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This thesis describes experiments carried out on two novel strongly correlated electron systems. The first, FeCrAs, is a new material that has not been studied before, while the second, Sr3Ru2O7, has been previously shown to have a very novel so-called ‘nematic’ phase around the metamagnetic quantum critical end point (QCEP). For these studies, a new variation on an established method for measuring the field dependence of susceptibility in a BeCu clamp cell has been developed, and is described, as is a relaxation heat capacity cell that works from 4 K down to 300 mK. A method of growing stoichiometric crystals of the hexagonal iron-pnictide FeCrAs has been developed, and transport and thermodynamic measurements carried out. The in-plane resistivity shows an unusual “non-metallic” dependence on temperature T, rising continuously with decreasing T from ∼800 K to below 100 mK. The c-axis resistivity is similar, except for a sharp drop upon entry into an antiferromagnetic state at T_N ∼ 125 K. Below 10 K the resistivity follows a non-Fermi-liquid power law, ρ(T) = ρ_0 − AT^x with x < 1, while the specific heat shows Fermi liquid behaviour with a large Sommerfeld coefficient, γ ∼ 30 mJ/molK^2. The high temperature properties are reminiscent of those of the parent compounds of the new layered iron-pnictide superconductors, however the T → 0 K properties suggest a new class of non-Fermi liquid. The metamagnetic critical end point temperature T^∗ in Sr3Ru2O7 as a function of hydrostatic pressure with H//ab has been studied using the ac susceptibility. It is found that T^∗ falls monotonically with increasing pressure, going to zero at Pc = 14±0.3 kbar. One sign of the nematic phase observed in the field-angle tuning, i.e. T^∗ rises as the novel phase emerges, has not been seen in our study. However, we see a slope change in T^∗ vs P at ∼12.8 kbar, and a shoulder at the upper field side of the peak in χ′ from ∼12.8 kbar to ∼16.7 kbar. These new features indicate that some new physics sets in near the pressure-tuned QCEP.

This thesis describes experiments carried out on two novel strongly correlated electron systems. The first, FeCrAs, is a new material that has not been studied before, while the second, Sr3Ru2O7, has been previously shown to have a very novel so-called ‘nematic’ phase around the metamagnetic quantum critical end point (QCEP). For these studies, a new variation on an established method for measuring the field dependence of susceptibility in a BeCu clamp cell has been developed, and is described, as is a relaxation heat capacity cell that works from 4 K down to 300 mK. A method of growing stoichiometric crystals of the hexagonal iron-pnictide FeCrAs has been developed, and transport and thermodynamic measurements carried out. The in-plane resistivity shows an unusual “non-metallic” dependence on temperature T, rising continuously with decreasing T from ∼800 K to below 100 mK. The c-axis resistivity is similar, except for a sharp drop upon entry into an antiferromagnetic state at T_N ∼ 125 K. Below 10 K the resistivity follows a non-Fermi-liquid power law, ρ(T) = ρ_0 − AT^x with x < 1, while the specific heat shows Fermi liquid behaviour with a large Sommerfeld coefficient, γ ∼ 30 mJ/molK^2. The high temperature properties are reminiscent of those of the parent compounds of the new layered iron-pnictide superconductors, however the T → 0 K properties suggest a new class of non-Fermi liquid. The metamagnetic critical end point temperature T^∗ in Sr3Ru2O7 as a function of hydrostatic pressure with H//ab has been studied using the ac susceptibility. It is found that T^∗ falls monotonically with increasing pressure, going to zero at Pc = 14±0.3 kbar. One sign of the nematic phase observed in the field-angle tuning, i.e. T^∗ rises as the novel phase emerges, has not been seen in our study. However, we see a slope change in T^∗ vs P at ∼12.8 kbar, and a shoulder at the upper field side of the peak in χ′ from ∼12.8 kbar to ∼16.7 kbar. These new features indicate that some new physics sets in near the pressure-tuned QCEP.

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Thesis (M.Phil.)--Hong Kong University of Science and Technology, 2007. / Includes bibliographical references (leaves 43-45). Also available in electronic version.

