Thesis advisor: Ilija Zeljkovic / Kagome lattice is a versatile platform that can host both strongly correlated electronic phenomena and topological Bloch electrons. Correlated electronic states in kagome metals show some resemblance to those in high-temperature superconductors, such as cuprates and iron-based superconductors, where rotational and/or translational symmetries of the electronic structure are spontaneously broken. Many of the kagome materials are now also known to break time-reversal symmetry, even if spin magnetism is entirely absent. In our studies, we use scanning tunneling microscopy/spectroscopy (STM/S) to discover novel emergent phenomena in several representative families of kagome metals.In the first part of the thesis, I focus on a family of kagome superconductors AV3Sb5 (A = Cs, Rb, K). Using STM/S, we visualize a surprising C6 to C2 rotation symmetry breaking in the charge density wave (CDW) state of AV3Sb5. Moreover, we discover distinct temperature scales associated with a two-fold symmetric 2a_0×2a_0 CDW (~70+ K), a unidirectional 4a0 stripe-charge order (~50-60 K), and unidirectional coherent states in AV3Sb5 (~30-35 K). In isostructural system CsTi3Bi5 Kagome crystal, we revealed rotational symmetry breaking, or electronic nematicity, without the underlying CDW state. Our experiments shed light on a rich phase diagram hosting a variety of symmetry-breaking electronic phases in kagome metals. In the second part of the thesis, we focus on the topological aspects of the electronic band structure of kagome metals. When electrons hop (nearly) freely in kagome lattices, spin-orbit coupling can open a topological Dirac gap at the K point and induce either quantum anomalous Hall or quantum spin Hall phases when the Fermi level is positioned in the gap. In strongly spin-orbit coupled kagome metals YMn6Sn6 and TbV6Sn6, we discovered enormous crystal momentum-dependent magnetic-field induced electronic band renormalization, which could be attributed to unusual orbital magnetization. Modern orbital magnetization theory describes that orbital magnetization comes from (spin) Berry Curvature associated with the Chern Dirac band. Using quasiparticle interference imaging, we map the Dirac band renormalization under external magnetic field and measure the values of orbital magnetic moments as a function of crystal momenta. Our experiments provide the first effort to resolve momentum-space orbital magnetic moments in a single crystal with atomic resolution. / Thesis (PhD) — Boston College, 2024. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.

La découverte en 2008 des supraconducteurs à base de fer a ouvert un nouveau champ d'investigation de la supraconductivité à haute température critique. En particulier, la phase nématique de ces matériaux pourrait jouer un rôle prépondérant dans le mécanisme de la supraconductivité. Nous avons étudié le composé FeSe par spectroscopie Raman, à pression ambiante et sous pression hydrostatique. Celui-ci ne possède pas d'ordre magnétique statique à pression ambiante, ce qui en fait un composé de choix pour l'étude de l'ordre nématique. Nous avons observé les fluctuations nématiques de charge. Leur évolution dans la phase tétragonale prouve l'existence d'une instabilité nématique d'origine électronique, qui gouverne la transition structurale. Dans la phase orthorhombique, le comportement des phonons souligne le rôle du couplage spin-phonon dans la transition nématique. Par ailleurs, la forme de la réponse Raman supraconductrice est compatible avec l'existence de deux gaps de symétrie s, dont un est anisotrope. Sous pression hydrostatique, les fluctuations nématiques s'atténuent rapidement. Le point critique quantique électronique associé se situe à très basse pression, peu avant l'apparition de l'ordre magnétique. Les fluctuations nématiques disparaissent complètement vers 2 GPa, quand la transition structurale passe de second ordre à premier ordre. C'est également proche de cette pression que se produit une anomalie dans le comportement des phonons, qui indique une modification de la structure électronique du système. Nos mesures révèlent en outre l'existence d'un pseudogap. Sa température d'apparition chute simultanément à la disparition de la phase magnétique, quand la température critique de supraconductivité atteint son maximum. Enfin, la réponse Raman de l'état supraconducteur à 7.8 GPa montre une signature claire d'un gap plein. / The discovery