This thesis addresses the tunnelling of charge carriers in different materials. First looking at the simplest case of electron tunnelling in metals at zero, then finite temperature, the current is obtained using the Fermi-Dirac golden rule and then the conductance is obtained. This is extended to take into account the spatial dependence of one of the metals being a tip since experimentally this is done by scanning tunnelling microscopy where a tip traces over the surface of a sample. The next step is to look at tunnelling between a metal and a semiconductor, again the current is found. Semiconductors can be doped and the effect this has on tunnelling is examined. Next superconductors are introduced. The purpose of my research has been to look at the tunnelling spectra of high-temperature superconducting cuprates for both extrinsic (metal-superconductor) and intrinsic (superconductor-superconductor) tunnelling. The main features seen experimentally with cuprate tunnelling are identified and then a theory capable of explaining these features is discussed. The theory is compared to experimental results and we find good agreement.

Il y a presque trente ans, un des problèmes les plus difficiles de la physique moderne voyait le jour: la supraconductivité à haute température critique dans les cuprates. Depuis, l'hypothèse nommée modèle Hubbard est rapidement devenu un des candidats les plus prometteurs à en détenir la solution. Dans ce contexte, ce mémoire présente des travaux de calculs numériques sur les phases de la matière prédites par le modèle de Hubbard. Le projet poursuit notamment deux objectifs. En premier lieu, on considère un couplage interplan dans le modèle, ce qui le rend plus réaliste que sa version 2D habituelle. Et en deuxième lieu, on laisse les phases antiferromagnétique et supraconductrice coexister avec en plus une autre phase supraconductrice de type pi-triplet. Plus de détails sur le contexte et ces deux objectifs sont présentés au chapitre 1 et le modèle de Hubbard est détaillé au chapitre 2. Pour obtenir des solutions numériques au modèle, les méthodes utilisées sont la théorie de champ moyen dynamique sur amas (CDMFT) et l'approximation de l'amas variationnel (VCA). Ces méthodes ainsi que le formalisme nécessaire pour les aborder sont présentés au chapitre trois. Notons qu'on utilise ces méthodes pour amas avec des méthodes de diagonalisation exacte qui ne feront pas partie de la discussion. Enfin, le dernier chapitre présente tous les résultats obtenus avec ce projet, qui mènent à deux conclusions principales. Premièrement, le couplage tridimensionnel tel qu'ajouté n'a pas fait ressortir de tendance nette dans les résultats. Cela indique une de deux choses: soit les effets interplans sont négligeables dans le modèle de Hubbard, soit il faudra les inclure d'une façon plus complète dans le futur. Deuxièmement, on observe que la phase pi-triplet apparaît lorsqu'il y a coexistence entre l'antiferromagnétisme et la supraconductivité dans le modèle mais que ces deux dernières phases se nuisent fortement l'une à l'autre, confirmant qu'il y a compétition de phases.

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.

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.

The quest for obtaining higher Tc superconductivity led to the discovery of cuprates about 20 years ago. Since then, they continue to puzzle the scientific community with their bizarre properties like non-BCS superconductivity, pseudo gap, Fermi arcs, linear T resistivity etc. Since these materials show unusually high Tc, a novel mechanism is at play and strong correlations are believed to play an important role. The theme of this thesis work is to study physics of such strongly correlated systems in two dimensions at T = 0 along with development of new theoretical tools necessary for the study. The focus of the thesis is on the ground state studies of strongly correlated models like t-J and Hubbard models using variational Monte Carlo (VMC) and renormalized mean field theory (RMFT). The general method is to propose a variational wave function, motivated by the physics ideas, to be a candidate ground state of the system. Methods to efficiently evaluate the ground state energy and minimizing it with respect to the variational parameters are developed in this work. Antiferromagnetism-superconductivity competition and electron-hole asymmetry in the extended t-J model is investigated. The main result of this work is that increasing the magnitude of the next neighbor hopping (t') on hole doped side strengthen superconductivity while it stabilizes antiferromagnetism on the electron doped side. It is also shown that it is possible to characterize the T = 0 phase diagram with just one parameter called as Fermi Surface Convexity Parameter (FSCP). Next, the possibility of phase separation in the t-J model on a square lattice is investigated using local RMFT technique. It is found that for certain doping, the system phase separates into regions with antiferromagnetic and superconducting orders. Next, the role played by crystalline anisotropy of orthorhombic YBCO cuprates on their properties is examined using anisotropic tx-ty-J model and this ground state study suggests that the anisotropies seen in their properties are plausible solely due to the crystalline anisotropy. A new general method to study strongly correlated systems with singlet ground states is developed and tested in this thesis work. The last part of the thesis explores the possibility of high Tc superconductivity in graphene which is a intermediate coupling resonating valence bond (RVB) system. It is found that undoped graphene is not a superconductor, consistent with the experiments. On doping, the ground state of graphene is found to be a superconductor with “d+id” symmetry whose strength shows a dome as a function of doping which is reminiscent of RVB physics.

