The interplay of partially filled d- or f-electron shells with conduction-band electrons is a key ingredient in new rare-earth transition-metal compounds for the emergence of unusual electronic and magnetic properties. Among which unconventional superconductivity is one of the most studied. Despite many years of intensive experimental investigations and plenty promising theoretical models, unconventional superconductivity still remains hotly debated a very rich topic. One of the fundamental unsolved problems for condensed-matter physicists is the mechanism that causes the electrons to form anisotropic superconductivity. Since electrons in the vicinity of the Fermi level are primarily responsible for superconductivity, in order to better understand the mechanism giving rise to this phenomenon and the origin of complex forces between correlated electrons, knowledge of the Fermi surface and band selective effective mass is essential. Of the many techniques used to study electronic band-structure properties, measurements of quantum oscillations in the magnetization, so-called de Haas-van Alphen (dHvA) effect, in combination with band-structure calculations is the traditional proven tool for studying Fermi-surface topology and quasiparticle effective mass. In the present work, electronic structure and Fermi-surface properties of Ybsubstituted heavy fermion superconductor CeCoIn5 and iron based ternary phosphides LaFe2P2 and CeFe2P2 have been investigated by means of dHvA measurements. For these measurements, capacitive cantilever-torque magnetometry was utilized. In Ce1−xYbxCoIn5, the evolution of the Fermi surface and effective mass was studied as a function of Yb concentration. The observed topology change is consistent with what is expected from the band-structure calculations. For a small Yb concentration, x = 0.1, the band-structure topology and the effective masses remain nearly unchanged compared to CeCoIn5. This contrasts clearly modified Fermi surfaces and light, almost unrenormalized effective masses for x = 0.2 and above. For LaFe2P2 and CeFe2P2, the obtained effective masses are light. Good agreement between the calculated and measured dHvA frequencies was identified only for LaFe2P2. However, for CeFe2P2 strong disagreement was observed. Moreover, different CeFe2P2 single crystals reveal different experimental results. In order to reconcile the results of the dHvA measurements and density-functional-theory calculations more work is necessary.

In this PhD thesis, we study the interplay between symmetry-breaking order and quantum-disordered phases in the milieu of frustrated quantum magnets, and further show how the excitation process of long-wavelength (semi-)classical modes in spin-orbit coupled antiferromagnets crucially depends on the nature and interactions of the underlying quantum quasiparticles. First, we focus on Kitaev's exactly solvable model for a Z2 spin liquid as a building block for constructing novel phases of matter, utilizing Majorana mean-field theory (MMFT) to map out phase diagrams and study occurring phases. In the Kitaev Kondo lattice, conduction electrons couple via a Kondo interaction to the local moments in the Kitaev model. We find at small Kondo couplings a fractionalized Fermi liquid (FL*) phase, a stable non-Fermi liquid where conventional electronic quasiparticles coexist with the deconfined excitations of the spin liquid. The transition between FL* and a conventional Fermi liquid is masked by an exotic (confining) superconducting phase which exhibits nematic triplet pairing, which we argue to be mediated by the Majorana fermions in the Kitaev spin liquid. We moreover study bilayer Kitaev models, where two Kitaev honeycomb spin liquids are coupled via an antiferromagnetic Heisenberg interaction. Varying interlayer coupling and Kitaev coupling anisotropy, we find both direct transitions from the spin liquid to a trivial dimer paramagnet as well as intermediate 'macrospin' phases, which can be studied by mappings to effective transverse-field Ising models. Further, we find a novel interlayer coherent pi-flux phase. Second, we consider the stuffed honeycomb Heisenberg antiferromagnet, where recent numerical studies suggest the coexistence of collinear Néel order and a correlated paramagnet, dubbed 'partial quantum disorder'. We elucidate the mechanism which drives the disorder in