Localization and persistent currents in a quasiperiodic disordered helical lattice

We investigate localization and persistent currents in a helical tight-binding lattice subject to two independent magnetic fluxes and a quasiperiodic on-site potential. Working with non-interacting, spinless fermions under periodic boundary conditions, we solve the model by exact diagonalization and study localization with both inverse and normalized participation ratios. We identify boundaries separating extended, mixed, and localized regimes by constructing a diagram incorporating potential strength and inter-ring coupling. In the metallic regime, persistent currents flowing around both the toroidal and poloidal directions show oscillations whose amplitude decays as disorder grows and vanishes past the localization threshold; in the localized regime, currents become flux-insensitive. We demonstrate that tuning magnetic fluxes, hopping strengths, or quasiperiodic potential amplitudes provides control over the critical disorder threshold. Our results suggest a versatile platform for disorder-and flux-controlled switching between conductive and insulating states.