Scaling Behaviour and Resistance Calibration in Epitaxial Graphene Quantum Hall Devices

This dissertation presents the development and comprehensive analysis of epitaxial graphene-based Quantum Hall Array Resistance Standards (QHARS) with resistance values extending into the megaohm (MΩ) and gigaohm (GΩ) ranges. High-resistance QHARS are constructed using Y-∆ and star-mesh networks of monolayer graphene Hall bars, operating under cryogenic temperatures and strong magnetic fields. These networks exhibit robust quantised resistance, confirmed by precision measurements employing triple-series connections.To gain further insight into the quantum Hall regime, the scaling behaviour of epitaxial graphene is investigated through both a single Hall bar quantum Hall device and a more complex quantum Hall array device. Temperature- and current-dependent magnetotransport measurements yield critical parameters such as the localisation exponent (γ), critical exponent (κ), and inelastic scattering exponent (p), derived from finite-size scaling and current-scaling analyses. The study also highlights discrepancies between the exponents $p$ and p', obtained respectively from current heating and weak localisation, shedding light on the interplay of electron-electron and electron-phonon interactions under non-equilibrium and equilibrium conditions.