this model by perturbatively integrating out magnons to derive an effective model for the disordered sublattice. This effective model is close to a transition between two competing ground states, and we conjecture that strong fluctuations associated with this transition lead to disorder. Third, we study the generation of coherent low-energy magnons using ultrafast laser pulses in the spin-orbit coupled antiferromagnet Sr2IrO4, inspired by recent pump-probe experiments. While the relaxation dynamics of the system at long time scales can be well described semi-classically, the ultrafast excitation process is inherently non-classical. Using symmetry analysis to write down the most general coupling between electric field and spin operators, we subsequently integrate out high-energy spin fluctuations to derive induced effective fields which act to excite the low-energy magnon, constituting a generalized 'inverse Faraday effect'. Our theory reveals a tight relationship between induced fields and the two-magnon density of states.:1 Introduction 1.1 Frustrated antiferromagnets 1.2 Quantum spin liquids 1.3 Fractionalization and topological order 1.4 Spin-orbit coupling 1.5 Outline I Novel phases by building on Kitaev’s honeycomb model 2 Kitaev honeycomb spin liquid 2.1 Microscopic spin model and constants of motion 2.2 Majorana representation of spin algebra 2.3 Exact solution 2.3.1 Ground state 2.3.2 Correlations and dynamics 2.3.3 Thermodynamic properties 2.4 Z2 gauge structure 2.5 Toric code 2.6 Topological order 2.6.1 Superselection sectors and ground-state degeneracy 2.6.2 Topological entanglement entropy 2.6.3 Symmetry-enriched and symmetry-protected topological phases 3 Mean-field theory 3.1 Generalized spin representations 3.1.1 Parton constructions 3.1.2 SO(4) Majorana representation 3.2 Projective symmetry groups 3.3 Mean-field solution of the Kitaevmodel 3.4 Comparisonwithexactsolution 3.4.1 Spectral properties 3.4.2 Correlation functions 3.4.3 Thermodynamic properties 3.5 Generalized decoupling 3.6 Comparison to previous Abrikosov fermion mean-field theories of the Kitaev model 3.7 Discussion 4 Fractionalized Fermi liquids and exotic superconductivity in the Kitaev Kondo lattice 4.1 Metals with frustration 4.2 Local-moment formation and Kondo effect 4.2.1 Single Kondo impurity 4.2.2 Kondo lattices and heavy Fermi liquids 4.3 Fractionalized Fermi liquids 4.4 Construction of the Kitaev Kondo lattice 4.4.1 Hamiltonian 4.4.2 Symmetries 4.5 Mean-field decoupling of Kondo interaction 4.5.1 Solution of self-consistency conditions 4.6 Overview of mean-field phases 4.7 Fractionalized Fermi liquid 4.7.1 Results from mean-field theory 4.7.2 Perturbation theory beyond mean-field theory 4.8 Heavy Fermi liquid 4.9 Superconducting phases 4.9.1 Spontaneously broken U(1) phase rotation symmetry 4.9.2 Excitation spectrum and nematicity 4.9.3 Topological triviality 4.9.4 Group-theoretical classification 4.9.5 Pairing glue 4.10 Comparison with a subsequent study 4.11 Discussion and outlook 5 Bilayer Kitaev models 5.1 Model and stacking geometries 5.1.1 Hamiltonian 5.1.2 Symmetries and conserved quantities 5.2 Previous results 5.3 Mean-field decoupling and phase diagrams 5.3.1 AA stacking 5.3.2 AB stacking 5.3.3 σAC stacking 5.3.4 σ ̄AC stacking 5.4 Quantum phase transition in the AA stacking 5.4.1 Perturbative analysis 5.5 Phase transition in the σAC stacking 5.6 Macro-spin phases 5.6.1 KSL-MAC transition: Effective model for Kitaev dimers 5.6.2 DIM-MAC transition: Effective theory for triplon condensation 5.6.3 Macro-spin interactions and series expansion results 5.6.4 Antiferromagnet in the AB stacking 5.7 Stability of KSL and the interlayer-coherent π-flux phase 5.7.1 Perturbative stability of the Kitaev spin liquid 5.7.2 Spontaneous interlayer coherence near the isotropic point 5.8 Summary and discussion II Partial quantum disorder in the stuffed honeycomb lattice 6 Partial quantum disorder in the stuffed honeycomb lattice 6.1 Definition of the stuffed honeycomb Heisenberg antiferromagnet 6.2 Previous numerical results 6.3 Derivation of an effective model 6.3.1 Spin-wave theory for the honeycomb magnons 6.3.2 Magnon-central spin vertices 6.3.3 Perturbation theory 6.3.4 Instantaneous approximation 6.3.5 Truncation of couplings 6.3.6 Single-ion anisotropy 6.3.7 Discussion of most dominant interactions 6.4 Analysis of effective model 