In this thesis, I present the discovery of novel features in the phase diagrams of the cuprate high-Tc superconductors using high magnetic field electrical transport measurements. These discoveries attempt to address two central questions pertaining to how the physics of the cuprate high-Tc superconductors evolve as a function of both temperature and hole-doping.

The first question addresses the nature of the underdoped regime of the cuprates. Here, by performing high magnetic field measurements using low applied measurement currents and milliKelvin temperatures, we reveal an unconventional quantum vortex matter ground state hosting quantum oscillations. This vortex matter ground state is highly resilient to applied magnetic field, but fragile to applied temperature and current. It is characterised by vanishing electrical resistivity, finite magnetic hysteresis, and non-ohmic electrical transport beyond the highest accessible static magnetic fields. This discovery of a vortex matter ground state indicates that alternative models are required to explain how quantum oscillations coexist with superconducting vortices.

The second question addresses how the underdoped regime evolves into the overdoped regime as a function of hole-doping. Here, by performing high magnetic field electrical transport measurements over a wide, finely spaced range of hole-dopings, we reveal a prominent peak feature in the inverse Hall coefficient centred at a critical hole-doping value. This peak feature is seen to remain centred at this critical hole-doping value with elevated temperature; effectively tracing out a vertical boundary line at critical hole-doping that bisects the strange metal regime and is accompanied by an abrupt change in the cotangent of the Hall angle. While the origin of the vertical boundary line remains to be ascertained, it appears distinct from the widely reported T* line and charge order, and potentially could be consistent with previous reports of a vertical boundary from electronic specific heat and ARPES.