Josephson Behavior of Phase-Slip Lines in Wide Superconducting Strips

Phase-slip lines can be viewed as dynamically created Josephson junctions in a homogeneous superconducting film. In contrast to phase-slip centers, phase-slip lines occur in wide superconducting strips, where the order parameter may vary in two dimensions. We investigated phase-slip lines in two different materials using several methods. We observed Shapiro steps under microwave radiation, which shows that the frequency of the order parameter oscillation is equal to Josephson frequency. A periodic oscillation of a critical current versus the applied magnetic field was found in strips with a hole in the middle. The latter effect provides a clear evidence of macroscopic quantum interference across a phase-slip line. We have used low temperature scanning laser microscopy to visualize the phase-slip lines and to distinguish them from possible local inhomogeneities in the films.

Figure 1

Current-voltage ($IV$) characteristics of a $15\mu \mathrm{m}$ wide Sn strip with a $5\mu \mathrm{m}\times 15\mu \mathrm{m}$ window in the middle shown in inset (a). Insets (b) and (c) present laser scanning microscope (LSM) images taken at points 1 and 2 of the $IV$ curve, respectively. White arrows indicate the phase-slip lines (PSLs).

Figure 2

Generation of PSLs in a uniform $30\mu \mathrm{m}$ wide Sn strip induced by the bias current increasing gradually from (a) to (d). Images (a), (b), and (c) are taken at the first, second, and third steps of the $IV$ curve. Image (d) is obtained in a high current region.

Figure 3

$IV$ characteristics of a $15\mu \mathrm{m}$ wide Sn strip with $5\mu \mathrm{m}\times 15\mu \mathrm{m}$ window under microwave irradiation with frequency $f$ of 0.5 GHz (1), 1 GHz (2), 2 GHz (3), 3 GHz (4), and with no microwaves (5). The zero of current for different curves is shifted as indicated on the plot.

Figure 4

Critical current $I_c$ versus magnetic field $H$ for $25\mu \mathrm{m}$ wide Sn strips with different window sizes: (a) $(5\times 5)\mu {\mathrm{m}}^2$; (b) $(5\times 10)\mu {\mathrm{m}}^2$; (c) $(5\times 15)\mu {\mathrm{m}}^2$.

Figure 5

Voltage variation versus magnetic field $H$ at different bias currents set with increment of $0.8\mu \mathrm{A}$. The strip width is $30\mu \mathrm{m}$, the window size is $(10\times 10)\mu {\mathrm{m}}^2$.