Organic conductors are of considerable interest to the condensed matter community. In contrast to conventional metal conductors, these organic materials allow for large variability in their construction giving both quasi-one and two dimensional behavior. Organic superconductors also give useful insight into the properties of general superconductivity as well as insight into the properties of strongly correlated electronic materials. These materials exhibit interesting phenomena like spin-Peierls, antiferromagnetic, and superconducting phases. The aim of this thesis is not only to inform the reader of various studies into organic superconductors but also to advance research into these materials through massively parallel numerical methods. This thesis will cover two studies: a quantum Monte Carlo study on an infinite one-dimensional chain and an exact diagonalization study on a 16-site two-dimensional lattice. These studies will be used to better understand the charge and bond behavior of quasi-one dimensional 1/4illed organic superconductors.

We use a combination of Density Functional Theory and Dynamical Mean Field Theory (DFT+DMFT) to study electronic correlations in unconventional superconductors, with a focus on nickelate analogs of cuprate superconductors. We study the infinite layer nickelate superconductor NdNiO₂ in parallel with the isostructural CaCuO₂. Our results point to superconductivity in the nickelate being cupratelike, with correlations dominated by a hybrid Ni-𝑑_{𝑥²-𝑦²} and O-𝑝 band, and with the extra bands not contributing substantially to the superconducting state. We find that the infinite layer nickelate NdNiO₂ and the trilayer nickelate Pr₄Ni₃O₈ are virtually identical in terms of correlation physics when compared at the same chemical doping, despite the differences in Fermiology, indicating that the number of layers can stand in for chemical doping for some properties related to electronic correlations. We find that as opposed to in narrow window DFT+DMFT, in wide window DFT+DMFT the choice of downfolding procedure leads to very different results. This is an important ambiguity in the method that must be resolved or the method is incomplete by itself. We also study Sr₂MoO₄ in parallel with the Hund's superconductor Sr₂RuO₄, and find that Sr₂MoO₄ is a particle-hole dual of Sr₂RuO₄ but without the van Hove singularity at the Fermi level, which disentangles the influence of the van Hove singularity from Hund's physics. We show that Sr₂MoO₄ has a characteristic Hund's peak on the occupied of the spectral function, indicating that the peak should be observable by photoemission experiments.

We investigate the nonequilibrium steady state of driven magnetic flux lines in type-II superconductors subject to strong point or columnar pinning centers and the aging dynamics of nonequilibrium relaxation process in the presence of weak point pinning centers. We employ a three-dimensional elastic line model and Metropolis Monte Carlo simulations. For the first part, we characterize the system by means of the force-velocity / current-voltage curve, static structure factor, mean vortex radius of gyration, number of double-kink and half-loop excitations, and velocity / voltage noise features. We compare the results for the above quantities for randomly distributed point and columnar defects. Most of both numerical works have been done in two-dimensional systems such as thin film in which the structure of flux lines is treated as a point-like particle. Our main point of investigation in this paper is to demonstrate that the vortex structure and its other transport properties may exhibit a remarkable variety of complex phenomena in three-dimensional or bulk superconductors. The second part devotes to the study of aging phenomena in the absence of a driving force in disordered superconductors with much weaker point disorder. By investigating the density autocorrelation function, we observe all three crucial properties of the aging phenomena; slow power-law relaxation, breaking of time-translation invariance, and the presence of the dynamical scaling. We measure the dynamical exponents b and lambda_c/z and compare to other work. We find exponent values increase for increasing pinning strength, smaller interaction range, lower temperature, and denser defect density while the exponents measured in other approach tend to decrease. / Ph. D.

Applications, converter topologies, and control schemes are examined for superconductive magnetic energy storage (SMES) systems. Diurnal load leveling for electric utilities and compensation for fluctuations in photovoltaic (PV) power generation are the primary applications discussed. It is demonstrated that a SMES system implemented with standard AC/DC converters offers energy storage capacity large enough, and dynamic response fast enough, to compensate for PV fluctuations due to changes in weather conditions. The method of control is developed so that the charging and discharging of the SMES system are changed in response to PV fluctuations, and the combined SMESIPV power output is smooth and controllable. An innovative control scheme is introduced for SMES that can simultaneously regulate real power and voltage independently without hardware modifications to the standard ACIDC bridge arrangement normally used for coordinated control of real and reactive power. The combination of SMES and PV systems could benefit from DCIDC converters that take advantage of the DC nature of both. It is established that DClDC converters can respond with sufficient speed to handle variations in PV power. A converter topology is devised where two DC/DC converters in cascade effectively maintain a PV array at its maximum power point and simultaneously control a SMES system to compensate for PV fluctuations. An alternative cascade configuration of an AC/DC converter with a DCIDC converter is proposed that could significantly reduce the reactive power requirements and improve the operational characteristics of a large scale SMES system connected to the utility grid. / Master of Science

