Integer and fractionalized vortex lattices and off-diagonal long-range order

TL;DR

This paper demonstrates that off-diagonal long-range order (ODLRO) constrains vortex lattice configurations in superconductors, allowing only integer flux vortices for single-component systems and fractional vortices for multi-component systems, regardless of specific microscopic theories.

Contribution

It generalizes known results from Ginzburg-Landau and BCS theories, showing that vortex lattice structures follow from macroscopic coherence and are valid beyond those models.

Findings

Single-component systems have integer flux vortex lattices.

Multi-component systems can host fractional vortices.

Results are valid even outside traditional microscopic theories.

Abstract

We analyze the implication of off-diagonal long-range order (ODLRO) for inhomogeneous periodic field configurations and multi-component order parameters. For single component order parameters we show that the only static, periodic field configuration consistent with ODLRO is a vortex lattice with integer flux in units of the flux quantum in each unit cell. For a superconductor with $g$ degenerate components, fractional vortices are allowed. Depending on the precise order-parameter manifold, they tend to occur in units of $1/g$ of the flux quantum. These results are well known to emerge from the Ginzburg-Landau or BCS theories of superconductivity. Our results imply that they are valid even if these theories no-longer apply. Integer and fractional vortex lattices are transparently seen to emerge as a consequence of the macroscopic coherence and single valuedness of the condensate.