Oscillatory magnetoresistance in nanopatterned superconducting ${\text{La}}_{1.84}{\text{Sr}}_{0.16}{\text{CuO}}_4$ films

A superconducting ${\text{La}}_{1.84}{\text{Sr}}_{0.16}{\text{CuO}}_4$ film patterned into a network of $100\times 100{\text{nm}}^2$ noninteracting square loops exhibits large magnetoresistance oscillations superimposed on a background which increases monotonically with the applied magnetic field. Neither the oscillations amplitude nor its temperature dependence can be explained by the Little-Parks effect. Conversely, a good quantitative agreement is obtained with a recently proposed model ascribing the oscillations to the interaction between thermally excited moving vortices and the oscillating persistent currents induced in the loops. Extension of this model, allowing for direct interaction of the vortices and antivortices magnetic moment with the applied field, accounts quantitatively for the monotonic background as well. Analysis of the background indicates that in the patterned film both vortices and antivortices are present at comparable densities. This finding is consistent with the occurrence of Berezinskii-Kosterlitz-Thouless transition in ${\text{La}}_{1.84}{\text{Sr}}_{0.16}{\text{CuO}}_4$ films.

Figure 1

(Color online) Main panel: schematic description of a sample consisting of $100\times 100{\text{nm}}^2$ loops (orange color) interconnected by 500 nm long wires (bright bars). Inset: SEM image of a single loop patterned by electron-beam lithography in a ${\text{La}}_{1.84}{\text{Sr}}_{0.16}{\text{CuO}}_4$ film. The whole sample contains $60\times 60$ small loops.

Figure 2

(Color online) Measured temperature dependence of the resistance in a continuous film (solid circles, the dotted line is a guide to the eyes) and the patterned film (open circles) at zero applied field. The solid blue line is calculated using Eq. (5) with $T_c=32\text{K}$ and $R_n=76\Omega$ yielding fit values ${\lambda }_0=750\text{nm}$, ${\xi }_0=2.5\text{nm}$, $d=23.4\text{nm}$, and $w=21\text{nm}$. The red dashed line is based on the Halperin-Nelson formula for a 2D superconductor (Ref. 21) using the Berezinski-Kosterlitz-Thouless transition temperature, $T_{\text{BKT}}=27.6\text{K}$, the fluctuation-corrected BCS critical temperature, $T_{\text{BCS}}=32\text{K}$, and $R_n=76\Omega$.

Figure 3

Resistance of the patterned film as a function of magnetic field perpendicular to the sample plane (i.e., parallel to the $c$-crystallographic axis) at different temperatures. The lowest and the uppermost curves correspond to 27 K and 32 K, respectively.

Figure 4

Temperature dependence of the measured oscillation amplitude (circles). The solid line is calculated using Eq. (7) with the parameters extracted from Fig. 2. The triangles show an upper limit for the resistance oscillations amplitude calculated for the Little-Parks effect; note that this scale is expanded tenfold.

Figure 5

(Color online) Solid circles: the amplitude of oscillations in $T_c$, $\Delta T_c=\Delta R\left(H\right)\left(dT/dR\right)$, derived from the experimentally measured oscillation amplitude, $\Delta R$, and the temperature derivative $dR/dT$. The solid black line connecting the experimental points is a guide to the eyes. The solid blue line presents the change in $T_c$, $\Delta T_c^{LP}$, that one would expect from the Little-Parks effect. Note that the two scales differ by 2 orders of magnitude.

Figure 6

Magnetoresistance oscillations at 29.5 K: measured (open circles) and calculated using Eq. (5) (the solid gray line). The solid black line is calculated with the same equations but assuming a size distribution of the loops, resulting in the spread of $\pm 8\mathrm{\%}$ in $H_0$ around the mean value of $\sim 2300\text{Oe}$.

Figure 7

(Color online) Theoretical fits of the nonoscillating background (the line connecting the minima of the oscillatory magnetoresistance) to the experimental data (black lines) taking into account (a) only vortices (left panel, red lines) and (b) both vortices and antivortices (right panel, blue lines).

Figure 8

(Color online) The calculated probabilities of thermally induced creation of a vortex (solid lines) and an antivortex (thin solid lines) as functions of the magnetic field.