Magnetotransport of dirty-limit van Hove singularity quasiparticles

Tuning of electronic density-of-states singularities is a common route to unconventional metal physics. Conceptually, van Hove singularities are realized only in clean two-dimensional systems. Little attention has therefore been given to the disordered (dirty) limit. Here, we provide a magnetotransport study of the dirty metamagnetic system calcium-doped strontium ruthenate. Fermi liquid properties persist across the metamagnetic transition, but with an unusually strong variation of the Kadowaki-Woods ratio. This is revealed by a strong decoupling of inelastic electron scattering and electronic mass inferred from density-of-state probes. We discuss this Fermi liquid behavior in terms of a magnetic field tunable van Hove singularity in the presence of disorder. More generally, we show how dimensionality and disorder control the fate of transport properties across metamagnetic transitions

Optical conductivity of overdoped cuprates from ab-initio out-of-plane impurity potentials

Dopant impurity potentials determined by ab-initio supercell DFT calculations are used to calculate the optical conductivity of overdoped LSCO and Tl-2201 in the superconducting and normal states. Vertex corrections are included, to account for the effect of forward scattering on two-particle properties. This approach was previously shown to provide good, semiquantitative agreement with measurements of superfluid density in LSCO. Here we compare calculations of conductivity with measurements of THz conductivity on LSCO using identical impurity, band, and correlation parameters, and find similarly good correspondence with experiment. In the process, we delineate the impact of the different disorder mechanisms on single-particle and transport relaxation processes. In particular, we reveal the critical role of apical oxygen vacancies in transport scattering and show that transport relaxation rates in LSCO are significantly reduced when apical oxygen vacancies are annealed out. These considerations are shown to be crucial for understanding the variability of experimental results on overdoped LSCO in samples of nominally identical doping but different types. Finally, we give predictions for Tl-2201 THz conductivity experiments.Comment: 12 pages, 7 figure

Effect of realistic out-of-plane dopant potentials on the superfluid density of overdoped cuprates

Recent experimental papers on hole-doped overdoped cuprates have argued that a series of observations showing unexpected behavior in the superconducting state imply the breakdown of the quasiparticle-based Landau-BCS paradigm in that doping range. In contrast, some of the present authors have argued that a phenomenological "dirty $d$-wave" theoretical analysis explains essentially all aspects of thermodynamic and transport properties in the superconducting state, provided the unusual effects of weak, out-of-plane dopant impurities are properly accounted for. Here we attempt to place this theory on a more quantitative basis by performing $\textit{ab-initio}$ calculations of dopant impurity potentials for LSCO and Tl-2201. These potentials are more complex than the pointlike impurity models considered previously, and require calculation of forward scattering corrections to transport properties. Including realistic, ARPES-derived bandstructures, Fermi liquid renormalizations, and vertex corrections, we show that the theory can explain semiquantitatively the unusual superfluid density measurements of the two most studied overdoped materials.Comment: 19 page, 13 figure

