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The magnetic flux dependence of order parameter and supercurrent is studiedin a hollow d-wave superconducting cylinder. It is shown that the existence ofline nodal quasiparticles in a pure $d_{x^2-y^2}$ pairing state gives rise toan $hc/e$ periodicity in the order parameter and a first-order quantum phasetransition for a large system size. We demonstrate that the flux periodicity inthe supercurrent is sensitive to the detailed electronic band structure andelectron filling factor. In particular, we find that, in cooperation with theincrease of the cylinder circumference, the $hc/2e$ periodicity can be restoredsignificantly in the supercurrent by avoiding the particle-hole symmetry point.A similar study of a $d_{x^2-y^2}+id_{xy}$ pairing state verifies thepeculiarity of unconventional superconductors with nodal structure.

Restoration of $hc/2e$ Magnetic Flux Periodicity in a Hollow $d$-Wave Superconducting Cylinder