Multiple correlation lengths and type-1.5 superconductivity in $U(1)$ superconductors due to hidden competition between irreducible representations of nonlocal pairing

TL;DR

This paper demonstrates that even single-component superconductors can exhibit multiple coherence lengths due to hidden competition between different pairing symmetries, leading to type-1.5 superconductivity and vortex clustering.

Contribution

It reveals the emergence of multiple coherence lengths in single-component superconductors caused by suppressed subdominant order parameters, a phenomenon previously associated only with multicomponent systems.

Findings

Multiple coherence lengths can exist in nominally single-component superconductors.

Hidden competition between pairing symmetries leads to type-1.5 superconductivity.

Vortex clustering occurs due to the hierarchy of coherence lengths.

Abstract

A fundamental characteristic of a superconducting state is the coherence length $\xi$. Multicomponent superconductors, particularly ones breaking multiple symmetries, are characterized by multiple coherence lengths. Here we show that even, nominally $single$-component superconductors under certain conditions are characterized by multiple coherence lengths. We consider nearest-neighbor pairing interactions on a square lattice that leads to $s$-wave and $d$-wave representations of link superconducting order parameter. We show that even if the subdominant order parameter is completely suppressed in the ground state, it results in multiple correlation lengths with nontrivial hierarchy, resulting in important physical consequences in inhomogeneous solutions. Under certain conditions, this leads to type-1.5 superconductivity, where magnetic field penetration length falls between two coherence lengths, leading to vortex clustering in an external magnetic field.