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**Team**

- Permanent members: Christophe Brun,Tristan Cren, François Debontridder

**We are interested in the ultimate limit where superconducting materials are composed of only one or a few atomic layers. One way to study these systems is to observe how they respond to perturbations induced by whether magnetic or non-magnetic defects. In the case of conventional superconductors, known as BCS, P.W. Anderson has shown that they are virtually insensitive to non-magnetic defects. However, we have recently observed that Pb monolayers show strong fluctuations induced by a non-magnetic disorder at an unexpected short length scale. This is a purely 2D dimensionality effect. Unlike non-magnetic defects, magnetic defects are known to be highly destructive for superconductivity. A low concentration of magnetic defects is sufficient to destroy the superconducting state. This effect is even more pronounced in the low dimensional range. Indeed, we have shown that in 2D the effect of a single magnetic atom is manifested by the appearance of a bound state in the gap whose wave function extends extremely far from the impurity. Finally, the magnetic and non-magnetic defects allow us to explore the symmetry of the superconducting wave function, allowing us to know if the Cooper pairs are spin singlet (non-polarized) or spin triplet (magnetic) and if they are of symmetry s, p, d or f or a mixture of all these symmetries. For this we use Fourier transform tunneling microscopy measurements.**

**A giant quantum magnetic state in a two-dimensional superconductor****What are the basic building blocks for superconductivity in an atomic monolayer?****Effects of strong non-magnetic disorder on ultra-thin films of conventional superconductors (NbN)**

**A giant quantum magnetic state in a two-dimensional superconductor **

About fifty years ago, physicists L. Yu, H. Shiba and A. Rusinov independently predicted the formation of localized quantum states around a magnetic atom immersed in a superconducting material. We have recently observed quantum states produced by individual magnetic atoms in a two-dimensional superconductor and measured their size and structure by tunneling. The spatial extension of these states is about 20 times larger than previously observed in three-dimensional systems. Theoretical modeling has made it possible to interpret this phenomenon quantitatively both from the point of view of the spatial extension and the oscillating structure or star shape of the wave function.

**Figure 1**: *(top) Spectroscopic map containing several magnetic impurities located at different depths in the material. (bottom) Tight binding stimulation of Yu-Shiba-Rusinov states*

We have studied NbSe2 crystals that become superconducting below 7 Kelvin and whose lamellar structure induces a quasi two-dimensional behavior. The growth of these single crystals was achieved by adding a low percentage of iron impurities leading to the inclusion of homogeneously distributed magnetic defects in the samples. We measured the spatial dependence of the tunnel current and reconstructed the electronic state distribution. We were thus able to reveal the presence of extended and star-shaped states isolated from each other. We conducted theoretical investigations and highlighted the link between dimensionality and spatial extension as well as the role of different coupling parameters in the fine structure of these states. Calculations based on the described electronic structure with a strong link model have demonstrated the impact of the band structure of the system on the six-branched star shape of the wave function of the Yu-Shiba-Rusinov states. These results pave the way for a new approach to couple distant magnetic impurities and produce quasi Majorana particles.

**Récent publication**

- G. C. Ménard, S. Guissard, C. Brun, S. Pons, V. S. Stolyarov, F. Debontridder, M. V. Leclerc, E. Janod, L. Cario, D. Roditchev, P. Simon et T. Cren. Coherent long-range magnetic bound states in a superconductor. Nature Physics
*(*2015) http://www.nature.com/nphys/journal/v11/n12/full/nphys3508.html

**Principales collaborations**

- Group of Laurent Cario, Institut Jean Rouxel, Université de Nantes.
- Group of Pascal Simon, LPS, Université Paris Saclay

**Funding**

- Projet-ANR-14-CE32-0021 Mistral https://anr.fr/Projet-ANR-14-CE32-0021
- Projet-ANR-16-CE30-0011ANR RODESIS https://anr.fr/Projet-ANR-16-CE30-0011

**Highlights**

**What are the basic building blocks for superconductivity in an atomic monolayer?**

The basic element of superconductivity is the Cooper pair and the spatial variations in superconductors are usually given by this length or by the penetration length of the magnetic field. However, by finely analyzing a monoatomic layer of superconducting lead, we have shown that there are spatial fluctuations in superconductivity at length scales much smaller than the size of Cooper pairs. This observation is an indication that in this system the superconducting state is more complex than previously thought and it soon became apparent that this is a new effect related to the extreme two-dimensionality of the Pb monolayer.