in 2008 of the iron-based superconductors opened a new field of investigation of high-temperature superconductivity. In particular, the nematic phase of these materials may play a major role in the mecanism of superconductivity. We studied the FeSe compound using Raman spectroscopy, at ambient pressure and under hydrostatic pressure. This material does not display any static magnetic order at ambient pressure and is therefore an excellent choice to study the nematic order. We observed the charge nematic fluctuations. Their evolution in the tetragonal phase proves the existence of an electronic nematic instability, which drives the structural transition. In the orthorhombic phase, the behaviour of the phonons underlines the role of the spin-phonon coupling in the nematic transition. Besides, the shape of the superconducting Raman response is compatible with the existence of two s-wave gaps, one of which is anisotropic. Under hydrostatic pressure, the nematic fluctuations reduce rapidly. The associated electronic quantum critical point is situated at very low pressure, just before the appearance of magnetic order. The nematic fluctuations completely disappear around 2 GPa, when the structural transition changes from second order to first order. An anomaly of the phonons also occurs close to this pressure, which indicates a modification of the electronic structure of the system. Our measurements additionally reveal the existence of a pseudogap. Its temperature of appearance reduces significantly simultaneously to the disappearance of magnetic order, when the critical temperature of superconductivity reaches its maximum. Finally, the Raman response in the superconducting state at 7.8 GPa shows a clear signature of a full gap.

Recent resonant inelastic x-ray scattering (RIXS) experiments have detected a significant high-energy spin-excitation anisotropy in the nematic phase of the enigmatic iron-based superconductor FeSe, whose origin remains controversial. We apply an itinerant model previously used to describe the spin-excitation anisotropy as measured by neutron scattering measurements, with magnetic fluctuations included within the RPA approximation. The calculated RIXS cross section exhibits overall agreement with the RIXS data, including the high energy spin-excitation anisotropy

In this thesis, we investigate strongly correlated phenomena in quantum spin systems. In the first part of this work, we study geometrically frustrated antiferromagnets (AFMs). Generalizing the SU(2) Heisenberg Hamiltonian to Sp(N) symmetry, we obtain, in the large-N limit, the mean-field phase diagrams for the planar pyrochlore and cubic AFMs. We then use gauge theories to consider fluctuation effects about their respective mean-field configurations. We find, in addition to conventional Neel states, a plethora of novel magnetically disordered phases: two kinds of spin liquids, Z2 in 2+1D and U(1)in 3+1D, and several valence bond solids such as two and three-dimensional plaquette and columnar singlet states. We use the same approach to study the diamond lattice AFM which possesses extended classical ground state degeneracy. We demonstrate that quantum and entropic fluctuations lift this degeneracy in different ways. In the second part of the thesis, we study ultracold spinor atoms confined in optical lattices. We first demonstrate the feasibility of experimental realization of rotor models using ultracold spin-one Bose atoms in a spin-dependent and disordered optical lattice. We show that the ground state of such disordered rotor models with quadrupolar interactions can exhibit biaxial nematic ordering in the disorder-averaged sense, and suggest an imaging experiment to detect the biaxial nematicity in such systems. Finally, using variational wavefunction methods, we study the Mott phases and superfluid-insulator transition of spin-three bosons in an optical lattice with an anisotropic two dimensional optical trap. We chart out the phase diagrams for Mott states with n = 1 and n = 2 atoms per lattice site. We show that the long-range dipolar interaction stabilizes a state characterized by antiferromagnetic chains made of ferromagnetically aligned spins. We also obtain the mean-field phase boundary for the superfluid-insulator transition, and show that inside the superfluid phase and near the superfluid-insulator phase boundary, the system undergoes a first order antiferromagnetic-ferromagnetic spin ordering transition.