비등방, 다층구조 물질에 적용가능한 준고전적인 볼츠만 수송 이론 및 디락 물질에서의 응용

학위논문(박사) -- 서울대학교대학원 : 자연과학대학 물리·천문학부(물리학전공), 2021.8. 민홍기.Topologiacal semimetals are novel materials that exhibit many fascinating properties, and they are at the center of the spotlight in the condensed matter physics studies, as their electronic structure near the band touching point gives rise to the unique quasiparticles that does not follow the Drude model of free electrons. Furthermore, their topological nature assures that such quasiparticles are robust against small perturbations, making them great platforms to test various physical behaviors of those non-conventional excitations. With that motivations, this thesis is devoted to studying the semiclassical electronic transport and electron-mediated magnetism of Dirac materials. First, we derive the semiclassical anisotropic multi-band Boltzmann transport equation that was extensively used throughout the thesis. Then we turn to investigating the transport properties of multi-Weyl semimetals and the few-layer black phosphorus in various phases using anisotropic multi-band Boltzmann transport equation. Multi-Weyl semimetals are topological semimetals with anisotropic band dispersion (linear on one axis; nonlinear on the other two axes) and their chiral charge is larger than one. Black phosphorus is normally a semiconductor, but recent studies have shown that its band gap can be tuned to show multiple phases (insulator phase, semi-Dirac transition point, and Dirac phase). We studied these materials using anisotropic multi-band Boltzmann transport theory and discovered their characteristic chiral charge, band dispersion, and band gap sign signature on the carrier density-dependent and the temperature-dependent conductivity calculations. We also examine the magnetic field effect on the semiclassical transport, as the external magnetic field couples with the Berry curvature, it gives rise to the anisotropy when the system is isotropic. Finally, we look into the Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction in three-dimensional (3D) isotropic chiral semimetals to study the power-law effect on the charge carrier spin-mediated magnetism in 3D semimetals. We calculated the transition temperature and temperature- and power-law-dependent static susceptibilities, and discovered that the magnetic ordering of dilute magnetic impurities on 3D chiral semimetals are always ferromagnetic.위상적 준금속은 많은 흥미로운 성질을 가진 새로운 물질으로서, 최근까지 응집물질물리학 연구의 화제의 중심이 되어 왔다. 이는 전자띠가 만나는 지점에서 나타나는 준입자 활성이 드루드 자유전자 모델을 따르지 않기 때문이기도 하다. 그리고 위상적 준금속은 위상적인 성질 덕분에 그러한 준입자 활성이 외부 섭동에 대하여 안정적이기 때문에 여기서 나오는 일반적이지 않은 활성에 대한 다양한 물리적 현상을 시험해보기 위한 훌륭한 시험대이기도 하다. 이러한 동기를 가지고, 해당 학위논문은 디락 물질에서 준고전적인 전자 수송 이론 및 전자 스핀에 의하여 매개되는 자화 현상에 대해 다룬다. 먼저 우리는 본 학위논문 전반에 걸쳐 사용되는 비등방적이고 다층전자띠 물질에 적용가능한 준고전적인 볼츠만 수송 이론을 유도한다. 그런 다음 우리는 다중 바일 준금속과 다층 흑린의 전자수송현상을 앞서 유도한 비등방, 다층전자띠 물질에 적용가능한 볼츠만 수송 이론을 통하여 연구한다. 다중 바일 준금속은 비등방적인 전자띠 구조를 가진 위상적 준금속으로서 (한 쪽 방향으로는 선형, 나머지 방향으로는 비선형적인 관계를 가진다) 카이랄 전하 값이 1보다 큰 물질이다. 흑린은 통상적으로는 반도체 물질이나, 최근 연구로 전자띠 간격을 자유롭게 조절 가능하며 이에 따른 여러 가지 상을 가질 수 있음이 밝혀지게 되었다 (부도체 상, 반디락 상, 디락 상). 우리는 이러한 물질들을 비등방적, 다층띠 물질에 적용가능한 볼츠만 수송 이론을 통하여 연구하였으며, 각 물질들의 특징적인 카이랄 전하값, 전자띠 구조, 그리고 전자띠 간격의 부호에 따라서 전하 밀도 및 온도에 따른 전기 전도도의 변화를 계산하였다. 우리는 또한 자기장이 준고전적인 전자 수송에 미치는 영향에 대해서도 연구하였다. 즉 외부 자기장이 물질의 베리곡률과 결합되어 발생하는 비등방성이 전자 수송에 미치는 영향을 조사하였다. 