Complete electrodynamics of a BCS superconductor with $\mu$eV energy scales: microwave spectroscopy on titanium at mK temperatures

TL;DR

This study conducts microwave spectroscopy on titanium at millikelvin temperatures to comprehensively analyze its electrodynamics in the superconducting state, confirming BCS theory predictions and characterizing its energy gap, penetration depth, and magnetic response.

Contribution

It provides the first detailed microwave electrodynamics measurements of titanium in the superconducting state at microelectronvolt energy scales, confirming BCS theory in the dirty limit.

Findings

Superconducting titanium follows BCS predictions for energy gap and temperature dependence.

Titanium is in the dirty limit, consistent with scattering rate measurements.

The energy gap is approximately 75 μeV, with 2Δ₀/k_B T_c ≈ 3.5.

Abstract

We performed resonant microwave measurements on superconducting titanium (Ti) down to temperatures of 40~mK, well below its critical temperature $T_\mathrm{c} \approx 0.5$~K. Our wide frequency range 3.3-40~GHz contains the zero-temperature energy gap $2\Delta_0$ and allows us to probe the full electrodynamics of the superconducting state, including excitations across the gap and the low-frequency responses of superfluid condensate and thermal quasiparticles. The observed behavior follows the predictions of the BCS-based Mattis-Bardeen formalism, which implies that superconducting Ti is in the dirty limit, in agreement with our determination of the scattering rate. We directly determine the temperature dependence of the energy gap, which is in accordance with BCS predictions, and $2\Delta_0/k_\mathrm{B}T_\mathrm{c}\approx3.5$ with $\Delta_0 \approx$ 75~$\mu$eV. We also evaluate the penetration depth, and we characterize the behavior of superconducting Ti in external magnetic field.