In the usual mechanism leading to superconductivity, electrons associate to form Cooper pairs, which all condense into a single quantum state. Generally, these “Cooper pairs” have a spatial extension of several tens of nanometers, which is much larger than the size of the atoms. By analyzing the spatial structure of a superconductor composed of a monoatomic layer of lead deposited on a silicon substrate, we have uncovered structures in the superconducting state that are comparable in size to the size of a few atoms, i.e. much smaller than the Cooper pairs, which are considered the basic building blocks of the superconducting state. This work is in contradiction with theoretical models of superconductivity in such systems. It suggests the existence of strong Bose-Einstein-type quantum corrections to the Cooper pairs, due to an increased importance of correlation effects between electrons via disorder in this purely two-dimensional system.

**Figure 2: ***Effects of defects on the superconductivity of a Pb/Si atomic monolayer (111)a) This map illustrates the role played by surface steps on the superconductivity of a single atomic plane. This topographic image measured by scanning tunneling microscopy (STM) shows a 600×600 nm2 area with several atomic terraces separated by monoatomic steps. In a weak magnetic field (0.04T) the blue areas remain superconducting and the vortices are trapped only on the weak spots (Josephson links) that are the step edges.b) Small scale zoom in the middle of a terrace. We can see the atomic resolution as well as several orientation domains containing different structural defects (adatoms, clusters, gaps, grain boundaries).c) This map measured on zone b) shows the collective role played by the defects. Large spectroscopic fluctuations (visualized by the contrast between red and blue-green areas) occur over lengths much smaller than the superconducting coherence length ξ= 50 nm*

We grew crystalline lead monolayers on a silicon substrate under ultra-high vacuum and then analyzed the electron structure of this system by tunneling microscopy at very low temperature and under a magnetic field. We thus determined the effect of point defects on the electron excitation spectrum. As a general rule, a tunnel conductance spectrum acquired on a conventional superconductor (BCS) shows two peaks, called quasiparticle or coherence peaks, surrounding an energy band gap where the conductance is zero. In the monolayers studied, we have shown a spatial variation of these spectra at a scale smaller than the coherence length of the Cooper pairs, the latter being about 50 nm in both systems. A second, equally surprising effect has been demonstrated for a lower density lead atomic monolayer: the spatial fluctuations of the band gap fill have a characteristic length that is also much smaller than the size of the Cooper pairs. The theoretical analysis of this system has allowed us to understand the origin of this second effect: a particular interaction at the surface of materials between the spin and the orbital moment of the electrons, known as the Rashba effect. These results also make it possible to anticipate similar effects on other ultrathin superconducting or interface films.

**Récent publications**

- C. Brun, T. Cren, V. Cherkez, F. Debontridder, S. Pons, D. Fokin, M. C. Tringides, S. Bozhko, L. B. Ioffe, B. L. Altshuler et D. Roditchev. Remarkable effects of disorder on superconductivity of single atomic layers of lead on silicon. Nature Physics (2014) https://www.nature.com/articles/nphys2937

**Fait marquant**

*Actualité Scientifique de l’Institut de Physique du CNRS 12 mai 2014*

**Effects of strong non-magnetic disorder on ultra-thin films of conventional superconductors (NbN)**

We seek to determine the ultimate conditions for the existence of conventional ultra-thin film superconductivity in the presence of non-magnetic disorder. This area of superconductivity is also called the study of the “superconductor-insulator transition”. The aim is to understand why and how certain superconducting systems become insulating as soon as a critical disorder is reached. It also raises the question of the nature of this insulating state as well as the nature of possible metallic intermediate states that can be reached before (or instead of) the insulating transition. These materials have applications in space (bolometers) or in quantum optics (single photon detectors).

