Fractional Quantization of the Magnetic Flux in Cylindrical Unconventional Superconductors

The magnetic flux threading a conventional superconducting ring is typically quantized in units of Phi(0) = hc/2e. The factor of 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 were observed.