마지막으로, 우리는 등방적인 3차원 카이랄 준금속 예시 물질에서 루더만-키텔-카즈야-요시다 (RKKY) 상호작용을 연구하였다. 우리는 성기게 배치된 자기적 불순물들이 전자의 스핀에 의하여 매개되는 자화 현상및 자화 감수성, 임계 온도를 멱수에 대하여 계산하였고, 멱법칙에 관계없이 해당 물질은 강자성을 띤다는 사실을 발견하였다.Chapter 1 Introduction 1 Chapter 2 Semiclassical Boltzmann transport theory 5 2.1 Boltzmann transport theory for isotropic, single-band non-magnetic systems 5 2.2 Boltzmann transport theory for anisotropic, multi-band non-magnetic systems 7 Chapter 3 Transport properties of multi-Weyl semimetals 9 3.1 Introduction 9 3.2 Model 10 3.2.1 Boltzmann transport theory in anisotropic systems 11 3.3 Density dependence of dc conductivity 13 3.4 Temperature dependence of dc conductivity 15 3.5 Discussion 18 Chapter 4 Transport properties of few-layer black phosphorus in various phases 24 4.1 Introduction 24 4.2 Methods 26 4.2.1 Model 26 4.2.2 Boltzmann transport theory in anisotropic multiband systems 29 4.3 Density dependence of dc conductivity 31 4.3.1 Semi-Dirac transition point 32 4.3.2 Insulator phase 33 4.3.3 Dirac semimetal phase 34 4.4 Temperature dependence of dc conductivity 35 4.4.1 Semi-Dirac transition point 36 4.4.2 Insulator phase 38 4.4.3 Dirac semimetal phase 39 4.5 Discussion and conclusion 40 Chapter 5 Semiclassical Boltzmann magnetotransport theory in anisotropic systems with a nonvanishing Berry curvature 51 5.1 Introduction 51 5.2 Magnetotransport equation in electron gas systems 54 5.3 Magnetotransport equation in anisotropic systems with a nonvanishing Berry curvature 57 5.4 Magnetoconductivity 61 5.5 Discussion 63 Chapter 6 Diluted magnetic Dirac-Weyl materials: Susceptibility and ferromagnetism in three-dimensional chiral gapless semimetals 65 6.1 Introduction 65 6.2 Model 68 6.3 RKKY interaction and effective magnetic coupling 71 6.4 Discussion and conclusion 74 Chapter 7 Conclusion 81 Appendix A Semiclassical Boltzmann transport theory for multiWeyl semimetals 83 A.1 Eigenstates and density of states for multi-Weyl semimetals 83 A.2 Density dependence of dc conductivity in multi-Weyl semimetals at zero temperature 85 A.3 Temperature dependence of chemical potential and Thomas-Fermi wavevector in multi-Weyl semimetals 90 A.4 Temperature dependence of dc conductivity in multi-Weyl semimetals 94 Appendix B Semiclassical Boltzmann transport theory of fewlayer black phosphorus in various phases 101 B.1 Eigenstates and density of states 101 B.2 Density dependence of dc conductivity in black phosphorus 104 B.3 Low-density approximate models for the insulator phase and Dirac semimetal phase 106 B.3.1 Insulator phase at low densities 107 B.3.2 Dirac semimetal phase at low densities 111 B.4 Temperature dependence of chemical potential and Thomas-Fermi wave vector in black phosphorus 114 B.5 Temperature dependence of dc conductivity at the semi-Dirac transition point 117 B.6 Temperature dependence of dc conductivity in the low-density approximate models for the insulator phase and Dirac semimetal phase 120 B.6.1 Insulator phase 120 B.6.2 Dirac semimetal Phase 121 Appendix C Magneto-thermoelectric transport equation in anisotropic systems 125 Appendix D Diluted magnetic Dirac-Weyl materials: Susceptibility and ferromagnetism in three-dimensional chiral gapless semimetals 129 D.1 Cutoff dependence of the range function 129 D.2 Effective RKKY coupling with the exponential disorder cutoff 131 국문초록 152 Acknowledgements 154박

