Measuring kinetic inductance and superfluid stiffness of two-dimensional superconductors using high-quality transmission-line resonators

TL;DR

This paper introduces a high-precision resonator-based method to measure kinetic inductance and superfluid stiffness in 2D superconductors, enabling detailed analysis of their pairing mechanisms and material properties.

Contribution

The authors develop and validate a novel technique using high-quality superconducting resonators to accurately measure kinetic inductance and related properties in 2D superconductors, overcoming previous experimental challenges.

Findings

Validated the technique with aluminum, matching BCS theory.

Measured kinetic inductance of NbSe₂ near its transition temperature.

Demonstrated applicability to layered 2D materials and heterostructures.

Abstract

The discovery of van der Waals superconductors in recent years has generated a lot of excitement for their potentially novel pairing mechanisms. However, their typical atomic-scale thickness and micrometer-scale lateral dimensions impose severe challenges to investigations of pairing symmetry by conventional methods. In this report we demonstrate a new technique that employs high-quality-factor superconducting resonators to measure the kinetic inductance -- up to a part per million -- and loss of a van der Waals superconductor. We analyze the equivalent circuit model to extract the kinetic inductance, superfluid stiffness, penetration depth, and ratio of imaginary and real parts of the complex conductivity. We validate the technique by measuring aluminum and finding excellent agreement in both the zero-temperature superconducting gap as well as the complex conductivity data when compared with BCS theory. We then demonstrate the utility of the technique by measuring the kinetic inductance of multi-layered niobium diselenide and discuss the limits to the accuracy of our technique when the transition temperature of the sample, NbSe$_2$ at 7.06 K, approaches our Nb probe resonator at 8.59 K. Our method will be useful for practitioners in the growing fields of superconducting physics, materials science, and quantum sensing, as a means of characterizing superconducting circuit components and studying pairing mechanisms of the novel superconducting states which arise in layered 2D materials and heterostructures.