Over the past 20 years a great deal of progress has been made towards understanding the physics of the high-temperature (high-Tc) cuprate superconductors. Much of the low- energy physics of these materials appears to be captured by two-dimensional Hubbard or t-J models which have provided significant insight into a number of properties such as the pseudogap, antiferromagnetism and superconductivity itself. However, intrinsically planar models are unable to account for the large variations in Tc observed across materials nor do they capture the electron-phonon (el-ph) interaction, the importance of which a number of experimental probes now indicate. This thesis examines the el-ph interaction in cuprates using a combination of analytical and numerical techniques. Starting from the microscopic mechanism for coupling to in-plane and c-axis polarized oxygen phonons, the theory of el-ph coupling is presented. The el-ph self-energy is derived in the context of Migdal-Eliashberg theory and then applied to understanding the detailed temperature and doping dependence of the renormalizations observed by Angle-resolved photoemission spectroscopy. The qualitative signatures of el- boson coupling in the density of states of a d-wave superconductor are also examined on general grounds and a model calculation is presented for el-ph coupling signatures in the density of states. Following this, the theory is extended to include the effects of screening and the consequences of this theory are explored. Due to the quasi-2D nature of the cuprates, screening is found to anomalously enhance the el-ph contribution to d-wave pairing. This result is then considered in light of the material and doping dependence of Tc and a framework for understanding the materials variations in Tc is presented. From these studies, a detailed picture of the role of the el-ph interaction in the doped cuprates emerges where the interaction, working in conjunction with a dominant pairing interaction, provides much of the materials variations in Tc observed across the cuprate families. Turning towards numerical techniques, small cluster calculations are presented which examine the effects of a local oxygen dopant in an otherwise ideal Bi2Sr2CaCu2O8+δ crystal. Here, it is demonstrated that the dopant locally enhances electronic properties such as the antiferromagnetic exchange energy J via local el-ph coupling to planar local oxygen vibrations. Finally, in an effort to extend the scope of this work to the underdoped region of the phase diagram, an examination of the properties of the single-band Hubbard and Hubbard-Holstein model is carried out using Determinant Quantum Monte Carlo. Here focus is placed on the spectral properties of the model as well as the competition between the the antiferromagnetic and charge-density-wave orders. As with the small cluster calculations, a strong interplay between the magnetic and lattice properties is observed.

