  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 experimental set up to measure the transverse
phase is proposed.
