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

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 $2{\Delta }_0/k_{\mathrm{B}}{T}_{\mathrm{c}}\approx 3.5$ 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.

arXiv comment6 figures

References in corpus (23)

• Electric Field Control of the LaAlO${}_3$/SrTiO${}_3$ Interface Ground State
• Bipolar supercurrent in graphene
• Superconducting phases of f-electron compounds
• Gate-tuned normal and superconducting transport at the surface of a topological insulator
• Strongly disordered TiN and NbTiN s-wave superconductors probed by microwave electrodynamics
• Shaping a superconducting dome: Enhanced Cooper-pairing versus suppressed phase coherence in coupled aluminum nanograins
• Experimental demonstration of a two-band superconducting state for lead using scanning tunneling spectroscopy
• Survival of superconducting correlations across the 2D superconductor-insulator transition: A finite frequency study
• Electrodynamics of the Superconducting State in Ultra-Thin Films at THz Frequencies
• Far-Infrared Conductivity Measurements of Pair Breaking in Superconducting Nb${}_{0.5}$Ti${}_{0.5}$N Thin Films Induced by an External Magnetic Field
• Proximity-Coupled Ti/TiN Multilayers for use in Kinetic Inductance Detectors
• Quasi-Particle Dynamics in Superconducting Aluminum
• A dynamical study of phase fluctuations and their critical slowing down in amorphous superconducting films
• Anomalous microwave conductivity coherence peak in c-axis MgB2 thin film
• Single-gap superconductivity and dome of superfluid density in Nb-doped SrTiO3
• Observing electron spin resonance between 0.1 and 67 GHz at temperatures between 50 mK and 300 K using broadband metallic coplanar waveguides
• Microwave spectroscopy on heavy-fermion systems: probing the dynamics of charges and magnetic moments
• Direct observation of the superconducting gap in thin film of titanium nitride using terahertz spectroscopy
• Optical conductivity of iron-based superconductors
• Nodal quasiparticle dynamics in the heavy fermion superconductor CeCoIn5 revealed by precision microwave spectroscopy
• Superfluid density and microwave conductivity of FeSe superconductor: ultra-long-lived quasiparticles and extended s-wave energy gap
• Surface-resistance measurements using superconducting stripline resonators
• Superconducting Pb stripline resonators in parallel magnetic field and their application for microwave spectroscopy

Cited by in corpus (9)

• Anomalous normal fluid response in a chiral superconductor UTe2
• Superconducting coplanar microwave resonators with operating frequencies up to 50 GHz
• Linear optical response from the odd parity Bardasis-Schrieffer mode in locally non-centrosymmetric superconductors
• Characterization of collective excitations in weakly-coupled disordered superconductors
• Superfluid Density in Conventional Superconductors: From Clean to Strongly Disordered
• Negative differential thermal conductance by photonic transport in electronic circuits
• Microwave probing of bulk dielectrics using superconducting coplanar resonators in distant-flip-chip geometry
• Characterization of harmonic modes and parasitic resonances in multi-mode superconducting coplanar resonators
• The Aharonov Bohm effect as a material phenomenon