Geometry-Induced Chiral Currents in a Mesoscopic Helicoidal Quantum Well

TL;DR

This paper demonstrates that a purely geometric, helicoidal quantum well can induce chiral currents and energy splitting without external fields, with potential for experimental observation in various platforms.

Contribution

The authors introduce a novel geometric quantum well that naturally produces chiral effects and energy splitting through intrinsic torsion, without external gating or magnetic fields.

Findings

Exact analytic energy spectrum with chiral splitting proportional to torsion and axial quantum number.

Measurable energy splitting (~0.5 meV) in realistic InAs nanoroll parameters.

Proposes experimental platforms for observing torsion-induced chiral phenomena.

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, $\Omega = 5\times10^{6} \mathrm{m^{-1}}$), 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.