Current in narrow channels of anisotropic superconductors

We argue that, in channels cut out of anisotropic single crystal superconductors and narrow on the scale of London penetration depth, the persistent current must cause the transverse phase difference provided the current does not point in any of the principal crystal directions. The difference is proportional to the current value and depends on the anisotropy parameter, on the current direction relative to the crystal, and on the transverse channel dimension. An idea on how to measure the transverse phase is proposed.