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 twist 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 twist-driven Zeeman-like 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 twist rate $$\Omega $$ 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 $$2\hbar \omega \simeq 1.040$$ meV. We propose three viable experimental platforms, ultracold atoms in optical traps, femtosecond-written photonic waveguides, and strain-engineered semiconductor nanorolls, where this twist-induced phenomenon should be accessible with current technology.