Fermi Surfaces and Where to Find Them: Quantum Oscillations in Kondo Insulators and High-Temperature Superconductors

Abstract

The Fermi surface is a geometric concept that codifies the momenta of all electrons at the Fermi level. It is these electrons that underpin most physical properties of metals, and have made quantum oscillations, the experimental manifestation of the Fermi surface, a hallmark signature of metals. In this thesis we have studied systems that are distinctly non-Fermi liquid, and discovered that, contrary to this canon, quantum oscillations occur even in the absence of a Fermi liquid. We present the high magnetic field studies of two classes of correlated electron systems. We survey the striking quantum oscillations in the magnetisation of SmB₆ and YbB₁₂, two strongly-correlated Kondo insulators. We also present magnetic and transport measurements of underdoped YBa₂Cu₃O₆₊ₓ, a high-temperature superconductor, that prompt us to reinterpret the quantum oscillations previously associated with the non-superconducting normal state. The surprising observation of quantum oscillations in the magnetisation of Kondo insulating SmB₆, but unaccompanied by oscillations in the electrical resistance, has attracted much attention. Here, we detail magnetic torque measurements that establish the intrinsic, bulk nature of the quantum oscillations, and reveal a moderate angular dependence of the oscillation frequencies, characteristic of a bulk, three-dimensional Fermi surface. We identify a finite linear specific heat coefficient down to the lowest temperatures, a distinguishing feature between metals and insulators. We demonstrate that the measured finite linear specific heat coefficient is in good agreement with the density of states at the Fermi level estimated from quantum oscillations. The unconventional nature of the ground state of SmB₆ is further evidenced by a non-zero thermal conductivity that is enhanced in a magnetic field. Through an extensive suite of characterisation techniques we confirm the high purity of our single crystals, with material properties consistent with an impurity concentration of less than 0.05%, and therefore further establishing the intrinsic character of the observed quantum oscillations. In the search for other non-Fermi liquids that are host to a Fermi surface, we identify YbB₁₂ as the second Kondo insulator that exhibits intrinsic, bulk quantum oscillations. We present a detailed study of the de Haas-van Alphen oscillations, corresponding to a heavy semimetal Fermi surface. Our results show many similarities with the ground state of SmB₆, including the large absolute size of the quantum oscillations and a finite linear specific heat coefficient, but also some key differences, namely the heavy effective masses and the proximity to a magnetic-field-induced or applied-pressure-induced insulator-metal transition. The observation of quantum oscillations in underdoped YBa₂Cu₃O₆₊ₓ refocused efforts to understand the pseudogap ground state of cuprate superconductors. Distinct from the large hole orbits of the Fermi liquid-like overdoped regime, the pseudogap regime was found to be characterised by a small electron pocket and the absence of antinodal states. A proposal associated the quantum oscillations with a conventional metallic state that emerges at a magnetic field of ∼20 T, however magnetic and thermal measurements have been at odds with the destruction of the superconducting order parameter at such modest magnetic fields. We employ high-magnetic fields to explore the region characterised by quantum oscillations, in search for the origin of the missing antinodal states in underdoped YBa₂Cu₃O₆₊ₓ, and the true extent of superconductivity. We find that the measured quantum oscillations display a signature sawtooth waveform, that rule out vestigial residual density of states, and instead point towards a complete gapping of the antinodal regions. We present current-dependent transport measurements performed in DC magnetic fields, down to millikelvin temperatures, that reveal the high-field superconducting state to be characterised by non-ohmic signatures associated with a quantum vortex matter state. In contrast to previous proposals, the quantum oscillations are found to occur well within this gapped vortex phase, as established by their co-existence with zero resistivity and hysteretic torque magnetisation, that are found to persist to magnetic fields beyond 45 T.