Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2410.18802 · Nature Communications

Recombination of localized quasiparticles in disordered superconductors

Steven A. H. de Rooij, Remko Fermin, Kevin Kouwenhoven, Tonny Coppens, Vignesh Murugesan, David Johannes Thoen, J. Aarts, J. J. A. Baselmans, Pieter de Visser

Published Sep 26, 2025• 1 citation
arXivHTMLPDF

Abstract

Disordered superconductors offer new impedance regimes for quantum circuits, enable a pathway to protected qubits, and can improve superconducting detectors due to their high kinetic inductance and sheet resistance. The performance of these devices can be limited, however, by quasiparticles—the fundamental excitations of a superconductor. While experiments have shown that disorder affects the relaxation of quasiparticles drastically, the microscopic mechanisms are still not understood. We address this issue by measuring quasiparticle relaxation in a disordered β-Ta film, which we pattern as the inductor of a microwave resonator. We observe that quasiparticle recombination is governed by the phonon scattering time, which is faster than conventional recombination in ordered superconductors. We interpret the results as recombination of localized quasiparticles, induced by disorder, which first delocalize via phonon absorption. We analyze quasiparticle relaxation measurements on superconductors with different degrees of disorder and conclude that this phenomenon is inherent to disordered superconductors. The authors study a disordered β-Ta film, finding that quasiparticle recombination is governed by the phonon scattering time, which is faster than conventional recombination in ordered superconductors. The authors interpret the results in terms of quasiparticle localization, which helps to understand the quasiparticle relaxation in disordered superconducting circuits.

DOI
10.1038/s41467-025-63321-5

Related papers

Localized quasiparticles in a fluxonium with quasi-two-dimensional amorphous kinetic inductors

Trevyn F. Q. Larson, Sarah C. Jones, Tamás Kalmár +11 more

Disordered superconducting materials with high kinetic inductance are an important resource for generating nonlinearity in quantum circuits and creating high-impedance environments. In thin films fabricated from these materials, the combination of disorder and low effective dimensionality leads to increased order parameter fluctuations and enhanced kinetic inductance values. Among the challenges of harnessing these compounds in coherent devices are their proximity to the superconductor-insulator phase transition and the two-level systems located in the disordered structure. Here, we fabricate tungsten silicide wires from quasi-two-dimensional films and embed them into microwave resonators and fluxonium qubits, where the kinetic inductance provides the inductive part of the circuits. In this work, we study the dependence of loss on the frequency, disorder, and geometry of the devices, and find that the loss increases with the level of disorder and is dominated by the localized quasiparticles trapped in the spatial variations of the superconducting gap. High kinetic inductance materials are widely used in superconducting circuits, yet their loss mechanisms are not fully understood. Here the authors study quantum circuits incorporating nanowires made of quasi-2D disordered superconductor WSi and identify localized quasiparticles as the dominant source of loss.

arXiv:2504.07950•Nature Communications•Feb 21, 2026•1 citation

Modeling the dynamics of quasiparticles in superconducting devices at low temperatures

Fischer, Paul Benedikt

Superconducting materials are useful for a wide range of applications, ranging from particle detectors to quantum computing. The presence of excitations (quasiparticles) in the superconductor can be a resource in some devices and a disturbance in others - in kinetic inductance detectors, the generation of quasiparticles by an incoming photon can be read out and used to calculate the energy of the photon, while the tunnelling of quasiparticles is a cause of decoherence in quantum computing. While early research mostly focused on superconductors close to the critical temperature, temperatures that are far below the critical temperatures are often used for current applications. At these low temperatures, the energy exchange between quasiparticles and phonons becomes slow, and even small disturbances may drive the energy distribution of the quasiparticles out of thermal equilibrium. In fact, experiments usually show a residual number of quasiparticles even at milikelvin temperatures, for which the thermal density of quasiparticles would be negligible. This thesis consists of two parts: In the first part, I model the energy distribution of quasiparticles in superconducting resonators: Quasiparticles absorb energy by absorbing photons and release it as phonons, which drives the superconductor out of thermal equilibrium. I solve a set of rate equations, both numerical and analytical, to calculate the energy distribution of the quasiparticles. For parameters typically used in kinetic inductance detectors made of aluminum, the microwave signal used to read out the resonator dominates the energy distribution of the quasiparticles, while their density is determined by other processes. At not too low temperatures, quasiparticles are mainly produced by thermal phonons, and my calculations reproduce recently measured quality factors of resonators at temperatures above 250 mK without free parameters. I show that even a very small number of photons of higher energy, which I ascribe to noise from the microwave generator, would dominate the quasiparticle density at lower temperatures. Under this assumption, my calculations also reproduce the quality factors at lower temperatures. In the second part of this thesis, I investigate the effects of spatial fluctuations of the superconducting energy gap on the dynamics of quasiparticles. Recently, it has been proposed that such fluctuations may lead to the localization of quasiparticles in states below the energy gap, which could cause a finite quasiparticle density even at very low temperatures. Using the Keldysh-Usadel formalism, I derive rates for the different processes (recombination/(de-) localization/generation) of quasiparticles in such systems. Using these rate equations I derive new upper limits for the quasiparticle density that could result from these localized states. These upper limits show that localization caused by weak magnetic impurities in typical aluminum systems does not lead to a relevant quasiparticle density. This contradicts previous theories, which only consider the recombination between two localized quasiparticles without examining their dynamics in detail.

