Disorder effects in NbTiN superconducting resonators

Disordered superconducting materials like NbTiN possess a high kinetic inductance fraction and an adjustable critical temperature, making them a good choice for low-temperature detectors. Their energy gap (Delta), critical temperature (T c), and quasiparticle density of states (QDOS) distribution, however, deviate from the classical BCS theory due to the disorder effects. The Usadel equation, which takes account of elastic scattering, non-elastic scattering, and electro-phonon coupling, can be applied to explain and describe these deviations. This paper presents numerical simulations of the disorder effects based on the Usadel equation to investigate their effects on the Delta, T c, QDOS distribution, and complex conductivity of the NbTiN film. Furthermore, NbTiN superconducting resonators with coplanar waveguide (CPW) structures are fabricated and characterized at different temperatures to validate our numerical simulations. The pair-breaking parameter alpha and the critical temperature in the pure state TcP of our NbTiN film are determined from the experimental results and numerical simulations. This study has significant implications for the development of low-temperature detectors made of disordered superconducting materials.