Fractional Flux Quantization in Loops of Unconventional Superconductors

TL;DR

This paper proposes that unconventional superconductors can exhibit fractional magnetic flux quantization, such as at half-integer multiples of the standard flux quantum, due to spatially modulated pairing states with coexisting condensates.

Contribution

It introduces a mechanism for fractional flux quantization involving modulated pairing states with different Cooper pair momenta, relevant to cuprate superconductors.

Findings

Existence of energy minima at fractional flux values, especially at multiples of .

Coexistence of condensates with different center-of-mass momenta.

Relevance to observed  and  flux periodicities in cuprates.

Abstract

The magnetic flux threading a conventional superconducting ring is typically quantized in units of $\Phi_0=hc/2e$. The factor 2 in the denominator of $\Phi_0$ originates from the existence of two different types of pairing states with minima of the free energy at even and odd multiples of $\Phi_0$. Here we show that spatially modulated pairing states exist with energy minima at fractional flux values, in particular at multiples of $\Phi_0/2$. In such states condensates with different center-of-mass momenta of the Cooper pairs coexist. The proposed mechanism for fractional flux quantization is discussed in the context of cuprate superconductors, where $hc/4e$ flux periodicities as well as uniaxially modulated superconducting states were observed.