This thesis describes work done in two separate areas of the field of superconductivity. The first part describes experiments performed to measure a predicted, but previously unmeasured non-equilibrium effect in superconducting aluminum. A charge imbalance, or charging of the normal fluid with respect to the superfluid, is generated by the interaction of an electric field and a supercurrent. We have shown that this effect does occur, however the measured temperature dependence of this effect does not agree with existing theory. In the second part of this thesis we report on efforts to make simple superconductor devices from the high-T$\sb{\rm c}$ ceramic oxide superconductors. We have made thin films of both $\rm YBa\sb2 Cu\sb3 O\sb{7-x}$ and BiSrCaCuO by several methods, and measurements of bulk film properties are presented. These films have been patterned into different structures in a number of ways, including an in-situ ion milling modification technique. Data on these devices, and grain-boundary SQUIDS are presented.
This thesis describes work done in two separate areas of the field of superconductivity. The first part describes experiments performed to measure a predicted, but previously unmeasured non-equilibrium effect in superconducting aluminum. A charge imbalance, or charging of the normal fluid with respect to the superfluid, is generated by the interaction of an electric field and a supercurrent. We have shown that this effect does occur, however the measured temperature dependence of this effect does not agree with existing theory. In the second part of this thesis we report on efforts to make simple superconductor devices from the high-T\sbc ceramic oxide superconductors. We have made thin films of both YBa\sb2Cu\sb3O\sb7−x and BiSrCaCuO by several methods, and measurements of bulk film properties are presented. These films have been patterned into different structures in a number of ways, including an in-situ ion milling modification technique. Data on these devices, and grain-boundary SQUIDS are presented.
This thesis reports on theoretical investigations of the ultrafast nonequilibrium dynamics in superconductors. In particular, two nonequilibrium scenarios are modeled by combining several analytical and numerical methods: transient superconducting phase transition and collective excitations of a superconducting condensate. In the first part of the thesis the possibility to induce singlet superconducting correlations far from equilibrium is explored by applying time-dependent Lanczos algorithm to the one-dimensional extended Hubbard model. Here, the system is driven into a nonequilibrium state by (i) interaction quench and (ii) quench by pulse. In both cases the buildup of the superconducting correlations is studied in view of several correlation functions. Moreover, a transient Meissner effect, which reflects fingerprints of the induced superconductivity, is observed in calculations of the important for experiments time-dependent optical conductivity. In addition, the differences between nonequilibrium dynamics of the extended Hubbard model initiated by interaction quench and by pulse quench are discussed in detail. The second part is devoted to the excitation of collective modes in a superconductor out of equilibrium. First of all, focus is given to the properties of collective modes close to equilibrium conditions, where a linearized response can be expected. Within the framework of the (Nambu-) matrix kinetic theory in the clean limit a comprehensive gauge-invariant description of the collective modes associated with phase fluctuations of the order parameter is analytically formulated for the generalized case of two- band superconducting systems. Particular emphasis is on the application to the recently discovered noncentrosymmetric superconductors. A detailed analysis of the collective modes includes specification of the gauge mode (common to all superconductors) and the Leggett mode (collective fluctuations of the interband phase difference), and investigation of their subtle interplay in view of validity of the charge conservation law and the participation in the Anderson-Higgs mechanism. Further, the nonequilibrium excitation of the superconducting gaps for the case of two-band superconductors with singlet pairing correlations is investigated in a view of optical pump-probe experiments. For this purpose a semi-numerical method based on the density- matrix theory is formulated. In this case additional amplitude (Higgs) modes were identified, which allow to directly detect the properties of the superconducting condensates as a function of time. Moreover, a new interplay between the phase (Leggett) and amplitude (Higgs) modes is studied in detail. In particular it was found that the nonadiabatic excitation process leads to strong coupling between both modes. Finally, based on calculations of the time-dependent optical conductivity the prediction is made that the coupled Higgs and Leggett modes can be clearly visible in the pump-probe absorption spectra.
This thesis is about unconventional superconductors out of equilibrium. More precisely, it summarizes our theoretical efforts in addressing a few questions related to the real-time evolution in models displaying unconventional superconductivity. Apart from the purely theoretical interest, the motivation for these studies comes from the recent achievement in the field of ultrafast time-resolved spectroscopy on correlated materials, such as the high-temperature copper-oxide superconductors. The task of describing such systems in nonequilibrium is a very difficult one. In this thesis we attack the problem from two different points of view: • the anisotropic unconventional d-wave symmetry, • the strong electron-electron correlations. The thesis is organized as follows: The first part introduces the basic concepts which lay at the foundation of the work presented in the other two parts. In Chapter 1, the concept of unconventional superconductivity is briefly introduced. This mainly includes the high-temperature copper-oxide superconductors and their phenomenology: d-wave symmetry of the super- conducting gap and strong electron-electron interaction. Chapter 2 is devoted to a review of the recent experimental advances in the field of ultrafast spectroscopy of high temperature superconductors and correlated materials, with a particular focus on time- and angle- resolved photoemission spectroscopy. Finally, Chapter 3 is a short review of some works in the field of cold-atom Fermi gases. In the second part we address the physics of the d-wave superconductor after a sudden excitation. First, in Chapter 4 we introduce in some detail a model of mean-field superconductor with a d-wave symmetry. The principal feature of this model is the anisotropy of the gap and the nodal lines along which the gap vanishes. The results concerning the dynamics of the gap after a “quantum quench” are exposed in Chapter 5 where we compare our model to the s-wave superconductor. This comparison allows to identify the consequences of the unconventional symmetry. In Chapter 6 we discuss the spectral features of the transient nonequilibrium state of the d-wave superconductor. This is particularly important to move a first step towards photoemission experiments. In the third part we concentrate on the attractive Hubbard model as a prototype of strongly correlated superconductor. In Chapter 8 we discuss the superconducting state at equilibrium with the use of dynamical mean-field theory. In Chapter 9 we discuss the extension of this technique to systems out of equilibrium. In particular it is described the implementation in the superconducting phase. At the end of the thesis two appendices give some details of the calculations.
