Theory of equilibrium flux lattice in UPt3 under magnetic field parallel to hexagonal crystal axis

investigate Abrikosov lattice structures in the unconventional superconduct or UPt3 under magnetic field parallel to the hexagonal crystal axis. Only t he two-dimensional E-2 superconducting state among the many other states of different symmetry is compatible with the recent observation [A. Huxley et al.. Nature (London) 406, 160 (2000)] of the flux lattice in the A phase m isaligned with crystallographic directions. It is shown that the inequality of the London penetration depths in the basal plane directions resulting f rom the superposition of hexagonal crystal and superconducting state anisot ropies leads fur E-2 to a slightly distorted triangular flux lattice.