Topological competition of superconductivity in Pb/Ru/Sr${}_2$RuO${}_4$ junctions

We devise an unconventional proximity junction configuration where an $s$-wave superconductivity and the superconductivity of Sr${}_2$RuO${}_4$ interfere with each other. We reproducibly observe in such a Pb/Ru/Sr${}_2$RuO${}_4$ junction with a single Pb electrode that the critical current $I_{\mathrm{c}}$ drops sharply just below the bulk $T_{\mathrm{c}}$ of Sr${}_2$RuO${}_4$ and furthermore increases again below a certain temperature below $T_{\mathrm{c}}$. In order to explain this temperature dependence of $I_{\mathrm{c}}$, we propose a competition effect involving topologically distinct superconducting phases around Ru inclusions. Thus, such a device may be called a topological superconducting junction.

Figure 1

(a) Differential resistance vs current. The critical current $I_{\mathrm{c},+}$ is defined at the peak with positive bias current, $-I_{\mathrm{c},-}$ with negative bias current. (b) Voltage-current characteristics of a Pb/Ru/Sr${}_2$RuO${}_4$ junction. The inset to (b) is a schematic of a junction. The bias current was applied via leads 1 and 2, and the voltage was measured across leads 3 and 4.

Figure 2

Differential resistance $dV/dI$ of a Pb/Ru/Sr${}_2$RuO${}_4$ junction at various temperatures. Each curve is shifted by 0.3 $\mathrm{m}\Omega$ for clarity. The critical current drops sharply below $T_{\mathrm{c},\mathrm{SRO}}$.

Figure 3

Variation of the critical current $I_{\mathrm{c}}$ with temperature of a Pb/Ru/Sr${}_2$RuO${}_4$ junction. The inset displays $I_{\mathrm{c}}$ of another Pb/Ru/Sr${}_2$RuO${}_4$ junction. The circles and the squares indicate critical currents of up sweeps and down sweeps, respectively. $I_{\mathrm{c}}$ sharply drops just below $T_{\mathrm{c},\mathrm{SRO}}$ but increases again below a certain temperature designated as $T^{*}$. The broken curve is a visual guide.

Figure 4

Asymmetric and hysteretic bias current dependence of differential resistance $dV/dI$ of a Pb/Ru/Sr${}_2$RuO${}_4$ junction at 0.55 K. The up-sweep curve is shifted by 0.3 $\mathrm{m}\Omega$. The down-sweep curve was obtained immediately following the up sweep to 1.45 mA.

Figure 5

Schematic images of the evolution of the order parameter at the Sr${}_2$RuO${}_4$/Ru interface. In the upper panels, the gradations in the small circles depict the momentum-directional dependence of the superconducting phase $\phi$ at each spatial position; the arrows denote the momentum direction for which $\phi =0$. The angle $\theta$ is defined as normal to the interface [see (a)]. The lower panels represent the superconducting phases $\phi \left(\theta \right)$ at the Sr${}_2$RuO${}_4$/Ru interface under no external current. The solid lines represent the phase of $s$-wave superconductivity in Ru and the broken lines that of $p$-wave superconductivity in Sr${}_2$RuO${}_4$. (a) $T_{\mathrm{c},\mathrm{SRO}}<T<T_{\varepsilon }$: The $p_{\parallel }\pm i\varepsilon p_{\perp }$ state with the winding number $N=0$ is realized ($A^{\prime }$ phase), matching with the $s$-wave order parameter induced in Ru. (b) $T\lesssim T_{\mathrm{c},\mathrm{SRO}}$: Replacement by $p_x\pm i{p}_y$, the bulk state of Sr${}_2$RuO${}_4$, with $N=\pm 1$ ($B$ phase). (c) $T\ll T_{\mathrm{c},\mathrm{SRO}}$: Increasing interfacial energy enlarges the phase deformation in the $s$ wave,[28] strengthening the Josephson coupling.