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

The ratio of magnetic field penetration length λ and superconducting coherence length ξ is a defining quantity that governs magnetic response and underpins the conventional type-I and type-II classification of superconductors. While multicomponent superconductors are known to exhibit multiple coherence lengths with rich and often exotic behavior, single-component superconductors are traditionally assumed to be fully characterized by a single Ginzburg-Landau parameter. Here we revisit this concept. We demonstrate that even nominally single-component superconductors are, in general, intrinsically characterized by multiple coherence lengths. Specifically, we analyze a common physical situation in which a subdominant pairing channel is fully suppressed in the ground state, yielding a nominally single-component superconducting ground state. We show that, nonetheless, proximity to a competing pairing instability generically gives rise to multiple correlation lengths with a nontrivial hierarchy. This has consequences for all inhomogeneous states. Especially near a competing pairing instability, the magnetic field penetration depth lies between two distinct coherence lengths, leading to a breakdown of the conventional type-I and type-II dichotomy and enabling the coexistence of vortex clusters and Meissner domains. More broadly, we find that superconducting states cannot, in general, be classified by a single fundamental length scale, even in ostensibly conventional single-component systems.