Path Integral Formulation of Quantum Propagation in a Dislocated Lattice

Abstract

One simple example of topological disorder is disorder caused by dislocations. A remarkable feature of a dislocation is the following; the numbering of atomic positions is not uniquely determined but rather it is dependent on the path of numbering. In order to make this statement clear, let us consider a straight screw dislocation line in a simple cubic lattice as shown in Fig. l. If we number atomic positions along the path A→C→B, the relative position of B with respect to A is +1 in the x direction, +1 in the y direction and 0 in the z direction. On the other hand, if we number atomic positions along another path A→D→E→B, the relative position of B is +1, +1 and +1 in the three directions respectively. Thus the relative position of B with respect to A is counted differently along different paths.