Long range coherent magnetic bound states in superconductors

Abstract: The quantum coherent coupling of completely different degrees of freedom is a challenging path towards creating new functionalities for quantum electronics. Usually the antagonistic coupling between spins of magnetic impurities and superconductivity leads to the destruction of the superconducting order. Here we show that a localized classical spin of an iron atom immersed in a superconducting condensate can give rise to new kind of long range coherent magnetic quantum state. In addition to the well-known Shiba bound state present on top of an impurity we reveal the existence of a star shaped pattern which extends as far as 12 nm from the impurity location. This large spatial dispersion turns out to be related, in a non-trivial way, to the superconducting coherence length. Inside star branches we observed short scale interference fringes with a particle-hole asymmetry. Our theoretical approach captures these features and relates them to the electronic band structure and the Fermi wave length of the superconductor. The discovery of a directional long range effect implies that distant magnetic atoms could coherently interact leading to new topological superconducting phases with fascinating properties.

Long Range Coherent Magnetic Bound States in Superconductors

The paper titled "Long Range Coherent Magnetic Bound States in Superconductors" explores the formation and characteristics of magnetic bound states around magnetic impurities in superconductors with a focus on the role of reduced dimensionality. The study is motivated by the quantum coupling of different degrees of freedom, which paves the way for novel functionalities in quantum electronics. Through a combination of theoretical modeling and experimental evidence, the authors present insights into the spatial extension of Yu-Shiba-Rusinov (YSR) bound states, which are induced by magnetic impurities in superconductors.

Experimental and Theoretical Insights

The research underscores the significance of dimensionality in the spatial extent of YSR states. Theoretical calculations grounded in Rusinov's approach reveal that a three-dimensional isotropic s-wave superconductor leads to a rapid decay of YSR states—a result consistent with earlier scanning tunneling microscopy (STM) studies of magnetic impurities such as Co, Cr, Mn, and Gd on Pb or Nb crystals. However, in the context of two-dimensional materials, such as 2H-NbSe(_2), these states exhibit a significantly longer spatial extent. Specifically, in the case of 2H-NbSe(_2), the spatial extent of YSR states was found to be approximately 10 nm, exceeding prior observations of a few angstroms in three-dimensional materials.

The study includes scanning tunneling spectroscopy at 320 mK, which reveals YSR bound states with a six-pointed star-shaped signature surrounding iron impurities embedded in the 2H-NbSe(_2) crystal lattice. The unique star-shaped structure aligns with the crystallographic axes and is indicative of the anisotropy within the Fermi surface, corroborated by simulations using the Bogoliubov-de Gennes formalism.

Implications and Future Directions

The implications of these findings have both theoretical and practical significance in the realm of quantum materials and devices. The extended spatial reach of YSR states in two-dimensional superconductors like 2H-NbSe(_2) creates opportunities for remote coupling of magnetic impurities through the superconducting state. This could simplify the manipulation of Majorana quasiparticles, crucial for the development of topological quantum devices.

The paper speculates on the broader impact of these findings, suggesting that the interaction between extensive YSR states may lead to novel topological phases in hybrid systems. Arrays of magnetic atoms, organized by self-assembly on templated substrates, could leverage this interaction to achieve a variety of topological orders. Notably, a chain of magnetic atoms with helical spin ordering could engender topological triplet superconductivity, potentially hosting Majorana quasiparticles.

In conclusion, the detailed exploration of YSR bound states within two-dimensional superconductors opens new avenues for research and applications in advanced quantum technologies. By shedding light on the effects of dimensionality on the coherence and range of magnetic bound states, this work enriches our understanding of the fundamental physics governing the interactions between superconductivity and magnetism. Such insights could be pivotal in steering future experimental endeavors and theoretical explorations in the rapidly advancing field of condensed matter physics.