X-Nico

Fractional vortices

LJJ reacts to the phase discontinuity by bending the Josephson phase $\backslash phi(x)$ in the Josephson penetration depth

where $d\; I$ is the thickness of the Josephson barrier (usually insulator), $d\; \{1,2\}$ are the thicknesses of superconducting electrodes, and $\backslash lambda\; \{1,2\}$ are their London penetration depths.

Long Josephson junction

In superconductivity, a long Josephson junction (LJJ) is a Josephson junction which has one or more dimensions longer than the Josephson penetration depth $\backslash lambda\; J$.

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where spatial coordinate is normalized to the Josephson penetration depth $\backslash lambda\; J$ and time is normalized to the inverse plasma frequency $\backslash omega\; p^\{-1\}$.

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where subscripts $x$ and $t$ denote partial derivatives with respect to $x$ and $t$, $\backslash lambda\; J$ is the Josephson penetration depth, $\backslash omega\; p$ is the Josephson plasma frequency, $\backslash omega\; c$ is the so-called characteristic frequency and $j/j\; c$ is the bias current density $j$ normalized to the critical current density $j\; c$.

see also