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arXiv:2610.10555

Magnetic localization and spectral asymmetry of a charged particle at a screw dislocation

Claudio Furtado, Omar Mustafa, Hassan Hassanabadi, Abdullah Guvendi

cond-mat.mes-hallphysics.class-phquant-phSubmitted Sep 27, 2026• Announced Sep 29, 2026
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Abstract

We study a charged particle moving outside a spiral (screw) dislocation in a uniform magnetic field. Although the geometry is locally Euclidean, its global screw identification couples the conserved axial and azimuthal quantities through the combination \(\mathcal{J}=\ell-βk\) After eliminating the cyclic coordinates, the radial motion is governed by an inverse-square term determined by $\mathcal{J}$ and a harmonic confining term generated by the magnetic field. The corresponding reduced quantum problem is exactly solvable for $q\mathcal{B}_0\neq0$, yielding an equally spaced spectrum with an orientation-dependent energy shift. The radial probability density depends on $\mathcal{J}$, and opposite values of the screw-modified quantum number have identical spatial profiles but different energies for a fixed magnetic-field orientation. The radial size scales as \(\sqrt{\langle r^2\rangle_n}\propto |q\mathcal{B}_0|^{-1/2}\), with the magnetic length setting the localization scale. At $q\mathcal{B}_0=0$, the confining term vanishes, and the problem reduces to a scale-free inverse-square system. Thus, the screw parameter enters the dynamics through the global coupling of the conserved axial and azimuthal quantities, whereas the magnetic field provides radial confinement and its orientation determines the spectral asymmetry.

Comments
18 pages, 5 figures

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We study a charged particle moving outside a spiral (screw) dislocation in a uniform magnetic field. Although the geometry is locally Euclidean, its global screw identification couples the conserved axial and azimuthal quantities through the combination (\mathcal{J}=\ell-βk) After eliminating the cyclic coordinates, the radial motion is governed by an inverse-square term determined by J\mathcal{J}J and a harmonic confining term generated by the magnetic field. The corresponding reduced quantum problem is exactly solvable for qB0≠0q\mathcal{B}_0\neq0qB0​=0, yielding an equally spaced spectrum with an orientation-dependent energy shift. The radial probability density depends on J\mathcal{J}J, and opposite values of the screw-modified quantum number have identical spatial profiles but different energies for a fixed magnetic-field orientation. The radial size scales as (\sqrt{\langle r^2\rangle_n}\propto |q\mathcal{B}_0|^{-1/2}), with the magnetic length setting the localization scale. At qB0=0q\mathcal{B}_0=0qB0​=0, the confining term vanishes, and the problem reduces to a scale-free inverse-square system. Thus, the screw parameter enters the dynamics through the global coupling of the conserved axial and azimuthal quantities, whereas the magnetic field provides radial confinement and its orientation determines the spectral asymmetry.
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We revisit the effective radial Schrödinger equation for a charged spinless particle in collinear static electric and magnetic fields that was formulated in our earlier work within the tridiagonal representation approach (TRA). In that model the angular factor of the electric coupling is replaced by the orientation parameter C=cos⁡θC=\cosθC=cosθ, the linear Zeeman term is diagonal in the azimuthal quantum number, and the effective field-modified central potential takes the form $V(r)=\Vt(r)+qECr$. Here we show that the same equation can be solved exactly without the TRA, by the Nikiforov--Uvarov (NU) method, once the potential component $\Vt(r)$ is prescribed. Three examples are worked out in closed form: a Kratzer-type component, which yields a linear-plus-Coulomb-plus-inverse-square central potential; a pseudoharmonic-type component, which yields a linear-plus-harmonic-plus-inverse-square potential; and a Hulthén-type component with a repulsive core (Manning--Rosen form), which yields a screened confining potential with a finite number of sss-wave bound states. For each case we obtain the energy spectrum, the normalized eigenfunctions in terms of Laguerre or Jacobi polynomials, the location of the potential minimum, and closed-form radial moments. The spectra are independent of the orientation θθθ and of the electric field, in agreement with the structure found by the TRA, while the field enters through the shape of V(r)V(r)V(r), the radial moments, and the expectation value ⟨V⟩k\langle V\rangle_k⟨V⟩k​. All analytical results are confirmed by an independent finite-difference diagonalization.
We study a single electron confined in a uniform-torsion medium, a continuum model of a screw dislocation density, in a perpendicular magnetic field, and in the presence of an Aharonov--Bohm flux. Torsion alone produces radial confinement without any \textit{ad hoc} potential, while the Aharonov--Bohm phase breaks the usual m↔−mm\leftrightarrow -mm↔−m symmetry. From the exact spectrum and wave functions, we find: (i) a torsion-controlled optical transition whose energy blue-shifts from ∼6.8\sim 6.8∼6.8 to ∼15.5\sim 15.5∼15.5~meV and whose saturation intensity varies by an order of magnitude, enabling geometry-programmable optical switching; (ii) an Aharonov--Bohm-tunable ``angular pseudospin'' formed by the m=±1m=\pm1m=±1 states, with flux-controlled level splitting and asymmetric oscillator strengths that allow selective optical addressability; and (iii) an approximately linear torsion dependence of the transition energy that enables nanoscale torsion metrology with an estimated resolution of ∼105 m−1\sim 10^{5}~\mathrm{m}^{-1}∼105 m−1. In this context, ``torsion'' refers to the experimentally relevant continuum limit of a uniform density of parallel screw dislocations, i.e., a crystal with finite torsion but vanishing curvature, which can, in practice, be engineered and probed in twisted nanowires and strained semiconductor heterostructures. We also show how torsion provides \textit{in situ} control of emitter--cavity detuning and light--matter coupling in cavity QED, in direct analogy with strain tuning of semiconductor quantum dots in nanocavities, but here arising from a purely geometric/topological parameter.
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We investigate the influence of a screw dislocation, characterized by the dislocation parameter, on the optical response of a parabolic GaAs cylindrical quantum wire under the combined effects of temperature, hydrostatic pressure, and the axial magnetic field. Using a torsion-modified metric together with pressure- and temperature-dependent material properties, namely the effective mass and dielectric permittivity, we obtain exact solutions of the Schrödinger equation in terms of Whittaker functions. The screw dislocation introduces a kzk_zkz​-dependent coupling that breaks the symmetry between the angular momentum states mmm and −m-m−m and modifies the centrifugal term in the effective potential. Based on the resulting eigenstates, we evaluate the linear and third-order nonlinear optical absorption coefficients, as well as the corresponding refractive index changes, for the dipole-allowed transitions m=0→+1m = 0 \to +1m=0→+1 and m=0→−1m = 0 \to -1m=0→−1. Our results show that increasing the dislocation parameter produces a pronounced redshift and suppresses the resonance amplitude for the m=0→+1m = 0 \to +1m=0→+1 transition, whereas the m=0→−1m = 0 \to -1m=0→−1 transition exhibits a blueshift accompanied by peak enhancement. We further find that increasing temperature shifts the resonances toward higher photon energies and enhances their amplitudes, while hydrostatic pressure causes a redshift and reduces the peak intensity for both transitions. In addition, the magnetic field strengthens the optical response and induces a blueshift for the m=0→+1m = 0 \to +1m=0→+1 transition, whereas the opposite behavior is obtained for the m=0→−1m = 0 \to -1m=0→−1 transition. We have also examined the behavior of the refractive index changes, which exhibit analogous asymmetric dependence on the dislocation parameter.