In this thesis, we investigate strongly correlated phenomena in quantum spin systems. In the first part of this work, we study geometrically frustrated antiferromagnets (AFMs). Generalizing the SU(2) Heisenberg Hamiltonian to Sp(N) symmetry, we obtain, in the large-N limit, the mean-field phase diagrams for the planar pyrochlore and cubic AFMs. We then use gauge theories to consider fluctuation effects about their respective mean-field configurations. We find, in addition to conventional Neel states, a plethora of novel magnetically disordered phases: two kinds of spin liquids, Z2 in 2+1D and U(1)in 3+1D, and several valence bond solids such as two and three-dimensional plaquette and columnar singlet states. We use the same approach to study the diamond lattice AFM which possesses extended classical ground state degeneracy. We demonstrate that quantum and entropic fluctuations lift this degeneracy in different ways. In the second part of the thesis, we study ultracold spinor atoms confined in optical lattices. We first demonstrate the feasibility of experimental realization of rotor models using ultracold spin-one Bose atoms in a spin-dependent and disordered optical lattice. We show that the ground state of such disordered rotor models with quadrupolar interactions can exhibit biaxial nematic ordering in the disorder-averaged sense, and suggest an imaging experiment to detect the biaxial nematicity in such systems. Finally, using variational wavefunction methods, we study the Mott phases and superfluid-insulator transition of spin-three bosons in an optical lattice with an anisotropic two dimensional optical trap. We chart out the phase diagrams for Mott states with n = 1 and n = 2 atoms per lattice site. We show that the long-range dipolar interaction stabilizes a state characterized by antiferromagnetic chains made of ferromagnetically aligned spins. We also obtain the mean-field phase boundary for the superfluid-insulator transition, and show that inside the superfluid phase and near the superfluid-insulator phase boundary, the system undergoes a first order antiferromagnetic-ferromagnetic spin ordering transition.

L'objectif principal de ma thèse porte sur les composés à base d'europium, une des terres rares qui est magnétique et qui forme des semiconducteurs magnétiques. Le but premier était de mesurer les corrélations magnétiques dans l'EuB6 à l'aide de la technique diffraction de neutrons à petits angles SANS (small angle neutron scattering en anglais), plus précisément de mesurer la longueur de corrélation des polarons magnétiques. La raison de sonder les polarons magnétiques dans l'EuB6 est que leur présence pourrait expliquer la grande magnétorésistance proche de la transition Curie associée avec l'ordre ferromagnétique. Ceci est une tâche particulièrement difficile puisque l'europium est un très grand absorbeur de neutrons, affectant donc la durée d'acquisition. De longs temps d'exposition étaient nécessaires pour obtenir un bruit de fond adéquat. Suite à l'analyse des données, nous avons pu conclure que les polarons magnétiques sont définitivement présents. De plus, leur présence augmente de façon non négligeable les fluctuations magnétiques. Par contre, la présence de ces fluctuations magnétiques rend la tâche de mesurer la longueur de corrélation plus difficile. La plus grande découverte de mon doctorat a été la phase nématique dans le EuB6 grâce à des mesures de magnétorésistance en fonction de l'angle. Ceci se manifestait avec une brisure de symétrie du cristal seulement dans les propriétés électroniques. Ces données m'ont permis de mieux comprendre le rôle que jouent les polarons magnétiques dans ce système. En dopant le système au calcium, nous avons confirmé la présence d'une transition vers un ordre de verre de spins à partir d'une concentration de 30% de calcium. Ce composé semble posséder la même phase nématique que le EuB6. Toutefois, cette phase est bien plus concentrée autour de la transition à cause du manque de fluctuations magnétiques au-dessus de celle-ci. / The main objective of my thesis is about Europium, a magnetic rare earth, based compounds which produces magnetic semiconductors. The primary goal was to measure magnetic correlations in the EuB6 using SANS (small angle neutron scattering) technique, more precisely, to measure the correlation length of magnetic polarons. The raison for studying magnetic polarons in EuB6 is that their presence can explain the large magnetoresistance near the Curie transition associated to a ferromagnetic order. This is a particularly difficult task since Europium (Eu2+) is a very strong neutron absorber, thus affecting the acquisition time. Long exposure times were necessary to obtain adequate background. After the analysis of the data, we have finally been able to conclude that magnetic polarons are definitely present. In addition, their presence increases significantly magnetic fluctuations. On the other hand, the presence of these magnetic fluctuations makes the task of measuring the correlation length more difficult. The biggest discovery of my Ph.D. was the nematic phase in the EuB6 using angle-based magneto-resistance measurements. The nematic phase is caracterized by a breaking of symmetry only in the electronic properties. These data have allowed me to better understand the role played by magnetic polarons in this system. By doping the system with calcium, we confirmed the presence of a transition to a spin glass order from a concentration of 30% calcium. This compound seems to have the same nematic phase as its parent compound. However, this phase is much more concentrated around the spin glass transition because of lack of magnetic fluctuations above it.