Superconducting qubits are at the forefront of efforts to develop scalable quantum computers due to their potential to perform complex computations beyond the capabilities of classical systems. However, maintaining the quantum coherence of these qubits remains a significant challenge, primarily due to various noise sources such as flux noise, dielectric loss, and quasiparticle poisoning. This dissertation presents a detailed theoretical investigation into two noise mechanisms affecting superconducting qubits: flux noise from spin impurities and charge/flux noise from non-equilibrium superconducting quasiparticle distributions. The first part of the research focuses on developing a general theoretical framework to calculate flux noise arising from spin impurities. This framework accounts for spin diffusion and spin-lattice relaxation, incorporating a discrete diffusion model to handle confinement effects and inhomogeneities. Analytical and numerical results show that the spin relaxation model aligns with experimental observations in aluminum devices, while the spin diffusion model better matches experiments in niobium devices. The second part of the thesis proposes a theory addressing charge and flux noise due to non-equilibrium superconducting quasiparticle distributions within superconducting wires. This theory highlights the significant impact of ohmic loss generated by these quasiparticles, revealing their contribution to charge noise at intermediate frequencies and a nearly white flux noise background. Comparative analysis with experimental data provides some validation for the theoretical models and gives insights into the temperature-dependent behavior of flux noise and the distinctive noise characteristics in aluminum and niobium devices. The findings highlight the necessity of addressing wire-resident quasiparticles
In this thesis I describe work on developing theoretical and numerical models of supercon- ducting thin-film microwave resonators. Superconducting resonators are used in a variety of applications, one of which is as kinetic inductance detectors (KIDs). KIDs are ultra-low noise, highly sensitive, multiplexable detectors, with uses in a wide variety of fields including astrophysics, medical imaging, and particle physics. Resonators are also crucial for supercon- ducting qubit readout, superconducting mixers and parametric amplifiers, and as multiplexers for other devices. The results described in this thesis apply to all thin film resonators, but are primarily described in the context of KIDs. I develop models of how constant absorbed power affects superconducting thin films, driving them out of thermal equilibrium with the bath. Using the Chang & Scalapino equations, I calculate numerically the steady-state quasiparticle and phonon distributions for various sources of power (sub-gap and above-gap photons and phonons, single frequency and broadband). Many new results emerge, a few of which are: the quasiparticle heating effects of microwave power, explaining the experimentally measured saturation of resonator performance; the frequency dependence of the quasiparticle generation efficiency in the sub-mm wavelength range; and the importance of phonon trapping in thin films at low temperatures. I then use these nonequilibrium results in higher-level device models. Starting from a generic framework for resonators, I present and implement a model of a KID with variable thermal isolation. I calculate the effects of quasiparticle heating on both the large-signal and small-signal behaviour, highlighting the effects of electrothermal feedback caused by readout power. Electrothermal feedback is shown to be able to increase or decrease the magnitude and bandwidth of the responsivity and noise, depending on the operating point. Finally, I propose an experimental measurement of quasiparticle heating effects in a new device – a four-port ring resonator. In such a device, unlike in the standard two-port resonator, the device can be heated and read out independently. I develop detailed models for the thermal and electrical behaviour of these devices, and suggest a scheme by which the quasiparticle heating effects of microwave power, predicted in this thesis, can be measured.
Static electric fields have a negligible influence on the electric and transport properties of a metal because of the screening effect. This belief was extended to conventional metallic superconductors. However, recent experiments have shown that the superconductor properties can be controlled and manipulated by the application of strong electrostatic fields. Here, the authors review the experimental results obtained in the realization of field-effect metallic superconducting devices exploiting this phenomenon. The authors start by presenting the pioneering results on superconducting Bardeen–Cooper–Schrieffer wires and nanoconstriction Josephson junctions (Dayem bridges) made of different materials, such as titanium, aluminum, and vanadium. Then, the authors show the mastering of the Josephson supercurrent in superconductor-normal metal-superconductor proximity transistors, suggesting that the presence of induced superconducting correlations is enough to see this unconventional field-effect. Later, the authors present the control of the interference pattern in a superconducting quantum interference device, indicating the coupling of the electric field with the superconducting phase. The authors conclude this review by discussing some devices that may represent a breakthrough in superconducting quantum and classical computation.
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.