Superconductor electronics based on the Single Flux Quantum (SFQ) technology are considered a strong contender for the ‘beyond CMOS’ future of digital circuits because of the high speed and low power dissipation associated with them. In fact, digital operations beyond tens of GHz have been routinely demonstrated in the SFQ technology. These circuits have widespread applications such as high-speed analog-to-digital conversion, digital signal processing, high speed computing and in emerging topics such as control circuitry for superconducting quantum computing. Rapid Single Flux Quantum (RSFQ) circuits have emerged as a promising candidate within the SFQ technology, with information encoded in picosecond wide, milli-volt voltage pulses. As is the case with any integrated circuit technology, scalability of RSFQ circuits is essential to realizing their applications. These circuits, based on the Josephson junction, require a DC bias current for the correct operation. The DC bias current requirement increases with circuit complexity, and this has multiple implications on circuit operation. Large currents produce magnetic fields that can interfere with logic operation. Furthermore, the heat load delivered to the superconducting chip also increases with current which could result in the circuit becoming ‘normal’ and not superconducting. These problems make reduction of the bias current necessary. Serial Biasing (SB) is a bias current reduction technique, that has been proposed in the past. In this technique, a digital circuit is partitioned into multiple identical islands and bias current is provided to each island in a serial manner. While this scheme is promising, there are multiple challenges such as design of the driver-receiver pair circuit resulting in robust and wide operating bias margins, current management on the floating islands, etc. This thesis investigates SB in a systematic manner, focusing on the design and measurement of the fundamental components of this technique with an emphasis on reliability and scalability. It presents works on circuit techniques achieving high speed serially biased RSFQ circuits with robust operating margins and the experimental evidence to support the ideas. It develops a framework for serial biasing that could be used by electronic design tools to automate design and synthesis of complex RSFQ circuits. It also investigates Passive Transmission Lines (PTLs) for use as passive interconnects between library cells in a complex design, reducing the DC bias current required by the active circuitry.

The optical spectroscopy techniques have been used to investigate left-handed behavior of metamaterials as well as the electron-bosonic spectral functions (or Bosonic spectra) of high-transition-temperature superconductors (or high-Tc superconductors) in the research work of this thesis. The periodic double-ring split-ring resonator (SRR) array was one of the first proposed magnetic metamaterials which could give rise to a negative magnetic permeability (μ<0). In the traditional design of negative index metamaterials, the SRR arrays were combined with continuous metallic wires that provide a negative electric permittivity (∊<0). However, the requirement of an unbroken electrical connection between unit cells would be challenging in building contoured devices. In our study, we carefully examine the electromagnetic properties of the double-ring SRR arrays on silicon substrates in the mid-infrared frequency regime experimentally and numerically. For light at normal incidence, we observe that an electric resonance in the outer ring and a magnetic resonance in the inner ring exist at similar frequencies in one of our samples, which suggests that the double-ring SRR array could have simultaneous a negative permittivity and a negative permeability, or a left-handed behavior. Our conjectures are confirmed by the numerical simulations. We also propose a new left-handed metamaterial composed of two single-ring SRRs in each unit cell. The left-handed behaviors in our designs originate from the SRR structure itself only and therefore, there are no metallic continuous wires involved compared to the conventional left-handed SRR metamaterials. The high-Tc superconductor samples studied here are highly under-doped YBa2Cu3O6.35 (YBCO6.35), nearly optimally doped monolayer HgBa2CuO4+ઠ (Hg1201), Zn- and Ni- doped Bi2Sr2CaCu2O8+ઠ (Bi2212) single crystals. We experimentally determine the optical constants of the samples and numerically extract the electronboson spectral functions from the optical scattering rate by either an analytic formula or a maximum entropy inversion technique. We find that the bosonic mode obtained from the optical data is consistent with a peak in the q-averaged susceptibility seen in the magnetic neutron scattering studies. The comparisons of the bosonic spectra between YBCO6.35 and YBCO6.50, monolayer Hg1201 and trilayer Hg1223 (HgBa2Ca2Cu3O8+ઠ), Zn-doped and Ni-doped Bi2212 characterize the variation of the bosonic spectra with the hole concentration, Tc as well as the magnetic and nonmagnetic atom substitution. / Thesis / Doctor of Philosophy (PhD)

