PIERLS-NABARRO POTENSIAL OF TOPOLOGICAL SOLITONS IN DISCRETE SYSTEMS

摘要

Topological solitons in continuous systems can be at rest, having any position along the spatial coordinate. The situation changes for discrete systems, when the energy of a soliton depends on its position relative to the lattice. The dependence of the energy of a soliton on its spatial coordinate in a discrete system is called the Peierls-Nabarro potential, and the difference between the maximum and minimum energy is called the height of the Peierls-Nabarro potential. The presence and height of this potential determine, in particular, the mobility of topological solitons and the minimum energy required for the motion of a soliton along the lattice. Crystals are discrete media for such topological solitons as dislocations or domain walls, on the mobility of which, for example, the flow stress of metals depends. The minimum shear stress required to activate the slip of dislocations is called the Peierls stress, which has been estimated for many metals and alloys by molecular dynamics and ab initio modeling. The aim of this work is to review various discrete models that support topological solitons, in which the Peierls-Nabarro potential can be significantly reduced or even reduced to zero. The derivation of discrete models free of the static Peierls-Nabarro potential was carried out by a number of authors using analytical calculations for one-dimensional nonlinear chains. Several classes of such models are constructed, for some of them the law of conservation of energy is fulfilled, for others - the law of conservation of momentum. These theoretical results are discussed in relation to Peierls stresses for dislocations in various crystals. The general conclusion of the studies carried out is that the discreteness of the medium does not exclude the high mobility of topological solitons.