•Jan 1, 2025•0 citations

Can slow recombination in ordered superconductors explain the excess quasiparticle population?

Eva Gurra, D. A. Bennett, Shannon M. Duff +2 more

An excess density of quasiparticles is widely observed in superconducting films. This excess causes performance degradation in a variety of superconducting devices, including decoherence in qubits. In this Letter, we evaluate the hypothesis of [1] that the quasiparticle excess is caused by anomalously slow recombination at low quasiparticle densities due to localization in sub-gap states. We probe the density of states in aluminum and niobium films using current-voltage measurements of tunnel junctions and extract upper bounds on the energy scales of the sub-gap states and gap smearing. With these parameters, we evaluate the recombination times predicted by [1] and find that slow recombination is not predicted to occur at observed quasiparticle densities in aluminumand niobium-based superconducting devices. These results suggest that the quasiparticle excess in ordered superconductors is primarily due to non-thermal sources of quasiparticle generation and not slow recombination.

arXiv:2507.03217•Jul 3, 2025•0 citations

Evaluating the contribution of slow recombination in localized subgap states to the excess quasiparticle population in ordered superconductors

Eva Gurra, D. A. Bennett, Shannon M. Duff +2 more

An excess density of quasiparticles is widely observed in superconducting films. This excess causes performance degradation in a variety of superconducting devices, including decoherence in qubits. In this Letter, we evaluate the hypothesis of Bespalov [] that the quasiparticle excess is caused by anomalously slow recombination at low quasiparticle densities due to localization in subgap states. We probe the density of states in aluminum and niobium films using current-voltage measurements of tunnel junctions and extract upper bounds on the energy scales of the subgap states and gap smearing. With these parameters, we evaluate the density-dependent recombination times calculated by Bespalov and find that slow recombination is not predicted to occur at observed quasiparticle densities in aluminum- and niobium-based superconducting devices. These results suggest that the quasiparticle excess in ordered superconductors is primarily due to nonthermal sources of quasiparticle generation and not slow recombination.

Physical Review Research•Jan 13, 2026•0 citations

Enhanced quasiparticle lifetime in a superconductor by selective blocking of recombination phonons with a phononic crystal

Karwan Rostem, Pieter de Visser, Edward J. Wollack

When quasiparticles in a BCS superconductor recombine into Cooper pairs, phonons are emitted within a narrow band of energies above the pairing energy at $2\mathrm{\ensuremath{\Delta}}$. We show that a phonon band gap restricting the escape of recombination phonons from a superconductor can increase the quasiparticle recombination lifetime by more than an order of magnitude. A phonon band gap can be realized and matched to the recombination energy with a phononic crystal, a periodically patterned dielectric membrane. We discuss in detail the nonequilibrium quasiparticle and phonon distributions that arise in a superconductor due to a phonon band gap and a pair-breaking photon signal. Although intrinsically a nonequilibrium effect, the lifetime enhancement in the small-signal regime is remarkably similar to an estimate from an equilibrium formulation. The equilibrium estimate closely follows $exp({\mathrm{\ensuremath{\Omega}}}_{bg}/{k}_{B}{T}_{b})$, where ${\mathrm{\ensuremath{\Omega}}}_{bg}$ is the phonon band gap energy bandwidth above $2\mathrm{\ensuremath{\Delta}}$ and ${T}_{b}$ is the phonon bath temperature of the coupled electron-phonon system. We discuss the impact of a phononic band gap on the performance of a superconducting circuit element and propose a microwave resonator to measure the enhancement in the quasiparticle lifetime.

arXiv:1805.06991•Physical review. B./Physical review. B•Jul 27, 2018•12 citations

