Screw-dislocation-engineered quantum dot: geometry-tunable nonlinear optics, orbital qubit addressability, and torsion metrology

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 ad hoc potential, while the Aharonov--Bohm phase breaks the usual mleftrightarrow -m symmetry. From the exact spectrum and wave functions, we find: (i) a torsion-controlled optical transition whose energy blue-shifts from sim 6.8 to sim 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=pm1 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 sim 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 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.