In spite of the failures to find an ultimate theory of unconventional superconductivity, after many years of research the scientific community possesses a considerable store of theoretical knowledge about the problem. Over time, the focus is gradually shifted from finding a theoretical description of an experimentally observed phenomenon to distinguishing between multiple models that offer comparably reasonable descriptions. From the point of view of an experimentalist, this means that any qualitative under-standing of an experimental observation would no longer suffice. Instead, the empha-sis in the experimental research should be shifted to accurate quantification of obser-vations, which becomes possible only if the results available from all the available ex-perimental methods are connected together by the theoretical glue. Among the meth-ods that are to be unified, ARPES plays a central role. The reason for this is that it gives access to the single-particle excitation spectrum of the material as a function of both momentum and energy with very high resolution. Other experimental techniques, such as inelastic neutron scattering (INS), Raman spectroscopy, or the newly estab-lished Fourier-transform scanning tunneling spectroscopy (FT-STS) probe more com-plicated two-particle spectra of the electrons and up to now can not achieve the mo-mentum resolution comparable with that of ARPES. Such reasoning serves as the mo-tivation for the present work, in which some steps are done towards understanding the anomalous effects observed in the single-particle excitation spectra of cuprates and relating the ARPES technique to other experimental methods. First, the electronic properties of BSCCO are considered — the superconducting cuprate most studied by surface-sensitive methods. The recent progress in un-derstanding the electronic structure of this material is reported, focusing mainly on the many-body effects (renormalization) and their manifestation in the ARPES spectra. The main result of this part of the work is a model of the Green’s function that is later used for calculating the two-particle excitation spectrum. Then, the matrix element effects in the photoemission spectra of cuprates are discussed. After a general introduction to the problem, the thesis focuses on the recently discovered anomalous behavior of the ARPES spectra that partially originates from the momentum-dependent photoemission matrix element. The momentum- and excitation energy dependence of the anomalous high-energy dispersion, termed “waterfalls”, is covered in full detail. Understanding the role of the matrix element effects in this phenomenon proves crucial, as they obstruct the view of the underlying excitation spectrum that is of indisputable interest. Finally, the work describes the relation of ARPES with other experimental methods, with the special focus on the INS spectroscopy. For the optimally doped bilayer Bi-based cuprate, the renormalized two-particle correlation function in the superconducting state is calculated from ARPES data within an itinerant model based on the random phase approximation (RPA). The results are compared with the experimental INS data on BSCCO and YBCO. The calculation is based on numerical models for the normal and anomalous Green’s functions fitted to the experimental single-particle spectra. The renormalization is taken into account both in the single-particle Green’s function by means of the self-energy, and in the two-particle correlation function by RPA. Additionally, two other applications of the same approach are briefly sketched: the relation of ARPES to FT-STS, and the nesting properties of Fermi surfaces in two-dimensional charge density wave systems.

Cette thèse s'inscrit dans le cadre de l'étude des excitations électroniques dans des matériaux fortement corrélés, ici les monoxydes de métaux de transition CoO, NiO et CuO, le cuprate La2CuO4 et le nickelate La2NiO4. Nous avons utilisé la diffusion inélastique résonante des rayons X (RIXS) pour étudier la dynamique des excitations de basse énergie (quelques eV) dans ces isolants de transfert de charge. Cette étude a été possible grâce à un développement instrumental permettant une amélioration de la résolution expérimentale d'un facteur 3 pour atteindre 300 meV. <br /><br /> Dans les monoxydes, nous avons étudié les excitations localisées du champ cristallin. Dans La2CuO4, et La2NiO4, nous avons plus particulièrement étudié les excitations de transfert de charge. Un exciton (état lié électron-trou) a été observé dans les deux matériaux avec cependant une dynamique différente. Dans La2CuO4, l'exciton a un comportement dispersif alors que dans La2NiO4, il est localisé par les corrélations antiferromagnétiques. Un modèle invoquant la formation d'un singulet de Zhang et Rice dans le cuprate a été proposé pour expliquer cette dynamique excitonique dans le réseau antiferromagnétique sous-jacent.