Ultrasensitive hot-electron kinetic-inductance detectors

A. Sergeev, Boris S. Karasik, I. G. Gogidze +1 more

While experimental studies of kinetic-inductance sensors have been limited so far by the temperature range near the superconducting transition, these detectors can be very sensitive at temperatures well below the transition, where the number of equilibrium quasiparticles is exponentially small. In this regime, a shift of the quasiparticle chemical potential under radiation results in the change of the kinetic inductance, which can be measured by a sensitive SQUID readout. We modeled the kinetic inductance response of detectors made from disordered superconducting Nb, NbC, and MoRe films. Low phonon transparency of the interface between the superconductor and the substrate causes substantial re-trapping of phonons providing high quantum efficiency and the operating time of ∼1 ms at ≈1 K. Due to the small number of quasiparticles, the noise equivalent power of the detector determined by the quasiparticle generation-recombination noise can be as small as ∼10−19 W/√Hz at He4 temperatures.

AIP conference proceedings•Jan 1, 2002•3 citations
Disordered superconductors offer new impedance regimes for quantum circuits, enable a pathway to protected qubits, and can improve superconducting detectors due to their high kinetic inductance and sheet resistance. The performance of these devices can be limited, however, by quasiparticles—the fundamental excitations of a superconductor. While experiments have shown that disorder affects the relaxation of quasiparticles drastically, the microscopic mechanisms are still not understood. We address this issue by measuring quasiparticle relaxation in a disordered β-Ta film, which we pattern as the inductor of a microwave resonator. We observe that quasiparticle recombination is governed by the phonon scattering time, which is faster than conventional recombination in ordered superconductors. We interpret the results as recombination of localized quasiparticles, induced by disorder, which first delocalize via phonon absorption. We analyze quasiparticle relaxation measurements on superconductors with different degrees of disorder and conclude that this phenomenon is inherent to disordered superconductors. The authors study a disordered β-Ta film, finding that quasiparticle recombination is governed by the phonon scattering time, which is faster than conventional recombination in ordered superconductors. The authors interpret the results in terms of quasiparticle localization, which helps to understand the quasiparticle relaxation in disordered superconducting circuits.
Disordered superconducting materials with high kinetic inductance are an important resource for generating nonlinearity in quantum circuits and creating high-impedance environments. In thin films fabricated from these materials, the combination of disorder and low effective dimensionality leads to increased order parameter fluctuations and enhanced kinetic inductance values. Among the challenges of harnessing these compounds in coherent devices are their proximity to the superconductor-insulator phase transition and the two-level systems located in the disordered structure. Here, we fabricate tungsten silicide wires from quasi-two-dimensional films and embed them into microwave resonators and fluxonium qubits, where the kinetic inductance provides the inductive part of the circuits. In this work, we study the dependence of loss on the frequency, disorder, and geometry of the devices, and find that the loss increases with the level of disorder and is dominated by the localized quasiparticles trapped in the spatial variations of the superconducting gap. High kinetic inductance materials are widely used in superconducting circuits, yet their loss mechanisms are not fully understood. Here the authors study quantum circuits incorporating nanowires made of quasi-2D disordered superconductor WSi and identify localized quasiparticles as the dominant source of loss.
Superconducting materials are useful for a wide range of applications, ranging from particle detectors to quantum computing. The presence of excitations (quasiparticles) in the superconductor can be a resource in some devices and a disturbance in others - in kinetic inductance detectors, the generation of quasiparticles by an incoming photon can be read out and used to calculate the energy of the photon, while the tunnelling of quasiparticles is a cause of decoherence in quantum computing. While early research mostly focused on superconductors close to the critical temperature, temperatures that are far below the critical temperatures are often used for current applications. At these low temperatures, the energy exchange between quasiparticles and phonons becomes slow, and even small disturbances may drive the energy distribution of the quasiparticles out of thermal equilibrium. In fact, experiments usually show a residual number of quasiparticles even at milikelvin temperatures, for which the thermal density of quasiparticles would be negligible. This thesis consists of two parts: In the first part, I model the energy distribution of quasiparticles in superconducting resonators: Quasiparticles absorb energy by absorbing photons and release it as phonons, which drives the superconductor out of thermal equilibrium. I solve a set of rate equations, both numerical and analytical, to calculate the energy distribution of the quasiparticles. For parameters typically used in kinetic inductance detectors made of aluminum, the microwave signal used to read out the resonator dominates the energy distribution of the quasiparticles, while their density is determined by other processes. At not too low temperatures, quasiparticles are mainly