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↔−m symmetry. From the exact spectrum and wave functions, we find: (i) a torsion-controlled optical transition whose energy blue-shifts from
∼6.8 to
∼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=±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. 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.
We need to solve a suitable exponential form of the position-dependent mass (PDM) Schrödinger equation with a charged particle placed in the Hulthen plus Coulomb-like potential field and under the actions of the external magnetic and Aharonov–Bohm (AB) flux fields. The bound state energies and their corresponding wave functions are calculated for the spatially-dependent mass distribution function of interest in physics. A few plots of some numerical results with respect to the energy are shown.