Emergent electronic phenomena in iron-based superconductors have been at the forefront of condensed matter physics for more than a decade. Much has been learned about the origins and intertwined roles of ordered phases, including nematicity, magnetism, and superconductivity, in this fascinating class of materials. In recent years, focus has been centered on the peculiar and highly unusual properties of FeSe and its close cousins. This family of materials has attracted considerable attention due to the discovery of unexpected superconducting gap structures, a wide range of superconducting critical temperatures, and evidence for nontrivial band topology, including associated spin-helical surface states and vortex-induced Majorana bound states. Here, we review superconductivity in iron chalcogenide superconductors, including bulk FeSe, doped bulk FeSe, FeTe1−xSex, intercalated FeSe materials, and monolayer FeSe and FeTe1−xSex on SrTiO3. We focus on the superconducting properties, including a survey of the relevant experimental studies, and a discussion of the different proposed theoretical pairing scenarios. In the last part of the paper, we review the growing recent evidence for nontrivial topological effects in FeSe-related materials, focusing again on interesting implications for superconductivity.

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In dieser Arbeit werden Messungen elektrischer, thermischer und insbesondere thermoelektrischer Transportkoeffizienten in topologischen Weyl-Halbmetall-Kandidaten sowie in eisenbasierten Hochtemperatur-Supraleitern vorgestellt, analysiert und diskutiert. In TaAs und TaP, zwei Weyl-Halbmetall-Kandidaten mit gebrochener Inversionssymmetrie, liefert das anomale Verhalten des Nernst-Signals in Abhängigkeit des Magnetfeldes Hinweise auf die Existenz von Weyl-Punkten in der Nähe der Fermi-Fläche, wobei sich die Verschiebung des chemischen Potenzials sowie ein Lifshitz-Übergang detektieren lassen. Die Temperaturabhängigkeit des Nernst-Signales erlaubt außerdem Rückschlüsse auf den Abstand der Weyl-Punkte zur Fermi-Fläche. In Mn3Ge, einem Weyl-Halbmetall-Kandidaten mit gebrochener Zeitumkehrsymmetrie, zeigt sich für alle gemessenen Temperaturen ein komplett anomales Verhalten des Nernst-Signals in Abhängigkeit des Magnetfeldes mit einer rechteckigen Hysterese bei kleinen Feldern, welches im Vergleich mit Daten der Magnetisierung einen eindeutigen Hinweis auf die Präsenz von Weyl-Punkten in diesem Material liefert. Mithilfe eines minimalen theoretischen Modells zweier Weyl-Punkte in der Nähe der Fermi-Fläche lässt sich eine Anpassungsformel für die Temperaturabhängigkeit des Nernst-Signals gewinnen, aus welcher sowohl geometrische Parameter der Bandstruktur als auch die Stärke der Berry-Krümmung an der Fermi-Energie extrahiert werden können. Für eisenbasierte Supraleiter besteht seit Langem der Verdacht, dass nematische Fluktuationen einen Einfluss auf die Supraleitung haben. Hier vorgestellte theoretische Betrachtungen zeigen im Rahmen eines Zweibandmodells eindeutig, dass eine endliche nematische Kopplung zu einer starken Erhöhung und einer nicht-monotonen Abhängigkeit des Nernst-Koeffizienten von der Dotierung führt, welcher ein Maximum über dem supraleitenden Dom aufweist. Dies wird anhand von Nernst-Messungen in Co-dotiertem LaFeAsO bestätigt. Ein Vergleich der Ergebnisse des Nernst-Effekts mit Elasto-Widerstandsmessungen enthüllt eine erstaunliche Ähnlichkeit der Dotierabhängigkeiten. Die