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Thesis advisor: Kevin S. Bedell / One of the many achievements of renowned physicist L.D. Landau was the formulation of Fermi Liquid Theory (FLT). Originally debuted in the 1950s, FLT has seen abundant success in understanding degenerate Fermi systems and is still used today when trying to understand the physics of a new interacting Fermi system. Of its many advantages, FLT excels in explaining why interacting Fermi systems behave like their non-interacting counterparts, and understanding transport phenomena without cumbersome and confusing mathematics. In this work, FLT is applied to systems whose low energy excitations obey the massless Dirac equation; i.e. the energy dispersion is linear in momentum, ε α ρ, as opposed to the normal quadratic, ε α ρ². Such behavior is seen in numerous, seemingly unrelated, materials including graphene, high T[subscript]c superconductors, Weyl semimetals, etc. While each of these materials possesses its own unique properties, it is their low energy behavior that provides the justification for their grouping into one family of materials called Dirac materials (DM). As will be shown, the linear spectrum and massless behavior leads to profound differences from the normal Fermi liquid behavior in both equilibrium and transport phenomena. For example, with mass having no meaning, we see the usual effective mass relation from FLT being replaced by an effective velocity ratio. Additionally, as FLT in d=2 has been poorly studied in the past, and since the most famous DM in graphene is a d=2 system, a thorough analysis of FLT in d=2 is presented. This reduced dimensionality leads to substantial differences including undamped collective modes and altered quasiparticle lifetime. In chapter 3, we apply the Virial theorem to DM and obtain an expression for the total average ground state energy $E=\frac{B}{r_s}$ where $B$ is a constant independent of density and $r_s$ is a dimensionless parameter related to the density of the system: the interparticle spacing $r$ is related to $r_s$ through $r=ar_s$ where $a$ is a characterstic length of the system (for example, in graphene, $a=1.42$ \AA). The expression derived for $E$ is unusual in that it's typically impossible to obtain a closed form for the energy with all interactions included. Additionally, the result allows for easy calculation of various thermodynamic quantities such as the compressibility and chemical potential. From there, we use the Fermi liquid results from the previous chapter and obtain an expression for $B$ in terms of constants and Fermi liquid parameters $F_0^s$ and $F_1^s$. When combined with experimental results for the compressibility, we find that the Fermi liquid parameters are density independent implying a unitary like behavior for DM. In chapter 4, we discuss the alleged universal KSS lower bound in DM. The bound, $\frac{\eta}{s}\geq\frac{\hbar}{4\pi k_B}$, was derived from high energy/string theory considerations and was conjectured to be obeyed by all quantum liquids regardless of density. The bound provides information on the interactions in the quantum liquid being studied and equality indicates a nearly perfect quantum fluid. Since its birth, the bound has been highly studied in various systems, mathematically broken, and poorly experimented on due to the difficult nature of measuring viscosity. First, we provide the first physical example of violation by showing $\frac{\eta}{s}\rightarrow 0$ as $T\rightarrow T_c$ in a unitary Fermi gas. Next, we determine the bound in DM in d=2,3 and show unusual behavior that isn't seen when the bound is calculated for normal Fermi systems. Finally we conclude in chapter 5 and discuss the outlook and other avenues to explore in DM. Specifically, it must be pointed out that the physics of what happens near charge neutrality in DM is still poorly understood. Our work in understanding the Fermi liquid state in DM is necessary in understanding DM as a whole. Such a task is crucial when we consider the potential in DM, experimentally, technologically, and purely for our understanding. / Thesis (PhD) — Boston College, 2020. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.

Thesis advisor: Kevin Bedell / Over 20 years ago, Blagoev et. al. predicted an s-wave pairing instability in a ferromagnetic Fermi liquid (FFL) as a consequence of spin fluctuations [5]. Shortly after, it was discovered that, when magnetic interactions in the ferromagnetic superconductor UGe2 dominate, quasiparticles with parallel spin form pairs in odd-parity orbitals; i.e., a form of spin-triplet p-wave superconductivity emerges, in contrast to Blagoev et. al.'s prediction [6]. In this work, we return to this issue by introducing the effects of a gapped amplitude (or "Higgs") mode on the vertex corrections and subsequent form of Cooper pairing. As the Higgs mode only propagates in the presence of a finite spin current, such an amplitude mode results in strong momentum-dependence in the many-body vertex. This results in the emergence of an unconventional form of superconductivity mediated by unconventional low-energy modes in a weak itinerant ferromagnet. / Thesis (BS) — Boston College, 2021. / Submitted to: Boston College. College of Arts and Sciences. / Discipline: Scholar of the College. / Discipline: Physics. / Discipline: Mathematics.