Correlations and Quantum Dynamics of 1D Fermionic Models: New Results for the Kitaev Chain with Long-Range Pairing

In the first part of the thesis, we propose an exactly-solvable one-dimensional model for fermions with long-range p-wave pairing decaying with distance as a power law. We studied the phase diagram by analyzing the critical lines, the decay of correlation functions and the scaling of the von Neumann entropy with the system size. We found two gapped regimes, where correlation functions decay (i) exponentially at short range and algebraically at long range, (ii) purely algebraically. In the latter the entanglement entropy is found to diverge logarithmically. Most interestingly, along the critical lines, long-range pairing breaks also the conformal symmetry. This can be detected via the dynamics of entanglement following a quench. In the second part of the thesis we studied the evolution in time of the entanglement entropy for the Ising model in a transverse field varying linearly in time with different velocities. We found different regimes: an adiabatic one (small velocities) when the system evolves according the instantaneous ground state; a sudden quench (large velocities) when the system is essentially frozen to its initial state; and an intermediate one, where the entropy starts growing linearly but then displays oscillations (also as a function of the velocity). Finally, we discussed the Kibble-Zurek mechanism for the transition between the paramagnetic and the ordered phase.

Design and characterization of wideband Hall current sensors in BCD technology for smart power and metering applications

Power electronic circuits are moving towards higher switching frequencies, exploiting the capabilities of novel devices to shrink the dimension of passive components. This trend demands sensors capable enough to operate at such high frequencies. This thesis aims to demonstrate through experimental characterization, the broadband capability of a fully integrated CMOS X-Hall current sensor in current mode interfaced with a transimpedance amplifier (TIA), chip CH09, realized in CMOS technology for power electronics applications such as power converters. The system exploits a common-mode control system to operate the dual supply system, 5-V for the X-Hall probe and 1.2-V for the readout. The developed prototype achieves a maximum acquisition bandwidth of 12 MHz, a power consumption of 11.46 mW, resolution of 39 mArms, a sensitivity of 8 % /T, and a FoM of 569-MHz/A2mW, significantly higher than current state-of-the-art. Further enhancements were proposed to CH09 as a new chip CH100, aiming for accuracy levels prerequisite for a real-time power electronic application. The TIA was optimized for a wider bandwidth of 26.7 MHz with nearly 30% reduction of the integrated input referred noise of 26.69 nArms at the probe-AFE interface in the frequency band of DC-30 MHz, and a 10% improvement in the dynamic range. The expected input range is 5-A. The chip incorporates a dual sensing chain for differential sensing to overcome common mode interferences. A novel offset cancellation technique is proposed that would require switching of polarity of bias currents. Thermal gain drift was improved by a factor of 8 and will be digitally calibrated utilizing a new built-in temperature sensor with a post calibration measurement accuracy greater than 1%. The estimated power consumption of the entire system is 55.6 mW. Both prototypes have been implemented through a 90-nm microelectronic process from STMicroelectronics and occupy a silicon area of 2.4 mm2.

Study of charge, spin, and structural orderings in quantum materials using nuclei and muons as local probes

Quantum Materials are many body systems displaying emergent phenomena caused by quantum collective behaviour, such as superconductivity, charge density wave, fractional hall effect, and exotic magnetism. Among quantum materials, two families have recently attracted attention: kagome metals and Kitaev materials. Kagome metals have a unique crystal structure made up of triangular lattice layers that are used to form the kagome layer. Due to superconductivity, magnetism, and charge ordering states such as the Charge Density Wave (CDW), unexpected physical phenomena such as the massive Anomalous Hall Effect (AHE) and possible Majorana fermions develop in these materials. Kitaev materials are a type of quantum material with a unique spin model named after Alexei Kitaev. They include fractional fluctuations of Majorana fermions and non-topological abelian anyons, both of which might be used in quantum computing. Furthermore, they provide a realistic framework for the development of quantum spin liquid (QSL), in which quantum fluctuations produce long-range entanglements between electronic states despite the lack of classical magnetic ordering. In my research, I performed several nuclear magnetic resonance (NMR), nuclear quadrupole resonance (NQR), and muon spin spectroscopy (µSR) experiments to explain and unravel novel phases of matter within these unusual families of materials. NMR has been found to be an excellent tool for studying these materials’ local electronic structures and magnetic properties. I could use NMR to determine, for the first time, the structure of a novel kagome superconductor, RbV3Sb5, below the CDW transition, and to highlight the role of chemical doping in the CDW phase of AV3Sb5 superconductors. µSR has been used to investigate the effect of doping on kagome material samples in order to study the presence and behaviour of an anomalous phase developing at low temperatures and possibly related to time-reversal symmetry breaking.