Landau levels in the presence of a screw dislocation

Abstract

We study electrons moving in a magnetic field in the presence of a screw dislocation. We focus on the influence of the screw dislocation on the energy spectrum of the electron (or hole) in the magnetic field, in a continuum theory of defects that is isomorphic to three-dimensional gravity. We find exact expressions for the eigenfunctions and eigenvalues of the energy and verify that the infinite degeneracy of the Landau levels is broken by the unusual boundary conditions imposed by the defect.

Landau quantization for a neutral particle in the presence of topological defects

“…Notice that this result is similar to the result obtained for Landau levels in the presence of a screw dislocation in [34]. Again, the infinite degeneracy of the Landau levels obtained in [16] is eliminated due the coupling of the torsion with the angular moment l, which agrees with the results given in [35].…”

“…In the same way as in the previous section, we find that the infinite degeneracy of the Landau levels obtained in [16] is broken since the parameters of the topology η and of the torsion χ in the expression (34) are not integer.…”

“…Recently, the quantum dynamics of relativistic [24,25,26,27,28] and non-relativistic [29,30,31,32] particles in the presence of a topological defects has been studied. The influence of a topological defect to the Landau levels in the presence of a topological defect has been investigated in recent years [33,34]. In [35], the Landau levels have been investigated in the continuum elastic medium with topological defect in the presence of an external magnetic field.…”

Landau quantization for an induced electric dipole in the presence of topological defects

“…In recent works, Landau quantization was studied in the presence of topological defects [35][36][37][38][39]. In [35,36] the influence of a disclination and dislocation in the energy levels was studied when an electron interacts with a magnetic field, respectively.…”

“…In recent works, Landau quantization was studied in the presence of topological defects [35][36][37][38][39]. In [35,36] the influence of a disclination and dislocation in the energy levels was studied when an electron interacts with a magnetic field, respectively. In [37], the Landau levels of an electron interacting with an external magnetic field are obtained with a continuum distribution of topological defects, and it is shown that the presence of topological defects breaks the infinite degeneracy of the Landau levels.…”