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arXiv:2511.13920

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

Edilberto O. Silva

cond-mat.mes-hallquant-phSubmitted Nov 17, 2025• Announced Nov 19, 2025
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Abstract

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 $m\leftrightarrow -m$ 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 $\sim 10^{5}~\mathrm{m}^{-1}$. 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.

Comments
10 pages, 5 figures

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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 $m=\pm1$ 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 $\sim 10^{5}~\mathrm{m}^{-1}$. 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 investigate the optical response of a conduction electron in a helically twisted mesoscopic medium containing a screw dislocation and a uniform torsional background, in the presence of an axial magnetic field and an Aharonov--Bohm flux. We show that the coupling between longitudinal motion and the geometric background produces an effective in-plane confinement, allowing bound states to emerge without the need for an external radial potential. Exact analytical solutions are obtained for the energy spectrum and radial wave functions, and these results are used to evaluate linear and third-order nonlinear absorption, changes in the refractive index, the photoionization cross section, and the oscillator strength. The combined action of torsion, magnetic field, and topological defect increases the interlevel spacing, compresses the radial electronic distribution, and breaks the dynamical symmetry between opposite angular-momentum channels, leading to strongly asymmetric and state-resolved optical spectra. Under intense optical excitation, the nonlinear contribution can overcome linear absorption, driving the system into a negative-absorption regime and enabling geometry-controlled optical gain. These results establish torsion and defect engineering as effective tools for tuning confinement, resonant energies, and selective amplification in mesoscopic nanophotonic platforms operating in the mid-infrared and terahertz ranges.
We investigate the nonlinear optical response of a two-dimensional mesoscopic quantum ring subjected to a spiral dislocation, with emphasis on third-harmonic generation (THG). The topological defect is modeled through a torsion-induced deformation of space, which modifies the effective metric without introducing curvature. By combining the minimal-coupling prescription in curved space with a radial ring confinement and a perpendicular magnetic field, we derive the effective radial Schrödinger problem, obtain the bound states, and evaluate the nonlinear susceptibilities within the electric-dipole approximation. We show that the axial symmetry of the topologically deformed ring preserves the dipole selection rule Δm=±1Δm=\pm 1Δm=±1 and therefore suppresses second-harmonic generation, while THG remains allowed through multistep transition chains. The study is further expanded through three complementary analyses that can be implemented without changing the Hamiltonian: a dephasing-controlled study of spectral resolution, three-dimensional waterfall spectra showing the dependence on βββ and BBB, and a channel-resolved decomposition of the THG amplitude. Together, these results establish the spiral dislocation as a robust geometric knob for tuning nonlinear optical activity in mesoscopic ring-shaped nanostructures.
We study how a uniform torsion background, modeling a continuous density of screw dislocations and induces effective spatial noncommutativity and reshapes the energy spectrum of a free quantum particle. Within the geometric theory of defects, the metric yields a first-order (magnetic-like) coupling in the transverse dynamics, equivalent to an effective magnetic field BeffB_{eff}Beff​ proportional to pzOmegap_z Omegapz​Omega, where OmegaOmegaOmega encodes the torsion strength. In the strong-coupling (Landau) regime, the planar coordinates obey [x,y] != 0 and the spectrum organizes into Landau-like levels with a slight electric-field-driven tilt and a uniform shift. Thus, increasing OmegaOmegaOmega drives the system continuously toward the familiar Landau problem in flat space, with torsion setting the noncommutativity scale and controlling the approach to the Landau limit.
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 J=ℓ−βk\mathcal{J}=\ell-βkJ=ℓ−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 ⟨r2⟩n∝∣qB0∣−1/2\sqrt{\langle r^2\rangle_n}\propto |q\mathcal{B}_0|^{-1/2}⟨r2⟩n​​∝∣qB0​∣−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.
Tuning spin-orbit coupling is essential in controlling both spin and charge in confined semiconductor nanostructures, yet it is rarely a truly controllable parameter. Here, we show control over the spin-orbit Hamiltonian in quantum dots and the resulting quantum states by tailoring the confinement potential with atomic-scale precision. Using scanning tunnelling microscopy and spectroscopy, we pattern individual Cs ions into designer quantum dot structures on the surface of indium antimonide, in which electrons from a two-dimensional electron gas are confined with chosen in-plane electric-field gradients. We then quantify the atomic level structure, both spatially resolving the orbital character of the electronic states and their magnetic-field evolution. We demonstrate that the level structure, including the induced zero-field splitting, can be tailored by the designed geometry of the local electric fields. These effects can be described using a Hamiltonian that allows consistent treatment of the confinement-induced spin-orbit coupling beyond the conventional Bychkov-Rashba description. This Hamiltonian is derived from a multiband k.p model and takes the energy dependence of the relevant physical parameters into account. Such precise control of spin-orbit coupling in semiconductor quantum dots is relevant to quantum and spintronic technologies.
Twisted light carries orbital angular momentum (OAM) and can drive excitations of confined, interacting electrons that are dark to uniform dipolar probes. Here we show how this ``beyond-Kohn's-Theorem'' optical channel can become a concrete control primitive for quantum computing. Correlation sectors in few-electron quantum dots -- characterized by the relative angular momentum quantum number -- form a tunable ladder of many-body states that are robust in the limited sense of symmetry-protected selection rules and persistent chiral spectroscopic fingerprints; full topological gap protection requires three or more electrons. A twisted-light pulse with prescribed OAM index and polarization provides fast optical write, read, and scalable addressing of these sectors via the selection rule Δ∣m∣=±(l+σ)Δ|m|=\pm(l+σ)Δ∣m∣=±(l+σ). In the analytically solvable Calogero (1/r21/r^21/r2) interaction limit, both the energy spectrum and the twisted-light matrix elements are closed-form functions of the interaction strength, allowing gate parameters (Rabi frequency, qubit frequency, anharmonicity, and leakage rates) to be written down explicitly. We map these results onto a universal single-qubit gate set, propose a concrete two-qubit entangling mechanism via state-dependent Coulomb coupling between adjacent dots, and identify the dominant decoherence channel (quadrupolar charge noise). A semi-analytic N=3N=3N=3 extension using the 1/N1/N1/N expansion provides a design-level scaffold for the topological roadmap, including quasihole sector addressing. The central operational message is that twisted light enables WRITE (pulse-create a correlation sector), READ (spectroscopically diagnose correlations), and SCALE (optical addressing via spatial light modulator) in a unified photonic control layer. Throughout, screened and Coulomb interactions preserve the same qualitative chiral fingerprints established in the solvable limit.