Imaging the Anisotropic Nonlinear Meissner Effect in Nodal ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathbf{O}}_{7-\delta }$ Thin-Film Superconductors

We have directly imaged the anisotropic nonlinear Meissner effect in an unconventional superconductor through the nonlinear electrodynamic response of both (bulk) gap nodes and (surface) Andreev bound states. A superconducting thin film is patterned into a compact self-resonant spiral structure, excited near resonance in the radio-frequency range, and scanned with a focused laser beam perturbation. At low temperatures, direction-dependent nonlinearities in the reactive and resistive properties of the resonator create photoresponse that maps out the directions of nodes, or of bound states associated with these nodes, on the Fermi surface of the superconductor. The method is demonstrated on the nodal superconductor ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ and the results are consistent with theoretical predictions for the bulk and surface contributions.

Figure 1

(a) Schematic diagram of spiral geometry, definition of radial ($\rho$) and angular ($\Theta$) coordinates, and directions of the crystallographic $a$ and $b$ directions, along with the orientation of the $d$-wave gap in YBCO. (b)–(d) LSM photoresponse images of a $\mathrm{YBCO}/\mathrm{LAO}$ spiral resonator in the third harmonic mode at temperatures of (b) 81.9, (c) 4.40, and (d) 3.90 K. Also shown is the $d$-wave gap orientation as determined from twin domain boundary directions in the substrate.

Figure 2

Plot of radially integrated and unwrapped photoresponse (PR) vs angle on the $\mathrm{YBCO}/\mathrm{LAO}$ spiral at 81.9 and 4.66 K, along with a fit of the low-temperature integrated $\mathrm{PR}(\Theta )$ to the simple $d$-wave angular dependence. Inset shows PR image of $\mathrm{YBCO}/{\mathrm{LaAlO}}_3$ thin film spiral resonator taken at a temperature of 4.656 K in the 7th mode at 450.22 MHz.

Figure 3

Plot of temperature dependence of photoresponse (PR) magnitude taken at nodal and antinodal locations in a $\mathrm{YBCO}/\mathrm{\text{sapphire}}$ spiral resonator. The antinodal PR has opposite sign to the nodal PR above the crossover temperature (5.63 K, as deduced from the fit). Graphical inset shows temperature dependence of the nodal PR magnitude near its crossover temperature, along with a fit to the form predicted by ZDS. Other insets show LSM PR magnitude images of $\mathrm{YBCO}/\mathrm{\text{sapphire}}$ below (4.405 K) and above (6.641 K) its crossover temperature at 546.555 MHz. The phase of the PR in these images differ by $\pi$, corresponding to a sign reversal of the response.