Almost a century after its discovery, superconductivity (SC) is still the most challenging and fascinating topic in condensed matter physics. Organic superconductors show exotic phases and phase transitions with a change in temperature or pressure. In this dissertation, we studied the phases and phase-transitions in one-dimensional (1D) and two-dimensional (2D) organic materials. This dissertation itself is a group of three sub-projects. In project (i), we studied the properties of a novel state “paired electron crystal” (PEC) in the quarterfilled Hubbard model to understand the phases and properties of 2D organic materials. We also studied the effects of charge and spin frustration on the 2D strongly correlated quarterfilled band. Our conclusions are based on exact diagonalization (ED) studies that include electron-electron and adiabatic electron-phonon interactions. For moderate to strong frustration, the dominant phase is a novel spin-singlet PEC. We discuss the implications of the PEC concept for understanding several classes of quarterilled band materials that display unconventional superconductivity. In project (ii), we studied the thermodynamics of a zigzag ladder model, applicable to quasi-1D organic materials. Using the quantum Monte Carlo (QMC) method, we studied the thermodynamics of charge ordering in quarterilled quasi-1D organic charge transfer solids (CTS). Previous theoretical studies on these CTS have focused on ground state properties or purely 1D systems. In the zigzag ladder, no separate high-temperature ordering is expected; instead the ladder is metallic at high temperature, and as temperature decreases, a single transition to the PEC state with a spin-gap takes place. In project (iii), we studied superconducting pairing correlation and metal-insulator transitions in the halfilled Hubbard model. We employed the Hubbard model and used the path integral renormalization group (PIRG) method for this study. Antiferromagneticmediated SC was suggested for small to large frustration in anisotropic triangular lattices. Previous work on the halfilled Hubbard model using the ED method was successful in showing the absence of d-wave SC on a small anisotropic triangular lattice. We extended this study to larger lattices to investigate the existence of long-range order of superconducting pair-pair correlations. We also show the absence of d-wave SC in this model on larger lattices.

The first project of this dissertation focuses on an extension of the Path Integral Renormalization Group (PIRG) method to the extended Hubbard model (EHM) including on-site U and a nearest-neighbor interaction V. The PIRG method is an efficient numerical algorithm for studying ground state properties of strongly correlated electron systems. A major advantage of the PIRG is that it is free from the Fermion sign problem. Many observables can be calculated using Wick’s theorem. The EHM is particularly important in models of charge-transfer solids (CTS) and at 1/4illing the V interaction drives a charge-ordered state. We test the method with comparisons to small two-dimensional (2D) clusters and long one-dimensional (1D) chains. The second project of this dissertation focuses on the Coulomb enhancement of superconducting pair-pair correlations in frustrated quarterilled band lattice systems. A necessary condition for superconductivity (SC) driven by electron correlation is that electronelectron (e-e) interactions enhance long range superconducting pair-pair correlations relative to the noninteracting limit. We present high-precision numerical calculations within the 2D Hubbard model on up to 100 sites showing that long range superconducting pair correlations are enhanced only for electron density 0.5. At all other fillings e-e interactions suppress pair correlations. We argue that the enhancement of pairing is due to a tendency to form local spin singlets at density 0.5. Our work provides a key ingredient to the mechanism of SC in the 2D organic-CTS superconductors, as well as in many other unconventional superconductors with frustrated crystal lattices and density 0.5. In the third project we apply our proposed concept to a real material, kappa-(BEDTTTF)2X. We present numerical results for 32 and 64 site lattices using the Constrained Path Monte Carlo and PIRG methods over a wide range of carrier density. We show that superconducting pair-pair correlations in this model are enhanced by e-e interactions for d-wave pairing symmetry uniquely for a hole density close to quarterilling. Our results indicate that this enhancement of superconductivity is not related to the presence of antiferromagnetic order, but to the strong tendency to spin-singlet formation in the quarterilled band.

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