On an electron in an elastic medium with a spiral dislocation

Abstract

Topological effects of a spiral dislocation on an electron are investigated when it is confined to a hard-wall confining potential. Besides, it is analysed the influence of the topology of the spiral dislocation on the interaction of the electron with a non-uniform radial electric field and a uniform axial magnetic field. It is shown that a discrete spectrum of energy can be obtained in all these cases. Moreover, it is shown that there is one case where an analogue of the Aharonov-Bohm effect for bound states is yielded by the topology of the spiral dislocation.PACS numbers:

Relativistic Landau quantization in the spiral dislocation spacetime

“…The second term of the energy levels (24) corresponds to the (nonrelativistic) Landau levels in the presence of a spiral dislocation. Note that the energy levels (24) are analogous to the Landau levels for a spinless quantum particle obtained in [70]. Therefore, we can see in the nonrelativistic limit that the degeneracy of the Landau levels [92] is broken by the effects of the topology of the spiral dislocation.…”

“…Note that the spatial part of the line element (1) describes the distortion of a circle into a spiral. In this case, the dislocation is parallel to the plane z=0; hence, it corresponds to an edge dislocation in the context to the description of topological defects in solids [70,74,78,85]. Even though we are dealing with a topological defect in the spacetime, we can consider the parameter β to be defined in the range b < < 0 1 in the same way as the description of topological defects in solids [70,74,78,85].…”

“…. Thereby, when  r 0 we can consider x to be very small, and thus, we can assume that the wave function vanishes when  r 0, without loss of generality [70]. Therefore, with the purpose of having the radial wave function well behaved at  ¥ r and  r 0, we can write a solution to equation (19) in the form…”

About the effects of rotation on the Landau levels in an elastic medium with a spiral dislocation

“…and Bakke [1] do not exhibit unit consistency. They did not indicate the chosen units explicitly but we assume that they followed early papers in which they stated that "we shall use the units h = 1, c = 1" [2]. Unfortunately, this expression does not mean anything because we do not know what are actually the units of length, energy, etc,.…”

Duffin-Kemmer-Petiau particles in the presence of the spiral dislocation

“…As shown in Ref. [40,41], the β parameter corresponds to the Burger vector b, that is, β = | b|/2π. It is worth mentioning that the spiral dislocation has the Burger vector which is parallel to the plane z = 0.…”