Transverse vortex commensurability effect and sign change of the Hall voltage in superconducting ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ thin films with a nanoscale periodic pinning landscape

The transverse (Hall) voltage in thin films of the high-temperature superconductor ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ with an artificial periodic pinning array is investigated. Columnar defect regions along the crystallographic $c$ axis, in which superconductivity is suppressed, are created by irradiation with ${\mathrm{He}}^{+}$ ions through a silicon stencil mask. The commensurate arrangement of magnetic flux quanta with the artificial defect lattice is confirmed by maxima of the critical current and minima of the resistance, respectively. The magnetic field dependence of the transverse voltage reveals a commensurability effect characterized by a narrow peak of the Hall coefficient with reversed polarity compared to the background signal. This signature of vortex matching disappears at larger vortex velocities substantiating its close connection with enhanced pinning of vortices at the periodic pinning landscape.

Figure 1

Vortex commensurability effects in a YBCO thin film (sample A) with an artificial pinning landscape demonstrated by peaks in the critical current density and minima of the magnetoresistance. The top axis is normalized to the matching field $B_m=22.7$ mT. To ensure equilibrium vortex arrangement the sample was heated to $T=100\mathrm{K}$ and then field cooled for every datum. The inset shows a scanning electron microscopy picture of the sample surface, where the black areas indicate the irradiated and thus nonsuperconducting defect columns.

Figure 2

Onset of the Hall coefficient of sample A at temperatures below the superconducting transition in various small magnetic fields. The matching field is $B_m=22.7$ mT according to Eq. (1). Inset: Hall coefficient measured at $B_m$ over a wider temperature range.

Figure 3

Contour plot of the Hall coefficient at various temperatures and magnetic fields of a YBCO film with a CDA. The bright area corresponds to a maximum of the Hall effect at the matching field. The dotted line indicates the bifurcation, where the Hall effect emerges with different sign.

Figure 4

Comparison of longitudinal and transverse vortex commensurability effects in the YBCO film with a CDA. Blue squares show the peak of the critical current at 34.3 K and green triangles show the magnitude of the Hall coefficient at 35.0 K near the matching field. Error bars indicate the 95% confidence intervals of the mean value.

Figure 5

Hall coefficient vs temperature at $B_m$, probed with different currents. Inset: Current dependence of the peak values of the $R_H\left(T\right)$ curves indicated by arrows in the main panel. Error bars indicate the 95% confidence intervals of the mean value.

Figure 6

Comparison of the peak of the critical current at 80.5 K (blue squares) and the Hall coefficient at 81.0 K (green triangles) in a sample with a wider-spaced CDA ($d=500$ nm). Inset: The current dependence of the peak value of the $R_H\left(T\right)$ curves, measured at 7.7 mT, the maximum of $R_H\left(B\right)$. Error bars indicate the 95% confidence intervals of the mean value.

Figure 7

Schematic diagram of the Hall coefficient's behavior at various temperatures and magnetic fields, based on data in sample A. Broken lines indicate a vanishing Hall effect. The inset shows a sketch of the possible situation in the vortex Mott insulator state, when a few mobile interstitial vortices are deflected by the circular currents around the pinned vortices in the CDA. Adapted from Nakai et al. [21].