AUTHOR=Zarea Mehdi , Ueki Hikaru , Sauls J. A. 

TITLE=Electromagnetic response of disordered superconducting cavities

JOURNAL=Frontiers in Electronic Materials

VOLUME=3

YEAR=2023

URL=https://www.frontiersin.org/journals/electronic-materials/articles/10.3389/femat.2023.1259401

DOI=10.3389/femat.2023.1259401

ISSN=2673-9895

ABSTRACT=<p>We present the results for the resonant frequency shift and quality factor of disordered niobium (Nb) superconducting radio-frequency cavities driven out of equilibrium by the resonant microwave field. The theory is based on the non-equilibrium theory of superconductivity for the current response to the electromagnetic field at the vacuum–metal interface. We are able to accurately predict the observed frequency shifts with a precision of order fractions of kHz over the full temperature range 0 &lt; <italic>T</italic> ≤ <italic>T</italic><sub><italic>c</italic></sub>, including the negative frequency shift anomalies that are observed very near <italic>T</italic><sub><italic>c</italic></sub>. The origin of these anomalies is shown to be the competition between the normal metal skin depth and the London penetration depth, which diverges as <inline-formula id="inf1"><mml:math id="m1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>T</mml:mi><mml:mo>→</mml:mo><mml:msubsup><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo></mml:mrow></mml:msubsup></mml:math></inline-formula>. An analytical approximation to the full current response, valid for |<italic>T</italic> − <italic>T</italic><sub><italic>c</italic></sub>|≪ <italic>T</italic><sub><italic>c</italic></sub>, accounts for the negative frequency shift near <italic>T</italic><sub><italic>c</italic></sub>. The non-monotonic dependence of the quality factor on the quasiparticle scattering rate is related to the pair-breaking effect of disorder on the superfluid fraction and, thus, the London penetration depth.</p>