Thesis advisor: Vidya Madhavan / It has been long established that the phenomenon of superconductivity is administered by lattice deformations (phonons) which act to pair electrons into spinless bosons free to condense into a coherent ground state. This superconducting phase is protected up to a critical temperature above which thermal fluctuations are potent enough to destroy the resistance free phase. The strength of this phonon mediation has been calculated by strong coupling theory and found to be capable of accommodating pairing up to near 40 K. So with the advent of copper-oxide (cuprate) superconductors boasting transitions temperatures exceeding 90 K it was clear that these material represented a new breed of superconducting physics. More than twenty years after the initial discovery of these high-transition temperatures the most basic questions are yet to be answered, the most fundamental of which is by what mechanism does pairing occur? The field splits between those who feel that a boson mediator is still necessary to act as the virtual glue which binds electrons into cooper pairs while others insist that really the Coulomb force alone is enough to induce pairing physics. Even within the boson-seeker community there is no consensus on what particular type of boson is contained in this system whether it be a lattice excitation or spin excitation. This answer has been clouded by previous experimental results on the hole-doped cuprates which have made strong cases for every scenario rendering them largely inconclusive. For this answer though it is possible to explore materials that have not yet been clouded by conflicting results by performing the first high resolution ultra-high-vacuum low-temperature scanning tunneling microscopy (STM) study of an electron-doped cuprate. A distinct and unambiguous bosonic mode is found at energy near 10.5 meV. Through comparison with other experimental data it is found that this mode does not fit the characteristics of a phonon. It is found, through comparison with neutron scattering experiments on the same sample, that this mode is consistent with a spin collective mode. Further more it is found that this mode is linked with the strength of superconductivity nominating it as the possible electron pairing mechanism. Doping and temperature dependence studies are performed to investigate this possibility. Finally the same procedures developed can be applied to the newly discovered iron based superconductors which may represent yet another type of new superconductor physics. Initial results on the first bosonic mode STM study of SrFe$_{2-x}$Co$_{x}$As$_{2}$ and BaFe$_{2-x}$Co$_{x}$As$_{2}$ are presented. / Thesis (PhD) — Boston College, 2009. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.

Thesis advisor: Michael J. Naughton / Synchrotron based experiments of quantum coupled states reveal a delicate balance of energy levels facilitating the Mott driven antiferromagnetic state responsible for High Temperature Superconductivity (HTSC). High resolution spectroscopic experiments including Angle Resolved Photoemission (ARPES), Resonant Elastic X-ray Scattering (REXS), X-ray Natural and Magnetic Circular Dichroism (XNCD & XMCD) are used to investigate the Cuprate, Iridate, and Rutheno-Iridate systems. Highly correlated Mott driven systems producing the antiferromagnetic Cuprate and Iridate series of layered perovskites are perturbed using doping and temperature to elucidate the correlation of states within the materials. Similar to the Cuprate HTSC, the Rutheno-Iridate system undergoes a phase segregation of magnetic domains resulting in Sr₃IrRuO₇ where ARPES measurements reveal a temperature and momentum dependent pseudogap. Electronic band structure investigations yield a Fermi surface with gap parameters similar to extended s-wave symmetry. Additional observations of a p-wave symmetry centered at the (π, π) scattering vector within Fermi surface maps provide evidence for long range magnetic coupling. / Thesis (PhD) — Boston College, 2019. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.

