In this thesis, we study the low-energy effective theory for the antiferromagnetic quantum critical metal in two dimensions. The theory has been the subject of intense study for more than twenty years, due to the novel physics of non-Fermi liquid metals and its potential relevance to high-temperature superconductors and heavy-fermion compounds. In the first part of the thesis, we present the perturbative study of the theory in 3 minus epsilon space dimensions by extending the earlier one-loop analysis to higher-loop orders. We show that the expansion is not organized by the standard loop expansion, and a two-loop graph becomes as important as one-loop graphs even in the small epsilon limit due to an infrared singularity caused by an emergent quasilocality. This qualitatively changes the nature of the infrared fixed point, and the epsilon expansion is controlled only after the two-loop effect is taken into account. Furthermore, we show that a ratio between velocities emerges as a small parameter, which suppresses a large class of diagrams. We show that the critical exponents do not receive quantum corrections beyond the linear order in epsilon in the limit that the ratio of velocities vanishes. In the second part of the thesis, we present a nonperturbative solution to the theory in two dimensions based on an ansatz that is inspired by the perturbative analysis. Being a strongly coupled theory, it can still be solved reliably in the low-energy limit as quantum fluctuations are organized by the ratio of velocities that dynamically flows to zero in the low-energy limit. We predict the exact critical exponents that govern the universal scaling of physical observables at low temperatures. / Thesis / Doctor of Philosophy (PhD)

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.

The formation of new phases close to itinerant electron quantum critical points has been observed experimentally in many compounds. We present a unified analytical model that explains the emergence of new types of phases around itinerant ferromagnetic quantum critical points. The central idea of our analysis is that certain deformations of the Fermi surface enhance the phase-space available for low-energy quantum fluctuations and so self-consistently lower the free energy. Using this quantum order-by-disorder mechanism, we find instabilities towards the formation of a spiral ferromagnet and spin-nematic phase close to an itinerant ferromagnetic quantum critical point. Further, we employ the quantum order-by-disorder mechanism to describe the partially ordered phase of MnSi. Using the simplest model of a Stoner-like helimagnetic transition, we show that quantum fluctuations naturally lead to the formation of an unusual phase near to the putative quantum critical point that shares many of the observed features of the partially ordered phase in MnSi. In particular, we predict an angular dependence of neutron scattering that is in good agreement with neutron-scattering data.

Magnetism of the rare earth intermetallics present some of the most important challenges for understanding correlated electron systems . In this thesis I distil this immense challenge, to understanding the unusual magnetic properties of the rare earth intermetallic PrPtAl. At first glance, PrPtAl appears to be a typical local f moment system, where the electronic states of Pr3+ are composed of nine singlet states, split by the crystal electric field for the J = 4 spin-orbit state in low crystal symmetry (orthorhombic, Pnma). The absence of a magnetic ground state would naively lead us to expect PrPtAl to be a simple paramagnet, but the results from this thesis show that the material is more complex, ordering magnetically at 5.7 K in spite of its singlet ground state. This thesis investigates the emergence of magnetic order in PrPtAl. For this purpose, the properties of PrPtAl were measured using high quality single crystals grown using the Czochralski technique. These crystals were used to measure: bulk properties at the Centre for Science at Extreme Conditions (CSEC, University of Edinburgh) and to perform neutron and x-ray magnetic scattering experiments at central facilities within Europe (ISIS, ESRF) and North America (NCNR). The results of this thesis conclusively show that PrPtAl does not directly realise ferromagnetism, but initially orders into two modulated magnetic states between 5.7-5.2 K and 5.2-4.7 K. These states cannot be explained using a simple local moment picture, but appear to be driven by a complex interaction between local moments and conduction electrons, in a possible quantum order-by-disorder type mechanism.

No description available.

No description available.

PhD Thesis / The superconductivity in heavy-fermion compounds, iron pnictides and cuprates has been intensively studied for over thirty years. Amongst some of these materials, the common denominator is the presence of strong antiferromagnetic fluctuations in their normal state, signaling an underlying quantum phase transition between a paramagnetic metal and a metal with antiferromagnetic long-range order. Although the quantum critical point is experimentally inaccessible due to the presence of superconducting order, it determines the physical properties of the normal state of the metal in a wide range of temperatures. In this thesis we study the low-energy theory for the critical metallic state that arises at the aforementioned quantum critical point. We present a nonperturbative study of the theory in spatial dimensions between two and three. We pay special attention to two dimensions where we show that our physical predictions are in qualitative agreement with experiments in electron-doped cuprates. We further develop a field theoretic functional renormalization group scheme that is analytically tractable. It provides a general framework to study the low-energy theory of metallic states with or without a quasiparticle description. Within this formalism we characterize the single-particle properties of the antiferromagnetic quantum critical metal. This allows one to study the superconducting instability triggered by critical antiferromagnetic quantum fluctuations quantitatively. / Thesis / Doctor of Science (PhD)

