Thermal effects in one dimensional Josephson chains

This work can be broadly classified into the study of critical phenomena in a one dimensional array of Josephson junctions. While we study quantum criticality when the array is in thermal equilibrium at zero bias, the non-equilibrium study involves understanding the bistability of the array at a critical non-zero bias. This work furthers our knowledge in understanding quantum critical behaviour at finite temperatures in a one dimensional Josephson array, while also establishing relaxation behaviour dual to that observed in a single Josephson junction. Chapter 1 briefly introduces the model to understand superconductor-insulator phase transition in a one dimensional Josephson array and points out the state of the field from where we started our zero-bias experiments. In this context it discusses the phase-charge duality observed in a Josephson array and its dual hysteretic behaviour to that of a single junction, setting the ground for our non-equilibrium study of the array. Chapter 2 shows the experimental setup and the chip layout of the device we measured. In chapter 3 we show that, unlike the typical quantum-critical broadening scenario, in one dimensional Josephson arrays temperature dramatically shifts the critical region. This shift leads to a regime of superconductivity at high temperature, arising from the melted zero-temperature insulator. Our results quantitatively explain the low-temperature onset of superconductivity in nominally insulating regimes, and the transition to the strongly insulating phase. We further present, to our knowledge, the first understanding of the onset of anomalous-metallic resistance saturation [30]. This work demonstrates a non-trivial interplay between thermal effects and quantum criticality. A practical consequence is that, counterintuitively, the coherence of high-impedance quantum circuits is expected to be stabilized by thermal fluctuations. In chapter 4, we show relaxation oscillations in a current-biased one dimensional array of Josephson junctions. These oscillations are well described by a circuit model, dual to the ordinary Josephson relaxation oscillations [72]. Injection locking these oscillations results in current plateaux. The relaxation step is found to obey a characteristic self-consistent relation, suggesting that it is governed by overheating effects. Chapter 5 describes the various checks and analysis we performed to support our conclusions made in chapters 3 and 4. Finally, chapter 6 describes the nanofabrication steps and the finite element electromagnetic simulations we performed to fabricate our devices.