Made available in DSpace on 2015-04-22T22:07:23Z (GMT). No. of bitstreams: 1 Dissertacao Final Marcio Gomes.pdf: 1885147 bytes, checksum: b68c412fc26d42c2c611a08b965c9c52 (MD5) Previous issue date: 2009-06-26 / Fundação de Amparo à Pesquisa do Estado do Amazonas / In this work, we study the properties of the high-temperature superconductors to analyze its rich phase diagram. We use the tight binding model within a mean-field formulation. The choice of the above model is due to its relative simplicity and also to verify the extent upto which it can provide satisfactory qualitative results. We use the tight binding model including terms upto second nearest hopping to study. These new superconductors in the underdoped and overdoped phases. We consider the charge density wave with d-wave symmetry (DDW), as a possible explanation for the pseudogap in the underdoped phase. The phase diagram of the cuprates are analyzed. We calculate some properties of these new materials, such as the chemical potential and specific heat and compare with other theories and experiments that attempt to explain superconductivity. We will also observe, to what extent the theory of mean field approximation is applicable. / Neste trabalho, estudaremos as propriedades que são universais aos supercondutes de altas temperaturas, analisando o seu rico diagrama de fase. Utilizamos-nos para isso, o modelo de tight binding numa formulação de campo m´edio. A escolha do modelo de tight binding foi devido ao interesse em verificar até que ponto, um método, relativamente simples que os demais, pode fornecer resultados quantitativos satisfatórios. Assumimos que o termo de hopping e as interações não locais ocorrem entre primeiros e segundos vizinhos. Consideraremos as ondas de densidade d (DDW), como possível explicação para o pseudogap no estado normal. Analisaremos o comportamento do diagrama de fase nos cupratos, o gap supercondutor e o pseudogap no estado normal e calcularemos algumas propriedades termodinâmicas, tais como, potencial químico e calor específico; fazendo um paralelo com outras teorias que tentam explicar a supercondutividade. Veremos, também, até que ponto a teoria de campo médio é útil.

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.

Des mesures de l'effet Nernst dans la phase pseudogap des cuprates YBa[indice inférieur 2]Cu[indice inférieur 3]O[indice inférieur y] (YBCO) et ceux de la famille de La[indice inférieur 2]-[indice inférieur x]Sr[indice inférieur x]CuO[indice inférieur 4] (LSCO) révèlent la sensibilité de cette sonde à l'apparition du pseudogap à la température T*. Ces mesures d'effet Nernst montrent aussi l'étendue restreinte en température des fluctuations supraconductrices par rapport à la contribution des quasiparticules normales. Ces deux observations permettent l'établissement d'un diagramme de phase dopage-température pour ces matériaux indiquant clairement les limites du pseudogap et des fluctuations supraconductrices. Ces mêmes mesures sur des cristaux d'YBCO et de Nd-LSCO démaclés et orientés dans les deux directions de la structure cristalline orthorhombique, a et b, montrent une importante anisotropie de l'effet Nernst indiquant une brisure de symétrie de rotation apparaissant justement à T*. Une compréhension plus approfondie de cette brisure de symétrie pointe vers une étude complète de l'anisotropie des coefficients de transport électrique et thermoélectrique d'YBCO et du test des relations de réciprocité d'Onsager. L'étude montre que la conductivité de Hall est isotrope et ne viole donc pas la relation d'Onsager en champ magnétique. L'observation d'une anisotropie des coefficients thermoélectriques longitudinaux et transverses indique tout d'abord la présence d'une forte nématicité, ensuite une violation de la relation de Mott. Il est suggéré que le pseudogap des cuprates consiste en une phase nématique de fluctuations d'ordre de charge se stabilisant à basse température et reconstruisant la grande surface de Fermi de trous en une surface anisotrope comportant des poches d'électrons et de trous.

Ce travail de thèse présente un nouvel ordre magnétique dans l'énigmatique phase de pseudo-gap des cuprates supraconducteurs à haute température critique. L'étude des composés YBa2Cu3O6+δ, HgBa2CuO4+δ et La1.92Sr0.08CuO4 par diffusion élastique de neutrons polarisés a permis de mettre en évidence un paramètre d'ordre magnétique en dessous d'une température comparable à celle de l'ouverture du pseudo-gap de ces systèmes. Nous avons également montré pour la première fois l'existence dans la famille HgBa2CuO4+δ de deux modes collectifs magnétiques associés à la phase de pseudo-gap. Tous ces résultats indiquent qu'à l'ouverture du pseudo-gap est associée une vraie transition de phase, avec un paramètre d'ordre magnétique et une symétrie brisée: la symétrie par renversement du temps. Il est toutefois important de noter que la symétrie de translation du réseau est préservée: on parle alors d'ordre à Q=0. Dans le système YBa2Cu3O6+δ, nous avons établi que lorsque l'on s'approche du composé parent, ou lorsque l'on introduit des impuretés telles que du Zn, les fluctuations de spin incommensurables autour du vecteur d'onde antiferromagnétique (QAF) se développent au détriment du nouvel ordre à Q=0. De manière similaire, nous avons pu mettre en évidence une interaction entre l'instabilité magnétique autour de QAF et le nouvel ordre à Q=0 dans La1.92Sr0.08CuO4. L'ensemble de ces résultats apporte une pièce maitresse au puzzle que représente toujours la supraconductivité à haute température critique, malgré 25 ans de recherche.