Among the various experimental systems studied in this field, we are studying a class of disordered thin films called “amorphous-homogeneous” NbN films (manufactured by sputtering on a sapphire substrate) which present for thicknesses as low as 10nm a spatially homogeneous superconducting state well described by the BCS (Bardeen-Cooper-Schrieffer) theory. When the thickness of the NbN layers is reduced, a concomitant progressive decrease of the Δ gap (about 3 meV at maximum) and of the critical temperature Tc (about 15 K at maximum) is observed. Our transport and STS measurements suggest that this is essentially a Finkelstein-like mechanism, i.e. induced by Coulombic repulsion between electrons which increases in NbN as the disorder increases and consequently weakens the electron pairing related to superconductivity.

We have been able to show that the spatial inhomogeneities observed for the superconducting gap at 300mK are correlated below Tc and above Tc at 4.2K where a so-called pseudogap temperature regime exists. We have also shown the existence of a systematic spatial correlation between the local reduction of the superconducting gap and the effect of Coulombic interactions combined with the potential for disorder which translate in the STS tunnel spectra into a reduction of the DOS around EF (an effect called Altshuler-Aronov from the name of the theorists who described it).

**Figure 3**:*Spatial cross correlations between the local superconducting gap Δ(r) and the exponent α(r) characterizing the Altshuler-Aronov effect. a) represents the STM topography of the studied area (300×300 nm2). b) represents on the same area the spatial distribution of the gap Δ(r). c) represents on the same area the spatial distribution of the exponent α(r) characterizing the Altshuler-Aronov effect. The latter is extracted by adjusting at each point of the topography the dI/dV(V) spectrum by a power law proportional to V α(r) between 5 and 30 mV. d) represents the cross-correlation between the topography in a) and the gap map in b). We can see that there are no cross-correlations. e) and f) respectively represent the statistical distribution of the gap and exponent values α. g) represents the cross-correlation between the local gap map b) and the local exponent map c). The strong negative signal in the center shows a strong anti-correlation (-0.55 in the center). This is the central result of this study. This means that as shown in graph h, in regions where the gap is larger (red spectrum), the dI/dV(V) spectrum measured at higher energy is less. deep (red spectrum) as shown in graph i). And vice-versa for regions with smaller gaps (blue spectra). This figure is figure 1 of paper C. Carbillet et al. Phys. Rev. B 102, 024504, 2020.*

These results show that the emerging granularity of superconducting properties is related to Coulombian effects. However, until now, theoretical treatments of the origin of this granularity have only involved the role of the disorder without Coulombian interactions. The Finkelstein mechanism describing the reduction of the gap and Tc due to the combination disorder + Coulombian effect was well known and documented theoretically and experimentally, but only as a macroscopic effect. Thanks to our study we have been able to show that there is a bridge between these two descriptions and that a microscopic “Finkelstein-like” quasi-quantitative description is possible to depict the emerging granularity in disordered superconducting thin films.

**Recent publication**

- C. Carbillet, V. Cherkez, M. A. Skvortsov, M. V. Feigel’man, F. Debontridder, L. B. Ioffe, V. S. Stolyarov, K. Ilin, M. Siegel, D. Roditchev, T. Cren, and C. Brun. Spectroscopic evidence for strong correlations between local superconducting gap and local Altshuler-Aronov density of states suppression in ultrathin NbN films. Phys. Rev. B 102, 024504 (2020) https://hal.archives-ouvertes.fr/hal-03060011/document

**Main collaborations**

- K. Ilin et M. Siegel du Karlsruhe Institute of Technology
- Lev Ioffe du laboratoire de physique théorique et des hautes énergies à SU
- Mikhail Skvortsov et Mikhail Feigel’man de l’institut Landau à Moscou

**Funding**

- Project-ANR-15-CE30-0026 Superstripes https://anr.fr/Project-ANR-15-CE30-0026