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

TL;DR

This work addresses how the geometry and topology of a host medium can serve as a programmable resource for quantum emitters. It studies a single electron in a uniform-torsion background with a perpendicular magnetic field and AB flux, deriving exact spectra and light-mMatter matrix elements to reveal three functional capabilities: (i) geometry-programmable nonlinear optics where torsion shifts the transition energy and nonlinear saturation threshold, (ii) an AB-tunable angular pseudospin formed by the $m=\pm1$ states with flux-controlled splitting and asymmetric oscillator strengths enabling selective optical addressability, and (iii) nanoscale torsion metrology through spectroscopic readout of screw-dislocation density with a resolution around $10^5\ \mathrm{m^{-1}}$. The results also map naturally onto cavity-QED, where torsion controls emitter–cavity detuning and the light–matter coupling $g$, offering a post-growth geometry-based knob for quantum photonics. Collectively, the findings promote uniform torsion as an active design parameter that unifies confinement, spectroscopy, and photonic coupling in a single analytic platform, with potential for practical torsion-engineered devices and sensors.

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.

Figures (5)

• Figure 1: Geometry-driven blueshift. Transition energy $\Delta E = E_{0,-1}-E_{0,0}$ (in meV) versus torsion density $\tau$. For $B=5T$, $k_z\simeq \pi/(10~\text{nm})$, and $l=0.1$, the optical line moves from $\sim 6.8meV$ at $\tau=0$ to $\sim 15.5meV$ at $\tau = 1.5\times10^{7}~\mathrm{m}^{-1}$, i.e. a $>100\%$ blueshift. This multi-meV, order-unity shift is comparable in magnitude to the strain tuning of semiconductor quantum dots in nanocavities. Here, however, it is driven purely by the torsion density (screw-dislocation density) rather than by externally applied stress.
• Figure 2: Dipole strength and nonlinear threshold. Left axis (solid blue): squared dipole matrix element $|M_{ge}|^2$ for the $\ket{0,0}\to\ket{0,-1}$ transition, showing a non-monotonic dependence on $\tau$ with a maximum near $\tau\sim5\times10^{6}~\mathrm{m}^{-1}$. Right axis (dashed red): saturation intensity $I_{\text{sat}}$ (W/m$^2$) at which $\alpha^{(1)}+\alpha^{(3)}=0$ at resonance. Torsion can lower $I_{\text{sat}}$ down to $\sim 3\times10^{5}~\mathrm{W/m^2}$ near $\tau\sim5\times10^{6}~\mathrm{m}^{-1}$, then drive it back above $10^{6}~\mathrm{W/m^2}$ at higher $\tau$. This demonstrates that torsion sets both the transition energy and the nonlinear optical switching threshold. We emphasize that $I_{\text{sat}}$ here is not injected "by hand": it follows from the analytically accessible wavefunctions and dipole matrix elements of the torsion-confined electron.
• Figure 3: Aharonov--Bohm pseudospin splitting. Flux-controlled splitting $\Delta_{\mathrm{AB}} = E_{0,-1}-E_{0,+1}$ as a function of reduced flux $l=\Phi/\Phi_0$, at fixed $\tau$. The gap grows from $\sim 7.0meV$ at $l=0$ to $\sim 10.8meV$ at $l=0.2$, with an approximately linear slope $\sim 19meV$ per flux quantum. This defines an "angular pseudospin" formed by $m=\pm1$, whose level spacing can be continuously biased by a topological phase (the AB flux) and further strengthened by torsion.
• Figure 4: Selective optical addressability. Normalized oscillator strengths for the $\ket{0,0}\to\ket{0,+1}$ (blue) and $\ket{0,0}\to\ket{0,-1}$ (orange) transitions as a function of reduced flux $l$. At $l=0$, excitation into $m=+1$ dominates. As $l$ increases toward $0.2$, that channel is suppressed (down to $\sim 0.3$), while the $m=-1$ channel is enhanced toward unity. This implements an angular pseudospin ($m=\pm1$) that can be read out and selectively driven by frequency-resolved optics. The strong asymmetry in oscillator strengths implies that the two branches can serve as two addressable optical channels with minimal cross-talk.
• Figure 5: Spectral torsion sensitivity. Torsion responsivity $S_\tau = \partial(\Delta E)/\partial\tau$ in meV per $10^{6}~\mathrm{m}^{-1}$. $S_\tau$ grows from $\sim 0.26$ near $\tau=0$ to $\sim 0.7$ around $\tau\sim10^{7}~\mathrm{m}^{-1}$, and then saturates. Assuming a representative linewidth $\hbar\Gamma \approx 0.25meV$, this corresponds to a torsion resolution $\delta\tau \sim 3.6\times10^{5}~\mathrm{m}^{-1}$. The device therefore acts as a nanoscale "torsionometer." Here "torsion" is the continuum limit of an approximately uniform density of parallel screw dislocations, so the inferred $\delta\tau$ can be interpreted directly as a resolution in screw-dislocation density.