The stress field and energy of screw dislocation in smectic-A liquid crystals and on the mistakes of the classical solution

The mistakes of the classical solution of screw dislocations in smectic-A liquid crystals are pointed out. This reveals a serious problem of the well-known theory, which may be named de Gennes-Kleman-Pershan paradox, for many decades in the scientific community of liquid crystal study. The correct solution is given in this letter in terms of simplest, elementary and straightforward solution method. Furthermore, the stress filed and energy of dislocation are discussed in detail. The present article gives a corrected stress field and dislocation energy as well.