel oscillations in graphene-based systems probed by Scanning Tunneling Microscopy

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Observation of Kekulé vortices around hydrogen adatoms in graphene

International audienceAbstract Fractional charges are one of the wonders of the fractional quantum Hall effect. Such objects are also anticipated in two-dimensional hexagonal lattices under time reversal symmetry—emerging as bound states of a rotating bond texture called a Kekulé vortex. However, the physical mechanisms inducing such topological defects remain elusive, preventing experimental realization. Here, we report the observation of Kekulé vortices in the local density of states of graphene under time reversal symmetry. The vortices result from intervalley scattering on chemisorbed hydrogen adatoms. We uncover that their 2 π winding is reminiscent of the Berry phase π of the massless Dirac electrons. We can also induce a Kekulé pattern without vortices by creating point scatterers such as divacancies, which break different point symmetries. Our local-probe study thus confirms point defects as versatile building blocks for Kekulé engineering of graphene’s electronic structure