Search

Josephson junctions (JJs) are an integral component in quantum computing, low temperature electronics, and fundamental physics research. Hybrid superconductor-semiconductor JJs in two-dimensional materials have recently emerged as a paradigm for novel applications, harnessing gate-tunable supercurrents and strong spin-orbit coupling in a scalable platform. In this thesis, we present a detailed study of planar JJs in an InAs/Al heterostructure, when subjected to bias currents, microwave irradiation and in-plane magnetic fields. First, we investigate the stochastic dynamics of the superconducting-to-resistive transition of planar JJs and superconducting quantum interference devices (SQUIDs). We find that dynamics at low temperature are dominated by quantum fluctuations in the superconducting phase, which suppress the switching current to values less than half of the critical current. Phase dynamics are altered in a SQUID, such that the switching current of a JJ is more than doubled in a SQUID relative to being in isolation. Moderate damping leads to phase diffusion at higher temperatures, with a transition temperature that is tunable with gate voltages, magnetic fields and fluxes threading the SQUID. In a second experiment, we perform tunnelling spectroscopy measurements on a planar JJ irradiated by a microwave signal. Replicas in the conductance spectrum are shown to be consistent with photon assisted tunnelling (PAT) between the spectroscopic probe and Andreev bound states (ABSs) in the junction, rather than due to novel light-matter coupling in the form of Floquet-Andreev states. By tuning the tunnel-barrier transparency and Fermi energy with gate voltages, in addition to complementary current-phase relation (CPR) measurements, signatures unique to PAT are identified. Further, microwave-induced distortions to the CPR are shown to be consistent with a non-equilibrium occupation of ABSs, without invoking Floquet states. Finally, supercurrent and tunnelling spectroscopy measurements are performed on planar JJs in an in-plane magnetic field. Phase shifts in the CPR are reported relative to a phase reference, in devices with different superconducting lead sizes to investigate orbital effects. At low fields, we observe gate-dependent phase shifts of up to φ=0.5π, consistent with a Zeeman field coupling to highly-transmissive ABSs via Rashba spin-orbit interaction. A distinct phase shift at larger fields is concomitant with a switching current minimum and a closing and reopening of the superconducting gap. These signatures of a phase transition, which might resemble a topological transition, scale with the superconducting lead size indicating the crucial role of orbital effects in planar JJs. Our results give a new baseline understanding of planar JJs in InAs/Al heterostructures, and elucidate the interplay of Zeeman, spin-orbit and orbital effects in magnetic fields. This guides towards improved realisations of gate-tunable qubits, superconducting electronic.

In ferromagnets, scattering processes between magnon modes have been an active platform for the investigation of nonlinear wave interactions and chaotic dynamics for over six decades. Despite this rich history, questions remain regarding the nature of these interactions. In this regard, three-magnon scattering of the ferromagnetic resonance (FMR) mode is of particular appeal: the threshold FMR magnon population at which scattering occurs is distinctly low, enabling its investigation over a wide range of excitation powers. This particular scattering process requires the availability of magnon modes at half of the frequency of the FMR mode. This requirement is readily fulfilled in magnetic films of micrometer thickness, as the associated dipolar interactions lead to a dip in their magnon dispersion. Existing studies of three-magnon scattering have largely focused on its influence on the magnon populations and on the steady-state behavior. A comprehensive understanding of its transient behavior (i.e. how it evolves in time as it approaches steady state) is missing. Similarly, little is known about the influence of three-magnon scattering on the magnons' phases. This is largely the case for other magnon scattering processes as well. There is also a lack of a formal understanding of the relationship between the forward and backward three-magnon scattering processes, i.e. between splitting and confluence. These gaps are, in part, owing to the fact that there is a lack of a comprehensive time- and phase-resolved experimental investigation of the three-magnon scattering process. Magnon scattering processes are most commonly investigated through diode-based techniques, which are relatively insensitive and lack phase resolution. They are also most commonly investigated through Brillouin light scattering spectroscopy; this technique is typically employed for large excitation powers, and its phase-sensitive implementations have not been applied to three-magnon scattering. Motivated by the above, I have assembled a time- and phase-resolved homodyning spectrometer that is operable over six orders of magnitude in microwave power. This spectrometer demonstrates a time resolution of 2 ns, and its sensitivity enables measurement of the transient behavior down to an excitation power of 10 microwatts. Upon measuring the resonance peak of the FMR mode, I observed satellite peaks near that of the FMR resonance. Such satellite peaks are observed in the literature as well. I found that they originate from the excitation of magnon modes with finite in-plane wavevectors, due to the inhomogeneity of the microwave field throughout the sample. To address this inhomogeneity, I created a microstrip waveguide with a signal line width of approximately 3.4 mm, such that it is appreciably wider than the 2 mm-wide sample. This ensures a highly uniform microwave field and, therefore, the highly isolated excitation of the FMR mode. Isolating the excitation of the FMR mode in this manner enables a clear interpretation of the measured transient behavior, and contributes toward the strong agreement observed between my experiment and my semianalytical model. With the above developments, I have investigated the transient behavior of the FMR mode during this scattering process over five orders of magnitude in power. In addition to my observing the expected transient behavior, in which the scattering monotonically suppresses the FMR magnon population to its threshold value, I find a second nonlinear in which the FMR magnon population exhibits transient oscillations about its threshold value. I find that both these oscillations and the timescale of the initial transient peak are highly dependent on the excitation power. At high powers, I find a third nonlinear regime in which the scattering generates 180-degree phase shifts of the FMR magnons. Moreover, I find that both these phase shifts and the transient oscillations reappear upon removing the microwave excitation (i.e. after turn-off). To supplement the experiment, and to understand my findings, I have derived a simplified semianalytical model of this scattering process based on the Landau-Lifshitz-Gilbert equation. Upon linearizing my model, I found that the oscillatory regime corresponds to a transition of the nonlinear regime's fixed point from a stable node to a stable spiral. I also extracted the predicted scaling of the oscillation frequency with the microwave field amplitude. Upon extracting the associated scaling of the experimental data, I found it to be in quantitative agreement with the predicted scaling over several orders of magnitude in power. To investigate the 180-degree phase shifts observed in the experiment, I generalized my model to allow for phase dynamics by omitting the standard assumption of harmonic time dependence. Numerically solving this generalized model, I found that it predicts these 180-degree phase shifts. In order to derive the equations of motion of the magnon populations, one begins with the generalized model and assumes harmonic time dependence. Remarkably, when accounting for the 180-degree phase shift in this harmonic approximation, I found that the phase shifts correspond to reversals in the scattering direction: in the magnon populations' equations of motion, the phase shift switches the sign of the scattering terms such that the scattering is now driving the FMR mode instead of damping it. These reversals explain the observed transient oscillations after turn-off: even without the excitation field, the FMR population may still oscillate via reversals between the forward and backward scattering process. These experimental and theoretical developments further the state of the art of the investigation of magnon scattering processes. The findings of my investigation provide a more comprehensive understanding of the transient behavior of this scattering process, and reveal the nontrivial interplay between three-magnon scattering and the magnons' phases.

