Some properties of the magnetic response of mesoscopic superconducting rings
This thesis deals with two relatively independent topics pertinent to the physics of mesoscopic multiply connected superconducting samples (rings). In the first Chapter we consider a phenomenon of the entanglement of the center-of-mass and internal degrees of freedom of the Cooper pair which takes place when the size of the system becomes comparable to the characteristic decay length of the pair wave function. We show that this phenomenon provides a universal mechanism for distinguishing between odd and even parity center-of-mass states of the Cooper pair and, in particular, breaks hc/2e periodicity in observable quantities such as magnetic response. The violation of the hc/2e periodicity is usually attributed to the loss of superconductivity. Here we conclude that it is also possible in the superconducting state. In the subsequent Chapters we focus our attention on the topic of the half- quantum vortex. Such an object can exist in systems with spin triplet pairing in which the equal-spin-pairing state is realized. This state is found in the A-phase of 3 He and is currently believed to describe superconductivity of a strongly layered compound Sr2RuO4 . We show that a half-quantum vortex (HQV) should be accompanied by the kinematic spin polarization which is caused by the velocity mismatch between different superfluid components. We also suggest that under appropriate conditions the kinematic spin polarization can provide a handle on the stability of the HQV through the coupling to the external field. We then discuss how the sample’s geometry affects the energetics of the HQV and derive its stability criterion for a cylindrical geometry with arbitrary cross-section. We propose that the presence of a constriction i.e. thinning in the walls of the cylinder can substantially improve the stability of HQV. Results of Chapter 1 and partially Chapter 2 have been presented in the following publications: V. Vakaryuk Phys. Rev. Lett. 101, 16 (Oct 2008), 167002; V. Vakaryuk, A.J. Leggett Phys. Rev. Lett. 103, 5 (Jul 2009), 057003.
superconductivity, half-quantum vortex, magnetic response, mesoscopic, fluxoid
University of Illinois - Urbana-Champaign
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University of Illinois at Urbana-Champaign