Recently, an analysis of all available planar oxygen shift and relaxation data for the cuprate high-temperature superconductors showed that the data can be understood with a simple spin susceptibility from a metallic density of states common to all cuprates. It carries a doping dependent but temperature independent pseudogap at the Fermi surface, which causes the deviations from normal metallic behavior, also in the specific heat. Here, a more coherent, unbiased assessment of all data, including planar Cu, is presented and consequences are discussed, since the planar Cu data were collected and analyzed prior to the O data. The main finding is that the planar Cu shifts for one direction of the external magnetic field largely follow from the same states and pseudogap. This explains the shift suppression stated more recently, which leads to the failure of the Korringa relation in contrast to an enhancement of the relaxation due to antiferromagnetic spin fluctuations originally proposed. However, there is still the need for a second spin component that appears to be associated with the Cu 3𝑑(𝑥2−𝑦2) hole to explain the complex Cu shift anisotropy and family dependence. Furthermore, it is argued that the planar Cu relaxation which was reported recently to be rather ubiquitous for the cuprates, must be related to this universal density of states and the second spin component, while not being affected by the simple pseudogap. Thus, while this universal metallic density of states with a pseudogap is also found in the planar Cu data, there is still need for a more elaborate scenario that eludes planar O.

Planar oxygen nuclear magnetic resonance (NMR) relaxation and shift data from all cuprate superconductors available in the literature are analyzed. They reveal a temperature-independent pseudogap at the Fermi surface, which increases with decreasing doping in family-specific ways, i.e., for some materials, the pseudogap is substantial at optimal doping while for others it is nearly closed at optimal doping. The states above the pseudogap, or in its absence are similar for all cuprates and doping levels, and Fermi liquid-like. If the pseudogap is assumed exponential it can be as large as about 1500 K for the most underdoped systems, relating it to the exchange coupling. The pseudogap can vary substantially throughout a material, being the cause of cuprate inhomogeneity in terms of charge and spin, so consequences for the NMR analyses are discussed. This pseudogap appears to be in agreement with the specific heat data measured for the YBaCuO family of materials, long ago. Nuclear relaxation and shift show deviations from this scenario near Tc, possibly due to other in-gap states.

Conselho Nacional de Desenvolvimento Científico e Tecnológico / The specific heat and the condensation energy of a two-dimensional Hubbard model, suitable to discuss high Tc superconductors (HTSTC), is studied taking into account hopping to first (t) and second (t2) nearest neighbors. Results for the Hubbard model show that the specific heat as a function of the temperature C(T) presents a two peaks structure (DUFFY; MOREO, 1997). The low temperature peak has been associated with spin fluctuation while the high temperature peak is related to charge fluctuation. Experimental results for the specific heat of HTSC s (LORAM et al., 2001), for instance, the YBCO and LSCO, indicate a close relation between the pseudogap and the specific heat. In the present work, we investigate the specific heat by the Green s function method within the n-pole approximation proposed by L. Roth (ROTH, 1969). The specific heat is calculated on the pseudogap and on the superconducting regions. Superconductivity with dx2−y2- wave pairing is considered following the procedure proposed by Beenen and Edwards (BEENEN; EDWARDS, 1995). The analytical expressions for the specific heat and for the condensation energy have been obtained following the formalism presented in reference (KISHORE; JOSHI, 1971). In the present scenario, the pseudogap emerges when the antiferromagnetic (AF) fluctuations (present in the Roth s band shift) become strongly sufficient to push down the region of the nodal point (π,π) on the renormalized quasi-particle bands. We observed that above a given total occupation nT , the specific heat decreases signaling the pseudogap presence. The effects of the antiferromagnetic fluctuations on the condensation energy and on superconductivity are also investigated.x / No presente trabalho estuda-se o calor específico de um modelo de Hubbard considerado adequado para discutir supercondutores de altas temperaturas. Resultados para o modelo de Hubbard mostram que o calor específico em função da temperatura apresenta uma estrutura de dois picos (DUFFY; MOREO, 1997). O pico de baixa temperatura está associado às flutuações de spin, enquanto que o pico em alta temperatura está relacionado às flutuações de carga. Por outro lado, resultados experimentais do calor específico de supercondutores de altas temperaturas (LORAM et al., 2001), como por exemplo o Y BCO e o LSCO, indicam uma forte relação entre o calor específico e o pseudogap. Portanto, neste trabalho investiga-se a relação entre o pseudogap e o calor específico de um modelo de Hubbard usando a técnica das funções de Green em conjunto com a aproximação de n-pólos proposta por L. Roth (ROTH, 1969). O calor específico é calculado na região do pseudogap e da supercondutividade. Considera-se supercondutividade com simetria de onda dx2 − y2 e o parâmetro de ordem supercondutor é obtido seguindo-se o procedimento de fatorização proposto por Beenen e Edwards (BEENEN; EDWARDS, 1995). A expressão analítica do calor específico é obtida seguindo o formalismo proposto na referência (KISHORE; JOSHI, 1971). No cenário adotado, o pseudogap emerge quando flutuações antiferromagnéticas, as quais estão relacionadas a correlações antiferromagnéticas (presentes no deslocamento de banda da Roth), tornam-se fortes o suficiente para puxar as bandas renormalizadas para energias abaixo do potencial químico no ponto (π,π). Observou-se que acima de uma certa ocupação, o salto no calor específico decresce sinalizando a abertura do pseudogap. Os efeitos das flutuações antiferromagnéticas sobre a energia de condensação e sobre a supercondutividade também são investigados.

