Large Magnetoresistance Oscillations in Mesoscopic Superconductors due to Current-Excited Moving Vortices

We show in the case of a superconducting Nb ladder that a mesoscopic superconductor typically exhibits magnetoresistance oscillations whose amplitude and temperature dependence are different from those stemming from the Little-Parks effect. We demonstrate that these large resistance oscillations (as well as the monotonic background on which they are superimposed) are due to current-excited moving vortices, where the applied current in competition with the oscillating Meissner currents imposes or removes the barriers for vortex motion in an increasing magnetic field. Because of the ever present current in transport measurements, this effect should be considered in parallel with the Little-Parks effect in low-critical temperature ($T_c$) samples, as well as with recently proposed thermal activation of dissipative vortex-antivortex pairs in high-$T_c$ samples.

Figure 1

An oblique view of the system: a superconducting strip (of width $w=a+2\delta$, thickness $t\ll \lambda$, $\xi$, and periodically long in the $y$ direction) with a chain of holes (size $a$ and period $d=a+\delta$) under applied dc current $I$ and a perpendicular magnetic field $H$.

Figure 2

Time-averaged free energy $F$ (a) (in units of $F_0=H_c^2{V}_0/8\pi$ with $V_0$ the unit cell volume) and voltage $V$ (b) (in units of normal state voltage $V_n$) as a function of external flux $\varphi$ [calculated over the unit cell area $S=w\times (a+\delta )$] for different values of applied current $I$. The width of the simulated ladder is $w=40\xi (0)$, and the size of the holes is $a=20\xi (0)$. The temperature is $T=0.98T_c$, and the GL parameter is $\kappa =10$.

Figure 3

Voltage vs time response for the sample of Fig. 2 for $\varphi =0.64{\varphi }_0$ and $I/(j_{0}w)=0.04$. Insets show snapshots of $|\psi {|}^2$ at time intervals indicated by open circles on the $V(t)$ curves.

Figure 4

(a),(b) Time evolution of the free energy for the ladder considered in Fig. 2 at $\varphi =0.54{\varphi }_0$ (a) and $\varphi =0.71{\varphi }_0$ (b). Arrows indicate the penetration $\Delta F_p$ and expulsion $\Delta F_e$ barriers. (c) Time-averaged voltage (solid curve), $\Delta F_p$ (filled circles), and $\Delta F_e$ (open circles) as a function of external flux. The applied current is $I/(j_{0}w)=0.04$.

Figure 5

(a) Measured resistance (in units of normal state resistance $R_n=27.9\Omega$) vs magnetic field for a Nb superconducting strip (of width $w=385\mathrm{nm}$) with a chain of holes (of size $a=120\mathrm{nm}$ and period $d=385\mathrm{nm}$) in applied dc current $I=1\mu \mathrm{A}$ and at different temperatures (ranging from $T=7.35\mathrm{K}$ to $T=7.65\mathrm{K}$ with step 50 mK). Solid curves show theoretical results for the dimensions of the experimental sample and for $I/(j_{0}w)=0.05$. (b) $R(T)$ curve of the sample at zero magnetic field for $I=1\mu \mathrm{A}$. Lower inset shows the SEM image of the sample. Upper inset shows the amplitude of the first resistance peak, $\Delta R$, as a function of temperature (solid dots), compared to the amplitude of the resistance oscillations predicted by the Little-Parks effect, $\Delta R=0.14(dR/dT)T_c\mathbf{(}\xi (0)/(w+a)/4{\mathbf{)}}^2$ [2, 15] (open dots). Triangles present the results of the GL simulations. (c) $R(H)$ curves of the sample obtained at $T=7.42\mathrm{K}$ for different values of the bias current.