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

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 \(\mathcal{J}=\ell-\beta k\) 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.

Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Classical Physics (physics.class-ph); Quantum Physics (quant-ph)

arXiv:2610.10555 [cond-mat.mes-hall]

(or arXiv:2610.10555v1 [cond-mat.mes-hall] for this version)

https://doi.org/10.48550/arXiv.2610.10555 Focus to learn more arXiv-issued DOI via DataCite

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