## Open Access Dissertations and Theses

Fall 2012

Thesis

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Physics and Astronomy

Catherine Kallin

John Berlinsky

English

Paul Ayers

#### Abstract

In this thesis, we investigate the properties of a model of an anti-phase modulated d-wave superconductor, particularly in the presence of a magnetic field. This so-called model of $\pi$-striped superconductor has been proposed to describe the decoupling between Cu-O planes in $1/8$ doped La$_{2-x}$Ba$_{x}$CuO$_{4}$. The d-wave superconducting order parameter in a $\pi$-striped superconductor oscillates spatially with period 8 and zero average value. Unlike a uniform d-wave superconductor, this model has non-zero density of states at zero energy and exhibits an extended Fermi surface. Within Bogoliubov-de Gennes theory, we study the mixed state of this model and compare it to the case of a uniform d-wave superconductor. We find a periodic structure of the low-energy density of states, with a period that is proportional to $B$, corresponding to Landau levels that are a coherent mixture of particles and holes. These results are also discussed in the context of experiments which observe quantum oscillations in the cuprates.

Furthermore, within Bogoliubov-de Gennes theory, a semiclassical approximation is used to study quantum oscillations and to determine the Fermi surface area associated with these oscillations in this model. The Fermi surface is reconstructed via Andreev-Bragg scattering, and the semiclassical motion is along these Fermi surface sections as well as between them via magnetic breakdown. Oscillations periodic in 1/B are found in both the positions and widths of the lowest Landau levels. The area corresponding to these quantum oscillations for intermediate pairing interaction is similar to that reported for experimental measurements in the cuprates. A comparison is made of this theory to data for quantum oscillations in the specific heat measured by Riggs et al.

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