Induced Energy Gap in Finite-Sized Superconductor/Ferromagnet Hybrids

TL;DR

This paper theoretically investigates how finite-sized superconductor/ferromagnet hybrids can develop a tunable energy gap, influenced by magnetic configurations and geometrical parameters, with implications for designing magnetic superconducting devices.

Contribution

It introduces a comprehensive theoretical analysis of proximity effects in finite superconductor/ferromagnet hybrids, revealing conditions for inducing and enhancing a hard energy gap.

Findings

A hard gap emerges when ferromagnetic layers are weakly magnetized and their magnetizations are antiparallel.

The energy gap is maximized when the ferromagnetic layer thicknesses satisfy d_{F1} ≤ d_{F2}.

Increasing the spatial rotation period of the exchange field enhances the induced hard gap.

Abstract

We theoretically study self-consistent proximity effects in finite-sized systems consisting of ferromagnet ($\rm F$) layers coupled to an $s$-wave superconductor ($\rm S$). We consider both $\rm SF_1F_2$ and $\rm SH$ nanostructures, where the $\rm F_1 F_2$ bilayers are uniformly magnetized, and the ferromagnetic $\rm H$ layer possesses a helical magnetization profile. We find that when the $\rm F_1 F_2$ layers are weakly ferromagnetic, a hard gap can emerge when the relative magnetization directions are rotated from parallel to antiparallel. Moreover, the gap is most prominent when the thicknesses of $\rm F_1$ and $\rm F_2$ satisfy $\rm d_{F1}\leq d_{F2}$, respectively. For the $\rm SH$ configuration, increasing the spatial rotation period of the exchange field can enhance the induced hard gap. Our investigations reveal that the origin of these findings can be correlated with the propagation of quasiparticles with wavevectors directed along the interface. To further clarify the source of the induced energy gap, we also examine the spatial and energy resolved density of states, as well as the spin-singlet, and spin-triplet superconducting correlations, using experimentally accessible parameter values. Our findings can be beneficial for designing magnetic hybrid structures where a tunable superconducting hard gap is needed.