The Josephson effect is one of the macroscopic quantum phenomena and it was predicted by B.D Josephson in 1962. For a typical S-I-S Josephson junction, there exists a continuous supercurrent across the junction without any external voltage applied due to the Cooper pair tunneling. The Cooper pair is a bound state of a pair of electrons caused by a small attraction due to the electron-phonon interaction in a metal at low temperatures. When the temperature is increased or external bias voltage is imposed, the Cooper pairs could be broken due to the thermal motion or the voltage overcoming the binding energy of the paired electrons. The term “activation” or “switching” of Josephson junction from superconducting state to normal or resistive state refers to such a process, that the normal electrons formed from the broken Cooper pairs result in a normal current, which is higher than a threshold, namely, critical current, so that a voltage drop across the junction can be measured and the current-voltage relation satisfies the Ohm’s law.According to the Josephson relations, the current flowing through the junction is characterizes by the phase difference between the two superconductors of the junction, and the resistively and capacitively shunted junction (RCSJ) model was proposed in 1968 for the description of phase dynamics. The governing equation of the phase difference is a Langevin equation analogously describing a Brownian particle moving in a periodic potential well. Accordingly, the escape ofBrownian particles from the well was used to study the switching of the junction. The RCSJ model in the past five decades has been accepted as a good model for successfully providing a switching mechanism called “thermal activation (TA)” at high temperatures relative to the “crossover temperature”. As a series of Josephson experiments were reported during 1980s, the RCSJ model was considered failing to explain some phenomena, such as the saturation of the switching current distribution (SCD) as the temperature is down to zero. Meanwhile, the theory of macroscopic quantum tunneling (MQT) was built; the phase was quantized and the saturation of SCD was attributed to the tunneling of the phase particle through the potential barrier. As a test for the secondary quantum effect, MQT has been accepted as a main theory for the interpretation of saturation of SCD in Josephson switching experiments.In this dissertation, we try to explore a classical switching mechanism as an alternative and simpler description for the phase difference of the Josephson junction at low temperatures besides MQT. The content of this thesis is structured as follows: in Chapter 1, we review the background of Josephson effect and present some of the key concepts that will be used in thefollowing chapters. In Chapter 2, by solving the Langevin equation of the RCSJ model using the GJ thermostat method, we will investigate the effects of the parameters in the equation, such as damping, temperature, sweep rate and initial conditions. Non-equilibrium phenomena are observed and discussed. In Chapter 3, the effects of initial conditions, especially the saturation phenomena in non-equilibrium state will be discussed. In Chapter 4, with the understandings on the classical switching mechanism of the junction, we will compare the results generated by our model to the published experimental data. Up to Chapter 4, our discussion is based on a single Josephson junction, while in Chapter 5, the simulation will be generalized to a one-dimension long Josephson junction, which will be a more complex system in which additional phenomena, such as kink-soliton, can be studied. In Chapter 6, we summarize the discussion in this dissertation.