Zero-crossing Shapiro steps in high-$T_c$ superconducting microstructures tailored by a focused ion beam

Microwave response of S-shaped ${\mathrm{Bi}}_2{\mathrm{Sr}}_2\mathrm{Ca}{\mathrm{Cu}}_2{\mathrm{O}}_{8+x}$ (BI-2212) micron-scale samples, in which the supercurrent was forced to flow perpendicular to the crystal layers, was investigated. A treatment with a focused ion beam allowed us to reduce the plasma frequency down to $f_p\sim 5\mathrm{GHz}$ at $T=0.3\mathrm{K}$ in naturally stacked Josephson junctions in a crystal. We observed Shapiro steps at frequencies as low as $\sim 5\mathrm{GHz}$. Well-developed zero-crossing Shapiro steps were observed at frequencies as low as $\sim 10\mathrm{GHz}$. They appeared as constant-voltage plateaus with a nonzero voltage occurring at zero bias current. We confirmed that zero-crossing Shapiro steps in the Bi-2212 stacked junctions can be observed when the irradiated frequency is sufficiently larger than $f_p$. The observed high-order fractional steps in the microwave responses indicate that the interlayer-coupled Bi-2212 Josephson junctions have nonsinusoidal current-phase relation. Based on the temperature dependence of the steps, we also showed that the finite slope of the steps is due to the enhancement of the phase-diffusion effect.

Figure 1

$I\text{−}V$ curves of the Bi-2212 layered superconducting crystal, without microwave irradiation at $T=0.3\mathrm{K}$. The arrows indicate the quasiparticle branches. Upper inset: an SEM micrograph of the sample, where the scale bar is $5\mu \mathrm{m}$. Lower inset: schematic geometry of the sample and the measurement configuration. The gray region on the middle, marked with dashed lines, represents the volume of the sample in which the applied current flows perpendicular to the layers of the Bi-2212 superconductor.

Figure 2

Microwave response of the Bi-2122 layered superconductor to external microwave radiation at $T=0.3\mathrm{K}$. The dc voltage on the sample is plotted vs the dc bias current. (a) The radiation frequency is $f=26\mathrm{GHz},$ and the nominal radiation power is $P=-12.3\mathrm{dBm}$. (b) The frequency and the power are $f=13\mathrm{GHz}$ with $P=-2.9\mathrm{dBm}$. The numbers are defined as $n=2eV∕hf$ and represent the ratio of the frequency of the phase difference-temporal oscillation and the applied microwave signal frequency.

Figure 3

(Color online) Microwave response of the IJJs stack for $f=18\mathrm{GHz}$ with two different powers at $T=0.3\mathrm{K}$. The voltage axis was normalized by the voltage corresponding to the external frequency. The arrows indicate the half-integer steps at each power. The inset shows the quarter-integer steps as indicated by arrows and the fractional index numbers at two different powers at $f=18\mathrm{GHz}$.

Figure 4

(Color online) Microwave response of the IJJs stack for (a) $f=5\mathrm{GHz}$ with the irradiation power of $P=-22.4\mathrm{dBm}$ and for (b) $f=1\mathrm{GHz}$ with $P=-14.7$ and $-18.2\mathrm{dBm}$ at $T=0.3\mathrm{K}$. The index numbers and arrows in (a) are defined in the same manner as in Fig. 2. The arrows in (b) indicate the positions of the nearly constant-voltage current steps.

Figure 5

(Color online) Temperature dependence of Shapiro steps with $f=23\mathrm{GHz}$ and $P=-17\mathrm{dBm}$ at $T=0.6$, 1, 1.4, 2.28, and $3.53\mathrm{K}$, respectively, from the leftmost one. The data were shifted horizontally for clarity by $30\mathrm{nA}$.