| Summary: | The physics of Mott delocalisation is investigated from the perspective of Fermiology through a series of high resolution de Haas-van Alphen experiments. Two systems in which some or all electrons can be forced to Mott localise by an experimental tuning parameter were chosen. The first system is CeRh<sub>1-<i>x</i></sub>Co<i><sub>x</sub></i>In<sub>5</sub> where the 4<i>f</i> electron of CeRhIn<sub>5</sub> can be driven into a delocalised state by Co substitution. The Fermi surface of CeRh<sub>1-<i>x</i></sub>Co<i><sub>x</sub></i>In<sub>5</sub> was studied for six different values of <i>x</i>. By measuring the angular dependence of de Haas-van Alphen frequencies, a Fermi surface sheet with <i>f</i>-electron character was observed to undergo an abrupt change in topology as <i>x</i> is varied. This reconstruction does not occur at the quantum critical concentration <i>x<sub>c</sub></i>, where antiferromagnetism is suppressed to <i>T = </i>0. Instead this sudden change occurs well below <i>x<sub>c</sub></i>, deep inside the antiferromagnetic state. Across all concentrations, the quasiparticle effective mass of this sheet does not diverge, suggesting this critical behaviour is not exhibited equally on all parts of the Fermi surface. The second system of interest is the Mott insulator Ca<sub>2</sub>RuO<sub>4</sub>, which can be metallised at 0.6 GPa. A completely new setup, utilising a 10-turn signal pick-up coil in an anvil cell for field modulation measurements, was developed for performing de Haas-van Alphen experiments under pressure. This novel setup thus has the potential to reach much higher pressures than the existing piston-cylinder type setup, opening up a much bigger phase space for future exploration in materials physics. The newly developed method was tested using Sr<sub>2</sub>RuO<sub>4</sub> and the results are in excellent agreement with a broad body of literature. Subsequently, the method was applied to study the metallic state of Ca<sub>2</sub>RuO<sub>4</sub>. De Haas-van Alphen signals were successfully recorded at high pressure using both the cryomagnetic system in Cambridge up to 18 T and a resistive magnet in National High Magnetic Field Laboratory in Tallahassee up to 31 T. Comparisons to band structure calculations were made.
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