Imaging the spatial form of a superconducting order parameter via Josephson scanning tunneling spectroscopy

Abstract

Motivated by recent experiments, we investigate Josephson scanning tunneling spectroscopy in an s-wave superconductor. We demonstrate that the spatial oscillations in the superconducting order parameter induced by defects can be spatially imaged through local measurements of the critical Josephson current, providing unprecedented insight into the nature of superconductivity. The spatial form of the Josephson current reflects the nature of the defects, and can be used to probe defect-induced phase transitions from an S = 0 to an S = 1/2 ground state.Imaging the spatial variations of superconducting order parameters has been a long-sought goal, as it could provide direct insight into the nature of exotic superconducting phases ranging from the Fulde-Ferrell-LarkinOvchinnikov state [1][2][3][4] in the presence of magnetic fields, and intrinsically disordered superconductors [5] to the pair-density wave state predicted to exist in the cuprate superconductors [6][7][8][9][10]. As the oscillations of the superconducting order parameter are expected to occur on the length scale of a few lattice constants, and their detection hence requires near atomic resolution, recent experimental efforts have focused on the development of Josephson scanning tunneling spectroscopy (JSTS) [11][12][13][14]. The idea underlying JSTS is that the Josephson current, I J , [15] flowing between a superconducting JSTS tip and a superconductor probes the order parameter of the latter [16]. Using this technique, Hamidian et al. [12] have argued that the spatial oscillations in I J induced by defects in the cuprate superconductor Bi 2 Sr 2 CaCu 2 O 8+x provide evidence for the existence of a pair-density wave. Complementary to this study, Randeria et al. [14] showed that pair-breaking magnetic Fe atoms located on the surface of the s-wave superconductor Pb lead to a suppression of the local Josephson current. So far, however, there has been no proof for the assumption that the experimentally measured spatial variations of the Josephson current indeed reflect those of the superconducting order parameter.In this article, we provide this missing proof by theoretically demonstrating that even short length scale fluctuations of the superconducting order parameter can be spatially imaged through local measurements of the Josephson current, thus opening unprecedented possibilities for gaining insight into the nature of superconductivity. Using a Keldysh non-equilibrium Green's function formalism, we investigate the local Josephson current between a superconducting JSTS tip with s-wave symmetry, and an s-wave superconductor [as schematically shown in Fig. 1(a)], and its relation to the local superconducting order parameter. We demonstrate that spatial oscillations in the superconducting order parameter, ∆(r), induced by both magnetic and non-magnetic defects can be imaged at the atomic length scale by measuring the spatial form of the critical Josephson current, I c (r). Moreover, for magnetic defects, the existence of defect-induced Shiba states [17][1...

Topological Superconductivity in Skyrmion Lattices

“…The second unique feature is the presence of spintriplet superconducting correlations which are a crucial requirement for the emergence of topological superconductivity [15]. The development of Josephson scanning tunneling spectroscopy (JSTS) [25][26][27][28][29] has provided a unique opportunity to visualize not only these correlations in real space at the atomic level, but also to investigate the effects of the inhomogeneous magnetic structure of the skyrmion lattice on the superconducting swave order parameter, ∆(r) [30]. Specifically, pair breaking effects of the magnetic moments lead to a spatially non-uniform suppression of ∆(r) inside the skyrmion ribbon (see Fig.…”

Topological superconductivity in skyrmion lattices

“…The second unique feature is the presence of spin-triplet superconducting correlations which are a necessary requirement for the emergence of topological superconductivity 16 . The development of JSTS [26][27][28][29][30] has provided a unique opportunity to visualize not only these correlations in real space at the atomic level but also to investigate the effects of the inhomogeneous magnetic structure of the skyrmion lattice on the superconducting s-wave order parameter, Δ(r) 31 . Specifically, pair breaking effects of the magnetic moments lead to a spatially nonuniform suppression of Δ(r) inside the skyrmion ribbon (see Fig.…”

“…4f), that could be measured via JSTS using a tip with an s-wave superconducting order parameter (for details, see ref. 31 ), thus providing direct insight into the strength of local pair breaking effects. Moreover, the inhomogeneous magnetic structure of the skyrmion lattice enables the emergence of superconducting spin-triplet correlations not only in the equal-spin channels "" j i and ## j i (corresponding to Cooper pair spin states S z = ±1), but also in the mixed-spin (S z = 0) channel, "# j i þ #" j i (see Supplementary Note 5).…”

Single channel Josephson effect in a high transmission atomic contact

“…Impurities and defects, however, are known to induce sub-gap excitations, which lead to local changes in the superconductor's ground state. Yu-Shiba-Rusniov states, Majorana-bound states, Kondo resonances and pair density waves are all predicted to lead to local changes in the superconducting condensate [1][2][3][4][5] . Quantifying these modifications promises to improve the current understanding of superconductivity in mesoscopic systems and to open new avenues in material design for emerging applications, especially in quantum computing.…”

“…Quantifying these modifications promises to improve the current understanding of superconductivity in mesoscopic systems and to open new avenues in material design for emerging applications, especially in quantum computing. Detecting such local changes in the order parameter has since become a major goal of research in superconductivity 3,4,[6][7][8][9][10][11] .…”