Dynamic transition from Mott-like to metal-like state of the vortex lattice in a superconducting film with a periodic array of holes

We show that under an ac magnetic field excitation the vortex lattice in a superconductor with a periodic array of holes can undergo a transition from a Mott-like state where each vortex is localized in a hole, to a metal-like state where the vortices get delocalized. The vortex dynamics is studied through the magnetic shielding response which is measured using a low-frequency two-coil mutual inductance technique on a disordered superconducting NbN film having a periodic array of holes. We observe that the shielding response of the vortex state is strongly dependent on the amplitude of the ac magnetic excitation. At low amplitude the shielding response varies smoothly with the excitation amplitude, corresponding to the elastic deformation of the vortex lattice. However, above a threshold value of excitation the response shows a series of sharp jumps, signaling the onset of the Mott-to-metal transition. A quantitative analysis reveals that this is a collective phenomenon which depends on the filling fraction of vortices in the antidot lattice.

Figure 1

(a) Scanning electron micrograph showing the NbN film with an antidot array. The panels on the right show the Fourier transforms of the areas bounded in the respective boxes. The six spots in the Fourier transform show local hexagonal ordering. (b) Schematic diagram of the two-coil mutual inductance setup. (c) Schematic diagram showing the circulating ac supercurrent setup in a circular film with an antidot array due to the alternating magnetic field from the primary coil. The width of the circles is proportional to the amplitude of $J_S^{\mathrm{ac}}$. (d) Schematic description of the compression and rarefaction of the VL in one cycle of the alternating magnetic field. The leftmost panel shows the VL without an external ac field.

Figure 2

Variation of $M^{\prime }$ as a function H at different temperatures with $I_{\mathrm{ac}}\sim 5\mathrm{mA}$. VMEs manifest as minima in $M^{\prime }$ at matching fields.

Figure 3

(a) $M^{\prime }$ and $-M^{\prime \prime }$ as a function of $I_{\mathrm{ac}}$ for fixed values of the dc magnetic field $H=H_m=2.37\mathrm{kOe}$ at 1.7 K. Both quantities show a series of jumps above $I_{\mathrm{ac}}\sim 8.8\mathrm{mA}$. The vertical dashed arrows correspond to $I_{\mathrm{ac}}$ values for which $M^{\prime }-H$ and $-M^{\prime \prime }-H$ are plotted in Fig. 5. (b) $-M^{\prime \prime }$ as a function of $I_{\mathrm{ac}}$ for different H below and above $H_m$ at 1.7 K; for clarity, each successive curve for H>1.18 kOe is shifted upwards by 2 nH. The gray curve show the locus of $I_{\mathrm{ac}}^p$. (c) $-M^{\prime \prime }$ as a function of $I_{\mathrm{ac}}$ for $H=2.37\mathrm{kOe}$ at different temperatures; above 2 K the sharp jumps transform into a smooth variation.

Figure 4

(a) Simulated value of $J_S^{\mathrm{ac}}$ along the radius of the film for $I_{\mathrm{ac}}\sim 1-8.7\mathrm{mA}$. (b) Simulated value of $J_S^{\mathrm{ac}}$ along the radius of the films for $I_{\mathrm{ac}}\sim 8.8\mathrm{mA}$ for the 14th and 15th iteration cycle; here, the simulation does not converge to a unique value and the solution becomes bistable. The profile of the ac magnetic field ($B_{\mathrm{ac}}$) arising from the primary coil is shown in the same panel.

Figure 5

(a) $M^{\prime }-H$ and (b) $-M^{\prime \prime }-H$ at different $I_{\mathrm{ac}}$ at 1.7 K. The values of $I_{\mathrm{ac}}$ correspond to the vertical dashed arrows shown in Fig. 3. The data are recorded by sweeping H from 10 to −10 kOe and back. A small hysteresis between positive and negative field sweeps is observed in all curves. In (b) some of the curves have been shifted upward for clarity, by an amount mentioned next to the curve.