Scaling of Yu-Shiba-Rusinov energies in the weak-coupling Kondo regime

Abstract

The competition of the free-spin state of a paramagnetic impurity on a superconductor with its screened counterpart is characterized by the energy scale of Kondo screening compared to the superconducting pairing energy Δ. When the experimental temperature suppresses Kondo screening, but preserves superconductivity, i.e., when Δ/k B > T > T K (k B is Boltzmann’s constant and T K the Kondo temperature), this description fails. Here, we explore this temperature range in a set of manganese phthalocyanine molecules decorated with ammonia on Pb(111). We show that these molecules suffice the required energy conditions by exhibiting weak-coupling Kondo resonances. We correlate the Yu-Shiba-Rusinov bound states energy inside the superconducting gap with the intensity of the Kondo resonance. The observed correlation follows the expectations for a classical spin on a superconductor. This finding is important in view of many theoretical predictions using a classical spin model, in particular for the description of Majorana bound states in magnetic nanostructures on superconducting substrates.

Observation of Coexistence of Yu-Shiba-Rusinov States and Spin-Flip Excitations

“…3,7,12,[15][16][17][18][19][20][21][22][23][24][25][26][27][28][29] The bulk of recent experimental work on YSR states on superconducting (SC) substrates has demonstrated that the strength of the exchange interaction J can be significantly influenced by a small change in the adsorption site of the impurity or by spacers between the impurity and substrate. 3,18,[25][26][27][28][29][30][31][32][33][34] with α proportional to J, α = πρJS/2, where ρ is the normal-state density of states of the substrate at the Fermi level and S is the impurity spin. The bound state results from the spin-dependent scattering of Bogoliubov quasiparticles on the impurity and is thus associ-ated with the longitudinal part of the exchange interaction, JS z s z , where s represents the spin-density of the substrate electrons at the impurity position.…”

“…Fitting the data with a phenomenological spin Hamiltonian The exchange coupling between the magnetic impurity and the substrate can be modulated by changing the adsorption site of the molecule. 3,18,[30][31][32]51,52 We successfully posi- Due to the sensitivity of the YSR states and spin-excitations, they can be tuned continuously by the force exerted by the STM tip. 33,34,53 We expect to have attractive forces between the tip and the molecule; 54,55 this would result in pulling the molecule away from the substrate and reduction of the exchange coupling between the molecule and the substrate upon decreasing tip-molecule distance.…”

Magnetism and in-gap states of 3d transition metal atoms on superconducting Re

“…Recently, theoretical predictions and experimental indications of topological superconductivity in one- [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] and two-dimensional [16][17][18][19][20] arrays of magnetic atoms coupled to bulk superconductors have triggered renewed interest in the building blocks of such systems, i.e. single magnetic atoms coupled to bulk superconductors [21][22][23][24][25][26][27][28][29][30] . Magnetic atoms locally induce pairs of bound state resonances inside the gap of their host superconductor, known as Yu-Shiba-Rusinov (YSR) states [31][32][33][34][35] .…”

In-gap states of magnetic impurity in quantum spin Hall insulator proximitized to a superconductor

“…Upon introducing impurities into graphene, various in-gap states can emerge, manifesting whether it is in the topologically trivial or non-trivial phase 10 . In what follows we study the subgap states of a single impurity existing in the proximitized periodic honeycomb lattice, that have received a great deal of interest both in experimental [11][12][13][14][15] and theoretical studies [16][17][18] . In particular, more complex nanostructures embedded into such proximitized QSHI material could develop the Majorana-type quasiparticles 19 .…”