Magnetic Response of Mesoscopic Superconducting Rings with Two Order Parameters

The magnetic response and fluxoid transitions of superconducting aluminum rings of various sizes, deposited under conditions likely to generate a layered structure, show good agreement with a two-order-parameter Ginzburg-Landau model. For intermediate couplings, we find metastable states that have different phase winding numbers around the ring in each of the two order parameters. Those states, previously theoretically predicted, are analogous to fractional vortices in singly connected samples with two-order-parameter superconductivity. Larger coupling locks the relative phase so that the two order parameters are only manifest in the temperature dependence of the response. With increasing proximitization, this signature gradually disappears.

Figure 1

${\Phi }_a\mathrm{\text{−}}I$ curves for a ring with $w=120\mathrm{nm}$ and $R=1.2\mu \mathrm{m}$, fitted to a one-order-parameter Ginzburg-Landau model. The selected curves represent the regimes discussed in the text: (a) no transitions, (b),(c) hysteretic, and (d) thermal equilibrium.

Figure 2

(a) ${\lambda }^{-2}$ and (b) ${\xi }_{\mathrm{GL}}$ for rings representative of each annulus width $w$. The discrete symbols are obtained from fits to ${\Phi }_a\mathrm{\text{−}}I$ curves. Continuous curves represent fits to phenomenological expressions ($w=120\mathrm{nm}$) or the two-order-parameter GL model ($w\ge 190\mathrm{nm}$), which was only fitted above 1.2 K where GL applies.

Figure 3

(a)–(f) ${\Phi }_a-I$ curves for a ring with $w=190\mathrm{nm}$ and $R=2\mu \mathrm{m}$, where the coupling between the two order parameters is weak. In (a)–(c), states with two different fluxoid numbers lead to the observed transition pattern. In (d), no transition occurs because one component is stabilized by the other. Dotted lines show the contributions of ${\psi }_1$ and ${\psi }_2$ derived from the model. (e) and (f), taken above the lower $T_c$, reflect the response of a single order parameter. (g)–(i) Results from the two-OP model corresponding to (a)–(c). (j) Schematic of film structure (cross section).