Topological Aharonov-Bohm effect around a disclination

On noninertial effects inducing a confinement of a neutral particle to a hard-wall confining potential

“…It is worth mentioning that this assumption is consistent with studies of the analogue effects of the Aharonov-Bohm effect for bound states [28] yielded by the presence of topological defects in quantum rings [29][30][31], where the quantum particle is confined to moving between two concentric cylinder shells with fixed radii ρ and ρ (ρ > ρ ). Moreover, the assumption ηρ 0 1 is also consistent with a particular case studied in [29] given by the confinement a quantum particle to a cylindrical shell that corresponds to a quantum dot described by hard-wall confining potential [32,34,35]. In recent years, the study of the confinement of particles in two-dimensional quantum rings and quantum dots have been made in different models [32][33][34][36][37][38][39][40][41][42][43][44].…”

“…Furthermore, by describing the geometry of the system from the line element (1) or (3), we can see that this approach to studying the confinement of a quantum particle to a hard-wall confining potential via noninertial effects agrees with the geometric approach proposed to Katanaev and Volovich [18] to describe linear topological defects in crystalline solids, which allows us to study the influence of curvature and torsion on the hard-wall confining potential defined by the range (4) and, consequently, on the energy levels (20). As we have discussed above, examples of the influence of topological defects such as disclinations and dislocations on quantum rings have been made in [29,31].…”

“…Thus, we can write σ 3 φ = ±φ = φ . We also have that the operatorsĴ = − ∂ [52], andˆ = − ∂ commute with the Hamiltonian of the right-hand side of (29), thus, we can take the solutions of (29) in the form:…”

“…Substituting the solution (30) into the Schrödinger-Pauli equation (29) and by considering the spin of the neutral particle parallel to axis, we obtain two noncoupled equations for R + and R − . Since we are considering the magnetic dipole moment being parallel to the axis, we can see that there is no torque τ = µ × B on the dipole moment of the neutral particle produced by the magnetic field induced by non-…”

“…Other discussions about the confinement of particles in quantum rings and quantum dots can be found in the literature relating to magnetic quantum rings [35], in the presence of a dislocation [30] and in reference to the influence of curvature effects [45,46]. Hence, by accepting this approximation ηρ 0 1, we can write the Bessel function of first kind in the form [27,29]:…”