Topological superconductivity of spin-3/2 carriers in a three-dimensional doped Luttinger semimetal

We investigate topological Cooper pairing, including gapless Weyl and fully gapped class DIII superconductivity, in a three-dimensional doped Luttinger semimetal. The latter describes effective spin-3/2 carriers near a quadratic band touching and captures the normal-state properties of the 227 pyrochlore iridates and half-Heusler alloys. Electron-electron interactions may favor non-$s$-wave pairing in such systems, including even-parity $d$-wave pairing. We argue that the lowest energy $d$-wave pairings are always of complex (e.g., $d + i d$) type, with nodal Weyl quasiparticles. This implies $\varrho(E) \sim |E|^2$ scaling of the density of states (DoS) at low energies in the clean limit, or $\varrho(E) \sim |E|$ over a wide critical region in the presence of disorder. The latter is consistent with the $T$-dependence of the penetration depth in the half-Heusler compound YPtBi. We enumerate routes for experimental verification, including specific heat, thermal conductivity, NMR relaxation time, and topological Fermi arcs. Nucleation of any $d$-wave pairing also causes a small lattice distortion and induces an $s$-wave component; this gives a route to strain-engineer exotic $s+d$ pairings. We also consider odd-parity, fully gapped $p$-wave superconductivity. For hole doping, a gapless Majorana fluid with cubic dispersion appears at the surface. We invent a generalized surface model with $\nu$-fold dispersion to simulate a bulk with winding number $\nu$. Using exact diagonalization, we show that disorder drives the surface into a critically delocalized phase, with universal DoS and multifractal scaling consistent with the conformal field theory (CFT) SO($n$)${}_\nu$, where $n \rightarrow 0$ counts replicas. This is contrary to the naive expectation of a surface thermal metal, and implies that the topology tunes the surface renormalization group to the CFT in the presence of disorder.Comment: Published Version in PRB (Editors' Suggestion): 49 Pages, 17 Figures, 3 Table

Superstripes and complexity in high-temperature superconductors

While for many years the lattice, electronic and magnetic complexity of high-temperature superconductors (HTS) has been considered responsible for hindering the search of the mechanism of HTS now the complexity of HTS is proposed to be essential for the quantum mechanism raising the superconducting critical temperature. The complexity is shown by the lattice heterogeneous architecture: a) heterostructures at atomic limit; b) electronic heterogeneity: multiple components in the normal phase; c) superconducting heterogeneity: multiple superconducting gaps in different points of the real space and of the momentum space. The complex phase separation forms an unconventional granular superconductor in a landscape of nanoscale superconducting striped droplets which is called the "superstripes" scenario. The interplay and competition between magnetic orbital charge and lattice fluctuations seems to be essential for the quantum mechanism that suppresses thermal decoherence effects at an optimum inhomogeneity.Comment: 20 pages, 3 figures; J. Supercon. Nov. Mag. 201

Uniaxial stress technique and investigations into correlated electron systems

In the repertoire of an experimental condensed matter physicist, the ability to tune continuously through features in the electronic structure and to selectively break point-group symmetries are both valuable techniques. The experimental technique at the heart of this dissertation, uniaxial stress, can do both such things. The thesis will start with a thorough discussion of our new technique, which was continually developed over the course of this work, presenting both its unique capabilities and also some guidance on the best working practices, before moving on to describe results obtained on two different strongly correlated electron materials. The first, Sr₂RuO₄, is an unconventional superconductor, whose order parameter has long been speculated to be odd-parity. Of interest to us is the close proximity of one of its three Fermi surfaces to a Van Hove singularity (VHs). Our results strongly suggest that we have been able to traverse the VHs, inducing a topological Lifshitz transition. T[sub]c is enhanced by a factor ~2.3 and measurements of H[sub](c2) open the possibility that optimally strained Sr₂RuO₄ has an even-parity, rather than odd-parity, order parameter. Measurements of the normal state properties show that quasiparticle scattering is increased across all the bands and in all directions, and effects of quantum criticality are observed around the suspected Lifshitz transition. Sr₃Ru₂O₇ has a metamagnetic quantum critical endpoint, which in highly pure samples is masked by a novel phase. Weak in-plane magnetic fields are well-known to induce strong resistive anisotropy in the novel phase, leading to speculation that a spontaneous, electronically driven lowering of symmetry occurs. Using magnetic susceptibility and resistivity measurements we can show that in-plane anisotropic strain also reveals the strong susceptibility to electronic anisotropy. However, the phase diagram that these pressure measurements reveal is consistent only with large but finite susceptibility, and not with spontaneous symmetry reduction