L?????laboration d???exp??rience permettant de sonder la sym??trie du gap supraconducteur ?? l???aide d???une mesure de la phase de ce gap supraconducteur est l???une des techniques les plus directes pour observer la sym??trie ???d??? des cuprates dop??s au trous. Malheureusement, il existe tr??s peu d???exp??riences de ce type qui ont ??t?? r??ussies pour sonder la sym??trie du gap supraconducteur dans les cuprates dop??s aux ??lectrons. Effectivement, les exp??riences sondant la phase du gap supraconducteur demandent d???utiliser g??n??ralement des jonctions Josephson entre un cuprate et un supraconducteur conventionnel (Exemple : SQUID et jonctions Josephson en coin). Cependant, il est extr??mement difficile d???obtenir de telles jonctions Josephson avec les cuprates dop??s aux ??lectrons, car la croissance de ce mat??riau est extr??mement difficile et les propri??t??s physiques de ceux-ci sont tr??s sensibles aux diff??rentes ??tapes de fabrication que l???on doit effectuer pour obtenir une jonction Josephson. Cependant, de r??cents travaux effectu??s par notre groupe sur la purification des phases dans les couches minces de Pr[indice inf??rieur 2???x]Ce[indice inf??rieur x]CuO[indice inf??rieur 4], un cuprate dop?? aux ??lectrons, ainsi que sur la production de jonctions Josephson de qualit?? entre deux ??lectrodes supraconductrices de Pr[indice inf??rieur 2???x]Ce[indice inf??rieur x]CuO[indice inf??rieur 4] ont revigor?? l???int??r??t de fabriquer une jonction Josephson de qualit?? entre Pr[indice inf??rieur 2???x]Ce[indice inf??rieur x]CuO[indice inf??rieur 4] et un supraconducteur conventionnel. Dans ce m??moire, on propose une m??thode de fabrication de jonctions Josephson en rampe entre un cuprate dop?? aux ??lectrons (Pr[indice inf??rieur 1.85]Ce[indice inf??rieur 0.15]CuO[indice inf??rieur 4]) et un supraconducteur conventionnel (PbIn). Cette m??thode de fabrication nous a permis de fabriquer des jonctions Josephson poss??dant une densit?? de courant critique de 44 A/cm[indice sup??rieur 2] et un produit I[indice inf??rieur c]R[indice inf??rieur n] valant 40 ??V . On retrouve aussi, tel qu???attendu par la th??orie, les oscillations du courant critique de ces jonctions en fonction du champ magn??tique appliqu?? perpendiculairement sur celles-ci. Ces caract??ristiques nous permettent de conclure que nous avons r??ussi ?? produire les meilleures jonctions Josephson de ce type (Re[indice inf??rieur 2???x]Ce[indice inf??rieur x]CuO[indice inf??rieur 4] / Au /supraconducteur m??tallique) r??pertori??es dans la litt??rature. Ainsi, d???apr??s ces r??sultats il est maintenant possible de tenter l???exp??rience sondant la sym??trie du gap supraconducteur dans le Pr[indice inf??rieur 1.85]Ce[indice inf??rieur 0.15]CuO[indice inf??rieur 4] ?? l???aide d???une jonction Josephson en coin.

High-quality platelet single crystals of Tl₂Ba₂CuO₆±δ (Tl-2201) have been grown using a novel time-varying encapsulation scheme, minimizing the thallium oxide loss that has plagued other attempts and reducing cation substitution. This encapsulation scheme allows the melt to be decanted from the crystals, a step previously impossible, and the remaining cation substitution is homogenized via a high-temperature anneal. Oxygen annealing schemes were developed to produce sharp superconducting transitions from 5 to 85 K without damaging the crystals. The crystals' high homogeneity and high degree of crystalline perfection are further evidenced by narrow rocking curves; the crystals are comparable to YSZ-grown YBa₂Cu₃O₆₊δ by both metrics. Electron probe microanalysis (EPMA) ascertained the crystals' composition to be Tl₁.₉₂₀₍₂₎Ba₁.₉₆₍₂₎Cu₁.₀₈₀₍₂₎O₆₊δ; X-ray diffraction found the composition of a Tc = 75 K crystal to be Tl₁.₉₁₄₍₁₄₎Ba₂Cu₁.₀₈₆₍₁₄₎O₆.₀₇₍₅₎, in excellent agreement. X-ray refinement of the crystal structure found the crystals orthorhombic at most dopings, and their structure to be in general agreement with previous powder data. Cation-substituted Tl-2201 can be orthorhombic, orthorhombic crystals can be prepared, and these superconduct, all new results. X-ray diffraction also found evidence of an as yet unidentified commensurate superlattice modulation. The Tl-2201 crystals' electronic structure were studied by X-ray absorption and emission spectroscopies (XAS/XES). The Zhang-Rice singlet band gains less intensity on overdoping than expected, suggesting a breakdown of the Zhang-Rice singlet approximation, and one thallium oxide band does not disperse as expected. The spectra correspond very closely with LDA band structure calculations, and do not exhibit the upper Hubbard bands arising from strong correlations seen in other cuprates. The spectra are noteworthy for their unprecedented (in the high-Tc cuprates) simplicity. The startling degree to which the electronic structure can be explained bodes well for future research in the cuprates. The overdoped cuprates, and Tl-2201 in particular, may offer a unique opportunity for understanding in an otherwise highly confusing family of materials.