Duality symmetry and power-law fading of frustration in a quantum multiconnected superconductor
Sheng Nien Sun, John P. Ralston
DOI 10.1103/PhysRevB.43.5375 · Physical Review B
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Abstract
We generalize the Alexander–de Gennes equations to a new system of superconducting-wire networks, allowing for variation of the cross-sectional area of wires. The generalized equations are solved for a square lattice of different cross-sectional-area ratios λ in the x and y directions. A symmetry of λ→1/λ is related to the Aubry-André duality and an obvious geometric property. We find that even a slight geometric asymmetry can soften the fine structure of the magnetic phase boundary considerably. We obtain a power-law dependence on the parameter λ as λ→∞ and λ→0. For a finite-area ratio λ, we speculate that a simple analytic fit incorporating the dual symmetry is close to the exact nonperturbative behavior. The system is also related analytically to a recent study of Hu and Chen, which revealed a power-law behavior for a rectangular lattice.
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