Daten werden außerdem mit Messungen des Nernst-Effekts an Rh-dotiertem BaFe2As2 verglichen, wobei ebenfalls eine Erhöhung im Bereich optimaler Dotierung nachgewiesen werden kann. In Rh-dotietem BaFe2As2 zeigt sich jedoch ein Unterschied zwischen Elasto-Widerstands- und Nernst-Messungen, woraus abgeleitet wird, dass Elasto-Widerstandsmessungen kein vollständiges Bild der nematischen Fluktuation liefern. Der Nernst-Effekt ist hingegen aufgrund der Sensitivität auf nematische Fluktuationen universell in zwei Vertretern verschiedener Familien eisenbasierter Supraleiter maximal im Bereich des supraleitenden Doms. Dies liefert, zusammen mit den theoretischen Betrachtungen, einen starken Hinweis auf den Einfluss nematischer Fluktuationen auf die Supraleitung. / In this work the electric, thermal, and thermoelectric transport properties of several topological Weyl semimetal candidates and iron-based superconductors are investigated. In TaAs and TaP, two Weyl semimetal candidates with broken inversion symmetry, the Nernst signal exhibits anomalous behaviour as a function of magnetic field, consistent with Weyl points close to the Fermi surface. Furthermore, a shift of the chemical potential and a Lifshitz transition are detected. The temperature dependence of the Nernst signal allows for an estimation of the energy of the Weyl points with respect to the Fermi level. In Mn3Ge, a Weyl semimetal candidate with broken time reversal symmetry, the Nernst signal shows completely anomalous behaviour as a function of magnetic field that can be obtained at all measured temperatures. At low fields the signal exhibits a rectangular hysteresis cycle. A comparison with magnetization measurements evidently shows that these effects are caused by Weyl points lying close to the Fermi surface. With the help of a minimal model of two Weyl points in the vicinity of the Fermi level, a fitting formula of the temperature dependence of the Nernst signal can be obtained. The fit provides geometrical properties of the band structure, such as the $\boldsymbol{k}$-space separation of the Weyl points, their energy with respect to the Fermi level as well as the strength of the Berry curvature close to the Fermi energy. For a long time nematic fluctuations have been suspected to influence superconductivity in iron-based superconductors. A theoretical analysis, with the help of a two-band model, shows clearly that a finite nematic coupling causes a strong enhancement and non-monotonic behaviour of the Nernst coefficient, which develops a maximum above the superconducting dome. These findings are confirmed by Nernst measurements in Co-doped LaFeAsO. A comparison with elasto-resistivity measurements shows a stunning similarity of the doping dependencies of both quantities. Furthermore the data are compared with measurements on Rh-doped BaFe2As2, which also exhibits an enhancement of the Nernst coefficient in the region of optimal doping. However, in Rh-doped BaFe2As2 a difference between elastoresistivity and Nernst measurements is obtained, indicating that the elasto-resistivity measurements are not universally sensitive to nematic fluctuations. The Nernst effect, on the other hand, is enhanced in the vicinity of the superconducting dome in two members of different families of iron-based superconductors. Together with theoretical insights, these results provide strong evidence for the influence of nematic fluctuations on superconductivity in the iron-based superconductors.