Geometric Phase and Superconducting Flux Quantization
In a ring of s-wave superconducting material the magnetic flux is quantized in units of $Φ_0 = \frac{h}{2e}$. It is well known from the theory of Josephson junctions that if the ring is interrupted with a piece of d-wave material, then the flux is quantized in one-half of those units due to a additional phase shift of $π$. We reinterpret this phenomenon in terms of geometric phase. We consider an idealized hetero-junction superconductor with pure s-wave and pure d-wave electron pairs. We find, for this idealized configuration, that the phase shift of $π$ follows from the discontinuity in the geometric phase and is thus a fundamental consequence of quantum mechanics.
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