Geometry-Induced Chiral Currents in a Mesoscopic Helicoidal Quantum Well

• URL: http://arxiv.org/abs/2507.05015v1
• Date: Mon, 07 Jul 2025 13:56:16 GMT
• Title: Geometry-Induced Chiral Currents in a Mesoscopic Helicoidal Quantum Well
• Authors: Edilberto O. Silva,
• Abstract summary: We introduce a mesoscopic quantum well whose confinement and chirality emerge solely from the intrinsic torsion of a finite helicoidal metric.<n>We propose three viable experimental platforms, ultracold atoms in optical traps, femtosecond-written photonic waveguides, and strain-engineered semiconductor nanorolls.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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