On the effect of boundaries on confined vortex matter systems

• Main Author: Tomlinson, Austin Alexander
• Published: University of Birmingham 2018
• Subjects: 500; QC Physics
• Online Access: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.753071

In this thesis, we investigate the effects of boundaries on confined superconducting vortex matter systems. We are primarily interested in understanding the properties of the so-called `row-drop' transition in a density-driven, confined flow channel, reported by J. Watkins. We present numerical and analytic calculations that reveal chaos, structural progression, and novel energetic behaviour. Firstly, we study a cylindrical geometry of confined vortices. Vortices align to form a regular structure that wraps around the cylinder in a commensurate fashion. We find a set of analytic equations and solve them exactly to find all possible lattices. Combining numerical results with energetic arguments enables us to construct the phase diagram of structural ground states for arbitrary circumference and density. Following this, we generalise the results from the cylinder to a numerical study of a conical geometry of flowing vortices. We are able to accurately predict the lattice structures given the geometry of the cone and the density of vortices on its surface. By developing the theory of lattice structures on the cylinder, we propose a way of generating a single flowing lattice on the cone, subject to a source and sink reservoir of vortices at either end. Numerical simulations confirm this proposition. Finally, we simulate vortices confined to a narrow, constricted channel constructed out of static, pinned vortices. By carefully controlling system parameters, we observe the emergence of chaotic behaviour centred at the aperture of the constriction. We present results diagrammatically and analyse them using established techniques to extract Lyapunov exponents from time series data.