Thesis advisor: Ziqiang Wang / One of the most unconventional electronic states in high transition temperature cuprate superconductors is the pseudogap state. In the temperature versus doping phase diagram, the pseudogap state straddles across the antiferromagnetic (AF) state near half filling and the superconducting (SC) dome on the hole doped side above the transition temperature Tc. The relationship between the pseudogap state and these two well known states - the AF state and the SC state is believed to be very important for understanding superconductivity and the emergent quantum electronic matter in doped Mott insulators. The pseudogap is characterized by the emergence of a soft gap in the single-particle excitation spectrum in the normal state in the temperature range between Tc and a characteristic temperature T*, i.e. Tc < T < T*. The most puzzling feature of the pseudogap is the nodal-antinodal dichotomy. Observed by ARPES in momentum space, the Fermi surface is gapped out in the antinodal region leaving a Fermi arc of gapless excitations near the nodes. Whether the pseudogap is an incoherent superconducting gap (onegap scenario) or it is a different gap governed by other mechanisms, other than superconductivity, (two-gap scenario) is still under debate. In this thesis I study the particle-particle channel and the particle-hole channel of the valence bond fluctuations away from half filling. Based on a strong-coupling analysis of the t-J model, I argue that the superexchange interaction J induced incommensurate bond centered density wave order is the driving mechanism for the pseudogap state. Low energy density of states (DOS) are eliminated by multiple incommensurate scatterings in the antinodal region at the Fermi level. I show that the interplay between the incommensurate bond centered d-wave density wave instability and the intrinsic electronic inhomogeneity in real cuprate materials is responsible for the observed pseudogap phenomena. Utilizing the spatially unrestricted Gutzwiller approximation, I show that the off-stoichiometric doping induced electrostatic disorder pins the low-energy d-wave bond density fluctuations, resulting in a VBG phase. The antinodal Fermi surface (FS) sections are gapped out, giving rise to a genuine normal state Fermi arc. The length of the Fermi arc shrinks with underdoping below the temperature T* determined by thermal filling of the antinodal pseudogap. Below Tc, the d-wave superconducting gap due to singlet pairing coexists and competes with the VBG pseudogap. The spatial, momentum, temperature and doping dependence of these two gaps are consistent with recent ARPES and STM observations in underdoped and chemically substituted cuprates. The temperature versus doping phase diagram captures the salient properties of the pseudogap phenomena and provides theoretical support for the two-gap scenario. In addition to resolving the complexities of the quantum electronic states in hole-doped cuprates, my unified theory elucidates the important role of the interplay between the strong electronic correlation and the intrinsic electronic disorder in doped transition metal oxides. / Thesis (PhD) — Boston College, 2011. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.