Local Probe Insight into Kagome Lattice Magnets and Superconductors Featuring Charge Order

Research in condensed matter physics is driven by the synergy of technological development and the discovery of material platforms with novel electronic functionalities. In particular, the intertwining of quantum phases such as superconducting, magnetic, and topological states can give rise to a high degree of tunability driven by competing interactions. One of the most important and versatile structural platforms which has allowed for the exploration of novel physical emergent phenomena is the kagome lattice, an atomic structural motif comprised of an interlocking network of corner-sharing triangles. Kagome lattice metals have long been predicted to be the ideal platform [1] for hosting unconventional phases, given the band structure arising from the geometric frustration featuring flat bands, van Hove singularities, and topological Dirac points [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]. This two-dimensional lattice has long served as the archetype for geometrically frustrated systems in condensed matter physics and magnetism. However, this frustration has been shown to give rise to numerous diverse ordered phases which compete and can therefore be easily tuned from one to another. These diverse phases host exciting and complex properties from unconventional superconductivity [12, 13, 14, 15, 16, 17, 18, 19, 20, 21] to time-reversal symmetry-breaking charge order [12, 13, 14, 15, 16, 17, 19, 20, 22, 23, 24, 25] and topological magnetism [26], which could shed light on long-standing solid state physics quandaries and provide an innovative push towards future materials able to satisfy engineering demands. In the first part of this thesis, the interplay between magnetism and topologically nontrivial electronic structures is explored. Magnetically induced topological phases of quantum matter are an emerging frontier in materials science, beautifully exemplified by the topological Chern gap induced by the combination of Dirac fermions and out-of-plane ferromagnetic order. Along these lines, several kagome magnets have appeared as the most promising platforms. Such intertwined order was initially explored in the context of kagome band structures in the magnetic Co2Sn3S2 [27], where the competition of FM and AFM phases correlates directly to the observed anomalous Hall effect, and the FM correlations result in topologically nontrivial band structures. However, the onset of the ferromagnetic phase is limited to 100 K, which is unfortunately far below ambient temperature, thus limiting possible technological applications for a topological magnet. Since the combination of out-of-plane magnetism, kagome band structure, and ordering temperature above room temperature is a highly desirable combination of properties, the kagome magnet TbMn6Sn6 presents a seemingly perfect combination of characteristics to realize a topological kagome phase at ambient temperature. However, this topological order is elusive; the anomalous Hall effect only onsets at low temperatures, and magnetoresistance increases dramatically below 50 K [28]. At the same time, STM studies on a pristine Tb kagome layer find the opening of a Chern gap which displays a beautiful Landau fan diagram with applied field, but only below 20 K [28]. While these are clear indications of the topologically nontrivial nature of the low-temperature phase in TbMn6Sn6, the material orders magnetically at 425 K, experiencing a spin reorientation transition at ≃ 310 K, but then exhibits the same out-of-plane ferrimagnetic structure from ambient temperature to the base temperature [26, 28]. This seemingly paradoxical behavior was further deepened by the smooth evolution of magnetic moments and lattice parameters as found by neutron diffraction [26], with no indication of a low-temperature phase transition or change in nuclear or magnetic symmetry. What had not yet been explored and was not accessible through techniques like neutron scattering was the complex interaction between magnetic fluctuations and their coupling to and inhibition of the kagome band topology; this exploration required access by a magnetic microprobe, able to distinguish minute changes in the local magnetic environment. Our innovative combination of muon spin spectroscopy with neutron diffraction and local field analysis was able to identify an out-of-plane