Geometry-Induced Chiral Currents in a Mesoscopic Helicoidal Quantum Well

Abstract

We introduce a mesoscopic quantum well whose confinement and chirality emerge solely from the intrinsic torsion of a finite helicoidal metric. This purely geometric construction requires no external gates or fields: the metric itself induces both a harmonic radial potential and a torsion-driven Zeeman term that breaks the $m\leftrightarrow -m$ degeneracy. By imposing hard-wall boundary conditions at $z=\pm L/2$, we quantize the axial motion and obtain a genuinely zero-dimensional helicoidal quantum dot. An exact analytic solution reveals an energy spectrum with chiral splitting linear in both the torsion parameter $\Omega$ and the axial quantum number $n_z$. For realistic InAs nanoroll parameters ($L=100$ nm, $\Omega =5\times 10^6{\mathrm{m}}^{-1}$), this geometric effect results in a measurable splitting of $\sim 0.5$ meV. We propose three viable experimental platforms, ultracold atoms in optical traps, femtosecond-written photonic waveguides, and strain-engineered semiconductor nanorolls, where this torsion-induced phenomenon should be accessible with current technology.

11 pages, 9 figures, 1 table