# Dielectric Resonator Method For Determining Gap Symmetry Of Superconductors Through Anisotropic Nonlinear Meissner Effect

## TL;DR

This paper introduces a non-invasive microwave resonance technique using laser scanning to image the gap nodal structure of superconductors, successfully identifying isotropic and anisotropic gap symmetries.

## Contribution

The method allows imaging of superconducting gap anisotropy in unpatterned samples without complex lithography, enabling broader application to unconventional superconductors.

## Key findings

- Detected nearly isotropic gap in Nb film with <8% anisotropy.
- Identified 4-fold symmetric gap structure in YBa2Cu3O7−δ with ~12.5% anisotropy.
- Validated the method's effectiveness through simulation and experimental results.

## Abstract

We present a new measurement method which can be used to image gap nodal structure of superconductors whose pairing symmetry is under debate. This technique utilizes a high quality factor microwave resonance involving the sample of interest. While supporting a circularly symmetric standing wave current pattern, the sample is perturbed by a scanned laser beam, creating a photoresponse that was previously shown to reveal the superconducting gap anisotropy. Simulation and the measurement of the photoresponse of an unpatterned Nb film show less than 8\% anisotropy, as expected for a superconductor with nearly isotropic energy gap along with expected systematic uncertainty. On the other hand, measurement of a YBa$_2$Cu$_3$O$_{7-\delta}$ thin film shows a clear 4-fold symmetric image with $\mathtt{\sim}12.5$\% anisotropy, indicating the well-known 4-fold symmetric $d_{x^2-y^2}$ gap nodal structure in the $ab$-plane. The deduced gap nodal structure can be further cross-checked by low temperature surface impedance data, which is simultaneously measured. The important advantage of the presented method over the previous spiral resonator method is that it does not require a complicated lithographic patterning process which limits one from testing various kinds of materials due to photoresponse arising from patterning defects. This advantage of the presented technique, and the ability to measure unpatterned samples such as planar thin films and single crystals, enables one to survey the pairing symmetry of a wide variety of unconventional superconductors.