Quantized Vortices in Superfluid $^3$He

Regan, Robert Charles

doi:https://doi.org/10.21985/n2-nnm4-ae52

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Quantized Vortices in Superfluid $^3$He

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Liquid 3He is the paradigm system for studying exotic quantum mechanical phenomena observed in nature. The normal state of 3He is a strongly-correlated Fermi liquid with strong ferromagnetic spin fluctuations. However, as we cool 3He down to T = 0K, we find something fascinating and unexpected. This exotic fluid remains a fluid even down to absolute zero temperature, thus being called a ‘superfluid’. The ferromagnetic spin fluctuations provide the pairing glue to bind spin-triplet Cooper pairs which form this superfluid state. The superfluid phases of 3He host topological defects known as quantized vortices.Quantized vortices are exotic topological phases of matter that are formed in the superfluid phases of 3He. Vortices are typically formed by rotation of the superfluid, however they have also been observed to be generated even under zero rotation. Different quantized vortices live in different superfluid phases of 3He, and even within a single superfluid phase; there can be multiple different vortex phases of matter. Understanding the energetics and structures of quantized vortices in the superfluid phases is an important theoretical task. Symmetry breaking and phase transitions are another fundamental theme in condensed matter physics. The quantized vortex can have a variety of different kinds of symmetries and structures, they are connected to one another by phase transitions. Superfluid 3He is again the ideal candidate to exhibit and look for such phenomena. The vortex phases within the bulk phases of superfluid 3He have different symmetries and are connected by first-order phase transitions. The vortex phases of the confined phases of superfluid 3He have different symmetries but are now connected by second-order phase transitions. Equilibrium and metastable phase transitions between vortices is driven by symmetry- breaking and energetics. In this thesis, I calculate the structure of vortices and vortex phase diagrams in multiple phases of superfluid 3He. I first investigate the stability of singly-quantized vortices in the B phase of 3He, and calculate the phase diagram to determine the regions of stability for both equilibrium and metastable vortex phases in rotating superfluid 3He-B. I then stabilize confined phases of superfluid 3He in Nafen, and investigate half-quantum vortices within these phases of matter. I calculate the regions of energetic stability for the half-quantized vortices and determine the vortex phase diagram in these confined phases. Lastly, using the quasiclassical Eilenberger theory, I calculate the structure and excitation spectrum of half-quantum vortices in confined superfluid 3He.

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