6.4.1 Classical ground states 6.4.2 Stability of classical ground states in linear spin-wave theory 6.4.3 Minimal model for incommensurate phase 6.4.4 Discussion of frustration mechanism in the effective model 6.5 Partial quantum disorder beyond the effectivemodel 6.5.1 Competition between PD and the (semi-)classical canted state 6.5.2 Topological aspects 6.5.3 Experimental signatures 6.6 Discussion 6.6.1 Directions for further numerical studies 6.6.2 Experimental prospects III Optical excitation of coherent magnons 7 Ultrafast optical excitation of magnons in Sr2IrO4 7.1 Pump-probe experiments 7.2 Previous approaches to the inverse Faraday effect and theory goals 7.3 Sr2IrO4 as a spin-orbit driven Mott insulator 7.4 Spin model for basal planes in Sr2IrO4 7.4.1 Symmetry analysis 7.4.2 Classical ground state and linear spin-wave theory 7.4.3 Mechanism for in-plane anisotropy 7.5 Pump-induced dynamics 7.5.1 Coupling to the electric field: Symmetry analysis 7.5.2 Keldysh path integral 7.5.3 Low-energy dynamics 7.5.4 Driven low-energy dynamics 7.6 Derivation of the induced fields 7.6.1 Perturbation theory 7.6.2 Evaluation of loop diagram 7.6.3 Analytical momentum integration in the continuum limit 7.6.4 Numerical evaluation of effective fields 7.7 Analysis of induced fields 7.7.1 Polarization and angular dependence 7.7.2 Two-magnon spectral features 7.8 Applications to experiment 7.8.1 Predictions for experiment 7.8.2 Magnetoelectrical couplings 7.9 Discussion and outlook 8 Conclusion and outlook 8.1 Summary 8.2 Outlook IV Appendices A Path integral methods B Spin-wave theory B.1 Holstein-Primakoff bosons B.2 Linear spin-wave theory B.2.1 Diagonalization via Bogoliubov transformation B.2.2 Applicability of linear approximation B.3 Magnon-magnon interactions B.3.1 Dyson's equation and 1/S consistency B.3.2 Self-energy from quartic interactions in collinear states on bipartite lattices C Details on the SO(4) Majorana mean-field theory C.1 SO(4) Matrix representation of SU(2) subalgebras C.2 Generalized SO(4) Majorana mean-field theory for a Heisenberg dimer (Chapter 3) C.3 Dimerization of SO(4) Majorana mean-field for the Kitaev model (Chapter3) C.4 Mean-field Hamiltonian in the Kitaev Kondo lattice (Chapter 4) C.5 Example solutions in the superconducting phase for symmetry analysis (Chapter4) D Linear spin-wave theory for macrospin phase in the bilayer Kitaev model (Chapter 5) D.1 Spin-wave Hamiltonian and Bogoliubov rotation D.2 Results and discussion E Extrapolation of the effective couplings for the staggered field h -> 0 (Chapter 6) E.1 xy interaction E.1.1 Leadingorder ~ S0 E.1.2 Subleadingorder ~ S^(−1) E.2 z-Ising interaction F Light-induced fields by analytical integration (Chapter 7) F.1 Method F.2 Results Bibliography

We demonstrate a remarkable property of metallic Fermi liquids: the transverse conductivity assumes a universal value in the quasi-static (ω → 0) limit for wavevectors q in the regime l −1 mfp q pF, where lmfp is the mean free path and pF is the Fermi momentum. This value is (e2/h)RFS/q in two dimensions (2D), where RFS measures the local radius of curvature of the Fermi surface (FS) in momentum space. Even more surprisingly, we find that U(1) spin liquids with a spinon FS have the same universal transverse conductivity. This means such spin liquids behave effectively as metals in this regime, even though they appear insulating in standard transport experiments. Moreover, we show that transverse current fluctuations result in a universal low-frequency magnetic noise that can be directly probed by a spin qubit, such as a nitrogen-vacancy (NV) center in diamond, placed at a distance z above of the 2D metal or spin liquid. Specifically the magnetic noise is given by CωPFS/z, where PFS is the perimeter of the FS in momentum space and C is a combination of fundamental constants of nature. Therefore these observables are controlled purely by the geometry of the FS and are independent of kinematic details of the quasi-particles, such as their effective mass and interactions. This behavior can be used as a new technique to measure the size of the FS of metals and as a smoking gun probe to pinpoint the presence of the elusive spinon FS in two-dimensional systems. We estimate that this universal regime is within reach of current NV center spectroscopic techniques for several spinon FS candidate materials.

