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

TL;DR

This paper compares transport and magnetic properties of Hermitian and non-Hermitian Fibonacci rings, revealing how non-Hermiticity amplifies currents and magnetic responses, with sensitivity to system size, symmetry, and gain-loss configurations.

Contribution

It introduces a detailed theoretical analysis of non-Hermitian Fibonacci rings, highlighting their potential for enhanced current-driven magnetic responses compared to Hermitian systems.

Findings

Non-Hermitian rings show amplified transport and circular currents.

Current response is highly sensitive to gain-loss sign reversal.

Current scaling with system size is unconventional and depends on Fibonacci parity.

Abstract

We present an extensive theoretical analysis of transport and circular currents and the associated induced magnetic fields in Fibonacci rings, explored in both Hermitian and non-Hermitian descriptions, with particular attention to configurations preserving or breaking PT symmetry. By engineering physically balanced gain and loss following a Fibonacci sequence, we realize two distinct geometrical configurations in which the ring either preserve or explicitly break PT symmetry, and further explore complementary realizations obtained by reversing the signs of the on site potentials. Using the non equilibrium Green's function (NEGF) formalism, we analyze transmission properties and bond current densities to quantify both transport and circulating currents. A comparison with the Hermitian limit establishes a clear baseline, where the ring supports only weak responses upon introducing disorder. In sharp contrast, non-Hermiticity leads to a pronounced amplification of transport and circular currents, and hence of the induced magnetic field. We further demonstrate that non-Hermitian transport is highly sensitive to gain and loss sign reversal and, in the non-PT-symmetric case, exhibits an unconventional dependence on system size governed by the parity of the Fibonacci sequence and hopping correlations. Remarkably, the current does not decay monotonically with increasing system size, revealing a distinct scaling behavior absent in conventional Hermitian systems. Our results highlight non-Hermitian quasiperiodic rings as versatile platforms for engineering and amplifying current driven magnetic responses through symmetry, topology, and gain-loss design.