produced by thermal phonons, and my calculations reproduce recently measured quality factors of resonators at temperatures above 250 mK without free parameters. I show that even a very small number of photons of higher energy, which I ascribe to noise from the microwave generator, would dominate the quasiparticle density at lower temperatures. Under this assumption, my calculations also reproduce the quality factors at lower temperatures. In the second part of this thesis, I investigate the effects of spatial fluctuations of the superconducting energy gap on the dynamics of quasiparticles. Recently, it has been proposed that such fluctuations may lead to the localization of quasiparticles in states below the energy gap, which could cause a finite quasiparticle density even at very low temperatures. Using the Keldysh-Usadel formalism, I derive rates for the different processes (recombination/(de-) localization/generation) of quasiparticles in such systems. Using these rate equations I derive new upper limits for the quasiparticle density that could result from these localized states. These upper limits show that localization caused by weak magnetic impurities in typical aluminum systems does not lead to a relevant quasiparticle density. This contradicts previous theories, which only consider the recombination between two localized quasiparticles without examining their dynamics in detail.
An excess density of quasiparticles is widely observed in superconducting films. This excess causes performance degradation in a variety of superconducting devices, including decoherence in qubits. In this Letter, we evaluate the hypothesis of [1] that the quasiparticle excess is caused by anomalously slow recombination at low quasiparticle densities due to localization in sub-gap states. We probe the density of states in aluminum and niobium films using current-voltage measurements of tunnel junctions and extract upper bounds on the energy scales of the sub-gap states and gap smearing. With these parameters, we evaluate the recombination times predicted by [1] and find that slow recombination is not predicted to occur at observed quasiparticle densities in aluminumand niobium-based superconducting devices. These results suggest that the quasiparticle excess in ordered superconductors is primarily due to non-thermal sources of quasiparticle generation and not slow recombination.
An excess density of quasiparticles is widely observed in superconducting films. This excess causes performance degradation in a variety of superconducting devices, including decoherence in qubits. In this Letter, we evaluate the hypothesis of Bespalov [] that the quasiparticle excess is caused by anomalously slow recombination at low quasiparticle densities due to localization in subgap states. We probe the density of states in aluminum and niobium films using current-voltage measurements of tunnel junctions and extract upper bounds on the energy scales of the subgap states and gap smearing. With these parameters, we evaluate the density-dependent recombination times calculated by Bespalov and find that slow recombination is not predicted to occur at observed quasiparticle densities in aluminum- and niobium-based superconducting devices. These results suggest that the quasiparticle excess in ordered superconductors is primarily due to nonthermal sources of quasiparticle generation and not slow recombination.
When quasiparticles in a BCS superconductor recombine into Cooper pairs, phonons are emitted within a narrow band of energies above the pairing energy at $2\mathrm{\ensuremath{\Delta}}$. We show that a phonon band gap restricting the escape of recombination phonons from a superconductor can increase the quasiparticle recombination lifetime by more than an order of magnitude. A phonon band gap can be realized and matched to the recombination energy with a phononic crystal, a periodically patterned dielectric membrane. We discuss in detail the nonequilibrium quasiparticle and phonon distributions that arise in a superconductor due to a phonon band gap and a pair-breaking photon signal. Although intrinsically a nonequilibrium effect, the lifetime enhancement in the small-signal regime is remarkably similar to an estimate from an equilibrium formulation. The equilibrium estimate closely follows $exp({\mathrm{\ensuremath{\Omega}}}_{bg}/{k}_{B}{T}_{b})$, where ${\mathrm{\ensuremath{\Omega}}}_{bg}$ is the phonon band gap energy bandwidth above $2\mathrm{\ensuremath{\Delta}}$ and Tb{T}_{b}Tb​ is the phonon bath temperature of the coupled electron-phonon system. We discuss the impact of a phononic band gap on the performance of a superconducting circuit element and propose a microwave resonator to measure the enhancement in the quasiparticle lifetime.
While experimental studies of kinetic-inductance sensors have been limited so far by the temperature range near the superconducting transition, these detectors can be very sensitive at temperatures well below the transition, where the number of equilibrium quasiparticles is exponentially small. In this regime, a shift of the quasiparticle chemical potential under radiation results in the change of the kinetic inductance, which can be measured by a sensitive SQUID readout. We modeled the kinetic inductance response of detectors made from disordered superconducting Nb, NbC, and MoRe films. Low phonon transparency of the interface between the superconductor and the substrate causes substantial re-trapping of phonons providing high quantum efficiency and the operating time of ∼1 ms at ≈1 K. Due to the small number of quasiparticles, the noise equivalent power of the detector determined by the quasiparticle generation-recombination noise can be as small as ∼10−19 W/√Hz at He4 temperatures.