Thesis: Elec. E., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 1981 / Includes bibliographical references. / by Mansour Shayegan. / Elec. E. / Elec. E. Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science

Highly correlated electron materials are systems in which many new states of matter can emerge. A particular situation which favours the formation of exotic phases of the electron liquid in complex materials is that where a quantum critical point (QCP) is present in the phase diagram. Neighbouring regions in parameter space reveal unusual physical properties, described as non-Fermi liquid behaviour. One of the important problems in quantum criticality is to find out how the Fermi surface (FS) of a material evolves near a QCP. The traditional method for studying the FS of materials is the de Haas van Alphen effect (dHvA). A quantum critical end point (QCEP) has been reported in the highly correlated metal Sr₃Ru₂O₇, which is tuned using a magnetic field high enough to perform the dHvA experiment. It moreover features a new emergent phase in the vicinity of the QCEP, a nematic type of electron ordering. The subject of this thesis is the study of the FS of Sr₃Ru₂O₇ using the dHvA effect. Three aspects were explored. The first was the determination of the FS at fields both above and below that where the QCEP arises. The second was the search for quantum oscillations inside the nematic phase. The third was a reinvestigation of the behaviour of the quasiparticle effective masses near the FS. In collaboration with angle resolved photoemission spectroscopy experimentalists, a complete robust model for the FS of Sr₃Ru₂O₇ at zero fields was determined. Moreover, the new measurements of the quasiparticle masses revealed that no mass enhancements exist anywhere around the QCEP, in contradiction with previous specific heat data and measurements of the A coefficient of the power law of the resistivity. Finally, we report dHvA oscillations inside the nematic phase, and the temperature dependence of their amplitude suggests strongly that the carriers consist of Landau quasiparticles.

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A new approach is developed for evaluating the mixing properties of binary solutions at high pressure. This involves solving Poisson's equation throughout three-dimensional cubic lattices, consistent with Thomas-Fermi-Dirac (TFD) theory. Zero temperature calculations are carried out for a variety of compositions and crystal structures in 3 pressure groups relevant to Jovian planetary interiors. Pseudopotentials based on the two-component-plasma model (with a uniform electron background) are fitted to the solid-state results, and are then used in liquid-state calculations using hard-sphere perturbation theory. TFD results for H-He solutions find critical temperatures (above which all compositions are soluble) to be ∿ 0, 500, and 1500°K at pressures of 10, 100, and 1000 Mbar, respectively. These temperatures are much lower than those obtained using free electron perturbation theory, where T(crit) ∿ 10,000°K at 10 Mbar. Thus, unlike the perturbation theory results, the TFD results predict that helium should be soluble in metallic hydrogen in the deep interiors of both Jupiter and Saturn, and our calculations give an indication of the degree of model-dependence in computing high pressure mixing properties. In addition, TFD calculations for H-C and H-O solutions find phase separation temperatures to be≲ 10⁴ °K for pressures ≲ 10³ Mbar. These temperatures are considerably lower than those found assuming a uniform electron distribution (where T(crit) ≳ 10⁵ °K), and suggest that H-C and H-O solutions should also be miscible in the metallic zones of Jupiter and Saturn.

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