[Paper Review] Measurements of surface impedance of superconductors as a function of frequency in microwave range

S. Sarti, C. Amabile+1 more|arXiv (Cornell University)|Jun 14, 2004

Physics of Superconductivity and Magnetism3 citations

TL;DR

This paper presents a novel Corbino disk-based microwave technique to measure the frequency-dependent surface impedance of YBCO and MgB2 thin films across 2–20 GHz, enabling continuous spectroscopy of superconducting transitions. The key finding is a clear frequency-dependent broadening of the superconducting transition, with MgB2 showing a pronounced widening (ΔTc/Tc ≈ 0.15 at 20 GHz) and YBCO exhibiting a weaker but measurable frequency dependence.

ABSTRACT

We report measurements of the complex resistivity in YBCO and MgB$_2$ thin films over a continuous frequency spectrum in the microwave range, making use of a Corbino disk geometry. The paper mainly focuses on the extraction of the resistivity from raw data, displaying data analysis procedure and its limits of validity. We obtain and show resistivity curves as a function of frequency and temperature denoting a frequency dependent widening of the superconducting transition.

Motivation & Objective

• To develop a continuous-frequency microwave measurement technique for superconducting thin films, overcoming limitations of fixed-frequency resonant cavity methods.
• To extract accurate surface impedance (Rs and Xs) from reflection coefficient data despite signal distortions in long coaxial cables.
• To investigate the dynamical response of superconductors by measuring resistivity and penetration depth as functions of frequency and temperature.
• To quantify the frequency dependence of the superconducting transition width in high-Tc and conventional superconductors.

Proposed method

• Uses a Corbino disk geometry where the superconducting film short-circuits a coaxial cable, enabling continuous-frequency measurement of reflection coefficients.
• Applies a two-step data analysis: first, extracts effective reflection coefficient Γ̃m(ν) via daily calibration of the external cable section.
• Uses a modified S-parameter method to extract the sample's surface impedance Zs(ν) from measured reflection coefficients, correcting for cable distortions.
• Employs reference fields (Href = 0) and normal-state limits (H > Hc2) to reconstruct absolute Rs(ν; T, H) and Xs(ν; T, H) from ΔRs and ΔXs.
• Corrects for spurious contact capacitance via indium ring and frequency-dependent calibration, with validity limited to >6 GHz for YBCO and >2 GHz for MgB2.
• Validates the method by comparing field-sweep data to known normal-state behavior (Xs → 0 at H > Hc2), confirming reliability above upper critical field.

Experimental results

Research questions

• RQ1 How does the superconducting transition width in YBCO and MgB2 vary with microwave frequency?
• RQ2 To what extent do cable-induced distortions and contact capacitance affect the accuracy of surface impedance measurements in long-coaxial setups?
• RQ3 Can absolute values of surface resistance Rs and reactance Xs be reliably extracted from reflection coefficient data without full calibration?
• RQ4 What is the frequency dependence of the electromagnetic response in high-Tc and conventional superconductors near Tc?

Key findings

• The superconducting transition in MgB2 exhibits a strong frequency-dependent broadening, with ΔTc/Tc reaching approximately 0.15 when normalized to 2 GHz.
• For YBCO, the transition broadens less significantly, but a measurable frequency dependence is observed, particularly in the low-temperature tail of the transition.
• The surface resistance Rs of MgB2 remains nearly constant above μ0H ≈ 9 T, confirming that H = 13 T is in the normal state, validating the use of H = 13 T as a reference for Xs normalization.
• The contact capacitance limits data reliability below 6 GHz for YBCO and below 2 GHz for MgB2, necessitating frequency-dependent data exclusion.
• The method successfully reconstructs absolute Rs(ν; T, H) for both materials and Xs(ν; T, H) for MgB2, despite the absence of full cable calibration.
• Field-sweep measurements show that both Rs and Xs in MgB2 are insensitive to magnetic fields above 9 T, consistent with the system being in the normal state.