Phase-sensitive Harmonic Measurements of Microwave Nonlinearities in Cuprate Thin Films

TL;DR

This study uses phase-sensitive microwave measurements to explore the nonlinear electromagnetic response of YBCO superconducting thin films near their critical temperature, revealing doping-dependent behaviors and proposing a model linking nonlinearity to order parameter dynamics.

Contribution

It introduces a phase-sensitive harmonic measurement technique and a field-based analytical model to understand superconducting nonlinearities near T_c, highlighting doping effects.

Findings

Harmonic magnitude peaks near T_c with doping-dependent shifts.

Phase transitions from π/2 to minimum at T_m, varying with doping.

Model aligns with experimental data, linking nonlinearity to order parameter relaxation.

Abstract

Investigations of the intrinsic electromagnetic nonlinearity of superconductors give insight into the fundamental physics of these materials. Phase-sensitive third-order harmonic voltage data $\tilde{u}_{3f}=|u_{3f}|exp(i\phi_{3f})$ are acquired with a near-field microwave microscope on homogeneous YBa$_2$Cu$_3$O$_{7-\delta}$ (YBCO) thin films in a temperature range close to the critical temperature T$_c$. As temperature is increased from below T$_c$, the harmonic magnitude exhibits a maximum, while the phase, $\pi/2$ in the superconducting state, goes through a minimum. It is found that samples with doping ranges from near optimal ($\delta=0.16$) to underdoped ($\delta=0.47$) exhibit different behavior in terms of both the harmonic magnitude and phase. In optimally-doped samples, the harmonic magnitude reaches its maximum at a temperature $T_M$ slightly lower than that associated with the minimum of phase $T_m$ and drops into the noisefloor as soon as $T_m$ is exceeded. In underdoped samples $T_M$ is shifted toward lower temperatures with respect to $T_m$ and the harmonic voltage magnitude decreases slower with temperature than in the case of optimally-doped samples. A field-based analytical model of $\tilde{u}_{3f}$ is presented, where the nonlinear behavior is introduced as corrections to the low-field, linear-response complex conductivity. The model reproduces the low-temperature regime where the $\sigma_2$ nonlinearity dominates, in agreement with published theoretical and experimental results. Additionally the model identifies $T_m$ as the temperature where the order parameter relaxation time becomes comparable to the microwave probing period and reproduces semi-quantitatively the experimental data.