ferrimagnetic structure with slow magnetic fluctuations which exhibit a critical slowing down below T*c1 ≃ 120 K and finally freeze into static patches with ideal out-of-plane order below Tc1 ≃ 20 K. We further show that hydrostatic pressure of 2.1 GPa stabilizes the static out-of-plane topological ferrimagnetic ground state in the whole volume of the sample. Therefore the exciting perspective arises of a magnetically-induced topological system whose magnetism can be controlled through external parameters. Our findings provide a significant enhancement of the microscopic understanding of the relation between the low-temperature volume-wise magnetic evolution of the static c-axis ferrimagnetic patches and the topological electronic properties in TbMn6Sn6 [26]. The second and third sections of the main body of the thesis focus on the study of superconductivity and charge order in kagome lattice systems, respectively. In this context, the following systems have appeared of interest: the AV3Sb5 family (where A = K, Rb, and Cs) and intermetallic ScV6Sn6 featuring a vanadium kagome lattice; as well as LaRu3Si2 and CeRu2 hosting a ruthenium kagome lattice. The motivation for a detailed investigation of such systems lies in a long history of theoretical predictions of exotic superconducting (such as chiral p-wave or f-wave pairing) and charge ordered states in kagome lattice systems [2, 3, 4, 5, 6, 7]. The experimental realization of such states has long been missing. The recent discovery of the AV3Sb5 family [29, 30] provided an exciting realization of a kagome lattice tuned near the van Hove singularity [8, 9, 31] and was the first kagome system shown to host both superconductivity and charge order at high temperatures [30]. These materials present a large array of fascinating physical properties such as anomalous Hall effect [21, 32, 33, 34], anomalous Nernst effect [35, 36], field-switchable chirality of the charge order [37, 38], and time-reversal symmetry-breaking charge order [12, 13, 14]. A strong competition between numerous charge order phases and unconventional superconductivity was uncovered, which experiences significant tunability with hydrostatic pressure [13, 20, 33, 39, 40, 41, 42, 43], chemical substitution [44], and thickness [45, 46, 47]. This provided the ideal platform for the powerful combination of zero-field (ZF), high-field, high-pressure, and ultralow temperature µSR to be used to probe the unconventional superconductivity and charge order. In the superconducting state, our results reveal an unconventional nodal superconducting gap structure in KV3Sb5 and RbV3Sb5 at ambient pressure which can be tuned from nodal-to-nodeless by the aplication of hydrostatic pressure [12, 13]. The application of hydrostatic pressure also results in a significant enhancement (by a factor of 2 to 3 for Tc and a factor of 6 to 8 for the superfluid density) of the superconducting properties. Furthermore, the unconventional scaling of the Tc with the superfluid density is considered a hallmark of unconventional superconductivity [13]. In the normal state, charge order is accompanied by time-reversal symmetry-breaking in all three AV3Sb5 compounds [12, 13, 14]. In RbV3Sb5, the time-reversal symmetry-breaking signal becomes significantly enhanced at the surface [48]. Such symmetry-breaking is compatible with the theoretical proposal of chiral charge order hosting orbital currents [9, 8]. While there exist several known examples of time-reversal symmetry-breaking superconductivity, time-reversal symmetry-breaking charge order is exceptional and finds a direct analog with the fundamental Varma model for cuprates and Haldane model in graphene [49, 50]. Another vanadium kagome lattice with exceptional properties may be found in ScV6Sn6; indeed, this is the only member of the RT6M6 structural family found to host charge order [25, 51]. There are crucial differences between ScV6Sn6 and the AV3Sb5 family; namely, superconductivity has not been found down to the lowest temperatures even after full suppression of charge order by hydrostatic pressure [25, 52], and the charge ordering wave vector is different than in the AV3Sb5 family [25]. Despite these differences the unconventional nature of charge order in ScV6Sn6 appears similar to that of the AV3Sb5 family. We employ the powerful combination of ZF-µSR and high field µSR to uncover time-reversal symmetry breaking concomitant