Second-order phase transitions involve critical fluctuations just below and above the transition temperature. Macroscopically, they manifest in the power-law behaviour of many physical properties such as the susceptibility and the specific heat. The power-laws are predicted to be universal, i.e. the same exponents are expected for a certain class of transitions irrespective of the microscopic details of the system. The underlying commonality of such transitions is the divergence of the correlation length ξ and the correlation time ξ_τ of the critical fluctuations at the transition temperature. Both ξ and ξ_τ can be directly observed by neutron scattering experiments, making them an ideal tool for the study of critical phenomena. At classical phase transitions, the critical fluctuations will be thermal in nature. However, if a second-order transition occurs at T = 0, thermal fluctuations are frozen, and the transition is driven by quantum fluctuations instead. This is called a quantum critical point. The quantum nature of the fluctuations influences observable properties, also at finite temperatures, and causes unusual behaviour in the vicinity of the quantum critical point or the existence of exotic phases, e.g. unconventional superconductivity. Heavy-fermion compounds are a class of materials that is well suited for the study of quantum criticality. They frequently show second-order transitions into a magnetically ordered state at very low temperatures, which can easily be tuned to T = 0 by the application of pressure, magnetic fields or element substitution. In this thesis, fluctuations near a quantum critical point are investigated for three heavy-fermion systems. CeCu2Si2 shows unconventional superconductivity close to an antiferromagnetic quantum critical point. Results from single-crystal neutron spectroscopy and thermodynamic measurements are discussed and some details are also given about the synthesis of large single crystals. The focus of the study is the comparison of the inelastic response of magnetic and superconducting samples, which are found to be very similar for ΔE > 0.2 meV. CePdAl has an antiferromagnetic state with partial magnetic frustration. The ordering temperature can be suppressed by Ni substitution towards a quantum critical point. Single-crystal neutron diffraction experiments of three members of the substitution series were analysed. They revealed several unusual effects of the frustrated state in the pure sample, and show that magnetic order and frustration persist in the substituted samples. YbNi4P2 is a rare example of a compound with ferromagnetic quantum criticality, which has only been studied in the last few years. The aim of the powder neutron spectroscopy experiments presented here was to obtain an overview of the relevant energy scales, i.e. the crystal electric field, local magnetic fluctuations and ferromagnetic fluctuations. Simulations using the program McPhase were performed for a thorough understanding of the crystal electric field.

In this thesis, we study persistent currents and quantum critical phenomena in the systems of mesoscopic physics. As an introduction in Chapter 1 we familiarize the reader with the area of mesoscopic physics. We explain how mesoscopic systems are different from quantum systems of single atoms and molecules and bulk systems with an Avogadro number of elements. We also describe some important mesoscopic phenomena. One of the mathematical tools that we extensively use in our studies is Random Matrix Theorty. This theory is not a part of standard physics courses and for educational purposes we provide the basics of Random Matrix Theory in Chapter 2. In Chapter 3 we study the persistent current of noninteracting electrons in quantum billiards. We consider simply connected chaotic Robnik-Berry quantum billiard and its annular analog. The electrons move in the presence of a point-like magnetic flux at the center of the billiard. For the simply connected billiard, we find a large diamagnetic contribution to the persistent current at small flux, which is independent of the flux and is proportional to the number of electrons (or equivalently the density since we keep the area fixed). The size of this diamagnetic contribution is much larger than the previously studied mesoscopic fluctuations in the persistent current in the simply connected billiard. This behavior of persistent current can ultimately be traced to the response of the angular-momentum l = 0 levels (neglected in semiclassical expansions) on the unit disk to a point-like flux at its center. We observe the same behavior for the annular billiard when the inner radius is much smaller than the outer one. We also find that the usual fluctuating persistent current and Anderson-like localization due to boundary scattering are seen when the annulus tends to a one-dimensional ring. We explore the conditions for the observability of this phenomenon. In Chapter 4 we study quantum critical phenomena in a system of two coupled quantum dots connected by a hopping bridge. Both the dots and connecting region are assumed to be in universal Random Matrix crossover regimes between Gaussian orthogonal and unitary ensembles (defined in Chapter 2). We exploit a diagrammatic approach appropriate for energy separations much larger than the level spacing, to obtain the ensemble-averaged one- and two-particle Greens functions. We find that two main components of the twoparticle Green’s function (diffuson and Cooperon) can be described by separate scaling functions. We then use this information to investigate a model interacting system in which one dot has an attractive s-wave reduced Bardeen-Cooper-Schrieffer interaction, while the other is noninteracting but subject to an orbital magnetic field. We find that the critical temperature TC of the mean-field transition into the superconducting state in the first dot is non-monotonic in the flux through the second dot in a certain regime of interdot coupling. Likewise, the fluctuation magnetization above the critical temperature is also non-monotonic in this regime, can be either diamagnetic or paramagnetic, and can be deduced from the Cooperon scaling function. We end this thesis with conclusion in Chapter 5.