Monte Carlo Methods And Inductor-Capacitor Network Models In Two Dimensional Superconducting And Magnetic Systems

The first chapter of this book provides a brief history of the important developments in superconductivity. After a general introduction, the superconductor-insulator transition is discussed in regards to open questions in the field and some of the questions tackled in this dissertation. Also, a brief introduction to ferromagnetism and phase transition in ferromagnetic systems is presented. In the second chapter, the results of simulations of three types of random inductor-capacitor (LC) networks on square lattices are presented [1,2]. The dynamical conductivity was calculated using an equation-of-motion method. The critical exponent was extracted at low frequencies. The results suggest that there are three different universality classes and that classical percolative 2D superconductor-insulator transitions (SITs) generically have sigma(omega)-\u3einfinity as omega-\u3e0. The third chapter presents results of simulations of a quantum rotor model describing a Josephson junction array (JJA) in a perpendicular magnetic field B on a square lattice [3]. The SIT is tuned by the ratio of charging energy to Josephson coupling, U/J. Abrupt drops in the magnetization values were observed in the bigger lattices at certain values of B and U/J caused by the formation of vortices. Increasing U/J at a fixed B field causes quantum vortex lattice melting. The magnetization drops to zero around U/J ~ 5 indicating SIT. In the fourth chapter, results from simulations of anisotropic Ising models are presented. These simulations were performed for a Hf2MnC2O2 monolayer under uniaxial strain [4]. The Curie temperature increases with the increasing strain, which means magnetic ordering survives up to higher temperatures under strain. In the fifth and final chapter, important results accrued over the whole dissertation are presented

Non-singular and singular flat bands in tunable acoustic metamaterials

Dispersionless flat bands can be classified into two types: (1) non-singular flat bands whose eigenmodes are completely characterized by compact localized states; and (2) singular flat bands that have a discontinuity in their Bloch eigenfunctions at a band touching point with an adjacent dispersive band, thereby requiring additional extended states to span their eigenmode space. In this study, we design and numerically demonstrate two-dimensional thin-plate acoustic metamaterials in which tunable flat bands of both kinds can be achieved. Non-singular flat bands are achieved by fine-tuning the ratio of the global tension and the bending stiffness in triangular and honeycomb lattices of plate resonators. A singular flat band arises in a kagome lattice due to the underlying lattice geometry, which can be made degenerate with two additional flat bands by tuning the plate tension. A discrete model of the continuum thin-plate system reveals the interplay of geometric and mechanical factors in determining the existence of flat bands of both types. The singular nature of the kagome lattice flat band is established via a metric called the Hilbert-Schmidt distance calculated between a pair of eigenstates infinitesimally close to the quadratic band touching point. We also simulate an acoustic manifestation of a robust boundary mode arising from the singular flat band and protected by real-space topology in a finite system. Our theoretical and computational study establishes a framework for exploring flat-band physics in a tunable classical system, and for designing acoustic metamaterials with potentially useful sound manipulation capabilities.Comment: 11 pages (excluding references) and 7 figure