with charge order in this material [25]. The magnetic nature of the charge order in this kagome metal is furthermore supported by the appearance of magnetoresistance upon approaching the charge order transition, which becomes linear towards low temperatures, a hallmark feature of an unconventional quantum state [25]. The experimental signatures detected by our study serve as evidence for recent theoretical studies finding that the charge ordered state in ScV6Sn6 may host orbital currents [25, 53, 54]. This material provides a non-superconducting vanadium kagome lattice to explore the unconventional electronic states arising from the unique structural motif. Superconductivity has long been known in LaRu3Si2 [55, 56, 57, 58] but never been discussed in the context of kagome physics; its pristine Ru kagome lattice makes it the kagome superconductor with the highest transition temperature Tc ≃ 7 K at ambient pressure [16]. Our density functional theory (DFT) calculations reveal typical kagome band structure features found very near the Fermi energy, including flat bands and a van Hove singularity [16], which significantly enhance Tc, since the electron-phonon coupling only reproduces a small portion of Tc. This system presents other unconventional characteristics of superconductivity such as a robustness of superfluid density and Tc to the application of hydrostatic pressure [16]; additionally, we find an unconventional scaling of the superfluid density with Tc by Fe doping [17]. Such a combination of properties allowed us to identify this as the prototypical kagome superconductor. In the normal state, the band structure calculations fascinatingly reveal a lattice instability, indicating a tendency towards some type of lattice reconstruction [16, 22, 23]. This led to our experimental discovery of a cascade of charge orders, with one manifesting below below 400 K which preserves time-reversal symmetry and another appearing below 80 K which breaks time-reversal symmetry [22,23]. Finally, the superconductor CeRu2 has been investigated in terms of its three-dimensional interpenetrating kagome motif, found to play a crucial role in the determination of its electronic band structure dominated by kagome physics near the Fermi level [59]. Our investigations have probed the superconducting gap symmetry and find best agreement with an anisotropic s-wave gap structure, confirming previous studies investigating the unusual superconducting state, posited to host a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state [60, 61, 62]. We uncover superconducting properties (Tc, superfluid density, and superconducting gap value) which place it nearby the prototypical kagome superconductor LaRu3Si2 [15]. In the normal state, we uncover three characteristic magnetic temperatures, T*1 ≃ 110 K, T* 2 ≃ 65 K and T∗ 3 ≃ 40 K which signify the onset of weak static magnetism, as confirmed by our high-field µSR results [15]. The significant enhancement of these features under magnetic field provides clear evidence for the electronic origin of this weak magnetism in CeRu2. We even observe self-screening of the relaxation rate below Tc, an elegant self-consistent confirmation of weak magnetism present in this kagome superconductor [15]. The extraordinary electronic properties found in kagome lattice materials stand as testament to the unique symmetry. Such properties lead to a complex interplay of correlated electron phases and topologically nontrivial phases; the intertwined order promises a tantalizing tunability of ordered phases in this family of materials. From a simple two-dimensional structural motif arise an astonishing array of phases, from topological Chern magnetism to unconventional superconductivity to high-temperature charge order and may even realize orbital currents in an unconventional chiral charge density wave phase which breaks time-reversal symmetry. Since many of these phases occur together and appear to cooperate and/or compete, one arrives at an incredible tunability in kagome materials. The manipulation of quantum phases has been accomplished in the frame of my doctoral research through means of application of magnetic fields, hydrostatic pressure, thermodynamic means, and through chemical substitution. The complex ordered phases which arise have been principally investigated through the use of the exquisitely sensitive magnetic microprobe muon spin spectroscopy