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The variation of θ(x̃) causes the appearance of another length scale of φ. This is the length (Formula presented) over which φ varies by about π taking advantage of the fluctuation of θ. Note that this length is analogous to that found in the context of pinning of charge density wave on random impurities [see H. Fukuyama and P.A. Lee, Phys. Rev. B 17, 535 (1978).
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) to be (Formula presented)=(4(Formula presented)/3(Formula presented)(Formula presented)((Formula presented)/d(Formula presented)(d/σ(Formula presented), which is larger than (Formula presented) and in our case also larger than the linear extension L of the interface. Note that (Formula presented) increases with growing ratio (Formula presented)/d. In our discussion we need not to take (Formula presented) into account. The "wandering" of φ is, however, an interesting phenomenon which is not found in ordinary Josephson junctions
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P.A. Lee and T.M. Rice, Phys. Rev. B 19, 3970 (1979)]. This length (Formula presented) is easily estimated (in case d≪&ξtilde;) to be (Formula presented)=(4(Formula presented)/3(Formula presented)(Formula presented)((Formula presented)/d(Formula presented)(d/σ(Formula presented), which is larger than (Formula presented) and in our case also larger than the linear extension L of the interface. Note that (Formula presented) increases with growing ratio (Formula presented)/d. In our discussion we need not to take (Formula presented) into account. The "wandering" of φ is, however, an interesting phenomenon which is not found in ordinary Josephson junctions.
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