Transport characteristics in Hermitian and non-Hermitian Fibonacci rings: a comparative study

We present a comprehensive theoretical investigation of quantum transport, circular currents, and the resulting induced magnetic fields in Fibonacci rings, treating both Hermitian and non-Hermitian (NH) realizations with particular emphasis on parity-time (PT)-symmetric and symmetry-broken configurations. By engineering physically balanced gain and loss distributed according to Fibonacci sequence, we construct distinct ring geometries that either preserve or explicitly violatePTsymmetry, and further examine complementary scenarios obtained via gain-loss sign inversion of the on-site potentials. Employing the nonequilibrium Green's function formalism, we systematically analyze transmission characteristics and bond-resolved current densities to quantify transport and circulating current responses. While the Hermitian limit serves as a reference exhibiting only weak current modulation in the presence of disorder, the introduction of non-Hermiticity results in a dramatic enhancement of both transport and circular currents, accompanied by a strong amplification of the induced magnetic field. Remarkably, we reveal that NH transport is highly sensitive to gain-loss sign inversion and, inPT-broken regimes, exhibits an unconventional system-size dependence governed by the parity of the Fibonacci sequence and hopping correlations. Notably, the circulating current exhibits a nonmonotonic scaling with system size, a feature entirely absent in conventional Hermitian systems. Our results establish NH Fibonacci rings as tunable platforms for amplifying transport responses through symmetry control, Fibonacci parity dependence, and gain-loss sign inversion.