Shiba Lattices in Supramolecular Assembly / superconductor hybrids

The realization of novel quantum phases with specific topological properties has been one of the most important and competitive research fields in solid state physics in the last few years due to their importance for quantum computing. For instance, the theoretical prediction of topological protected states has been awarded with the Nobel Prize in physics in 2016. One of the most promising ways to achieve this purpose is the use of magnetic impurities in superconductors for the production of Majorana bound states (MBS): possible building blocks for quantum computing. A first step in this direction has been experimentally realized by the research group of A. Yazdani[1]. In their work the authors could have produced such states in monoatomic chains of Fe atoms deposited on lead. This study has inspired a tremendous amount of experimental work. From the theoretical point of view, the situation is quite settled in the abundant literature and the ingredients for the emergence of MBS in chains of magnetic building blocks in contact with superconductors are well known. For instance, spin-orbit coupling is a key interaction. It induces a triplet component of the Cooper pairing and potentially promotes the emergence of topologically protected states. We propose here the realization of systems where the magnetic centers are composed of (1D or 2D) assemblies of magnetic molecules at the surface of superconductors with strong Rashba spin-orbit interactions.

From single impurity to Bogoliubov quasiparticle bands
A single magnetic impurity with a strong spin momentum dipped in a BCS superconductor breaks locally Cooper pairs and gives rise to Yu-Shiba-Rusinov states (latter called Shiba states) inside the superconducting gap made of Bogoliubov quasiparticles (with magnetically polarized electron and hole components) bound to the impurity. As it was shown by some of us the Shiba states can propagate at lengthscales as long as the coherence length of the Cooper pairs[2]. If the spin momentum has some degrees of freedom, a strong interaction may lead to the Kondo physics. Kondo physics tends to cancel the magnetic moment of the impurity and thus, has to be avoided. A mediated interaction between neighboring Shiba impurities in a lattice yields the emergence of Bogoliubov quasiparticle bands inside the superconducting gap. These bands are the ones which may generate topologically protected states and MBS. So the control of the interaction between the magnetic centers themselves and with the superconductor is the key element of the project.

STM image of a supramolecular assembly of specially designed magnetic molecules on a single Pb crystal (22x22 nm²).
Top: STS of a single molecule at 1.1 K with a SC tip.
Bottom: deconvoluted spectrum showing the density of quasiparticle states with the SC gap of the substrate (2∆≈2.8 meV) and two very sharp Shiba peaks in the gap, close to EF.

This project proposes the investigation of lattices of Shiba impurities based on supramolecular assemblies. The use of magnetic supramolecular assembly at superconductor surface represents a promising route to achieve the necessary control of the molecule/molecule and molecule/substrate interactions. Indeed, one can anticipate that various interactions can be efficiently tuned by using properly functionalized molecules. Depending on the chemical composition of the molecules, their absorption sites and the manner the assembly organizes on the superconductor, different scenarios are possible concerning the quantum ground states of the system going from a collection of individual non interacting magnetic centers to the lattices of Kondo or Shiba impurities[3].

[1] S.Nadj-Perge et al., Science 346, 602-607 (2014).
[2] G.C. Ménard, et al., Nat. Phys. 11 (12), 1013-1016 (2015).
[3] K. J. Franke et al., Science 332, 940-944 (2011) ; N. Hatter et al., Nature Comm. 6, 8988 (2015) ; J. J. Park et al. Science 328, 1370-1373 (2010) ; at metal surface: N. Tsukahara et al., J. Chem. Phys. 141, 054702 (2014). J. Shuai-Hua et al. Chinese Phys. Lett., 27, 087202 (2010); N. Tsukahara et al., Phys. Rev. Lett. 106, 187201 (2011).

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