Little-Parks effect in single nanoscale ${\text{YBa}}_2{\text{Cu}}_3{\text{O}}_{6+x}$ rings

The properties of single submicron high-temperature superconductor (HTS) rings are investigated. The Little-Parks effect is observed and is accompanied by an anomalous behavior of the magnetic dependence of the resistance, which we ascribe to nonuniform vorticity (superfluid angular momentum) within the ring arms. This effect is linked to the peculiar HTS relationship between the values of the coherence length and the London penetration depth.

Figure 1

(Color online) (a) Detail of the resistance vs temperature curve in proximity of the critical temperature $T_c$ and on a larger scale (inset) for ring D1. In (b) $R\left(T\right)$ curves measured at $H=0\text{T}$ and $H=12\text{T}$, in an underdoped ring nominally identical to D1, are reported in proximity of $T_c$. In (c) scanning electron micrograph of ring (D1). In (d) oscillations of $\Delta T_c$ derived by measurements of the magnetoconductance (see text) on the same device, are shown at different temperatures, providing evidence of Little-Parks effect.

Figure 2

(a) Resistance oscillations of a ring with $R_{\text{max}}=445\text{nm}$ and $R_{\text{min}}=205\text{nm}$ (D2). (b) FFT of $R\left(H\right)$ data taken at three temperatures. Black arrows indicate the frequencies corresponding to a single-flux quantum in a ring with radius $R_{\text{min}}$, $R_{avg}$, and $R_{\text{max}}$, respectively.

Figure 3

(Color online) a) FFT of data in Fig. 2a in the range 0–90 mT (solid line) and 90–250 mT (dotted line). From the peaks marked in (a) we calculate an effective radius (see text) and plot it as function of peak order (b). In (c) we schematize the concentric vortex structure by plotting, in polar coordinate $\rho ={\left({\Phi }_{0}H/\pi \right)}^{0.5}$ and $\theta$, the amplitude of the FFT in (a).