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

TL;DR

This work addresses how non-Hermitian gain–loss engineering and $\\mathcal{PT}$-symmetry influence quantum transport and circulating currents in Fibonacci rings. It employs tight-binding modeling and nonequilibrium Green's function (NEGF) formalism to compute transmission $T(E)$, junction current $I_T(V)$, bond currents $I_{ij}$, and the circular current $I_C$, across Hermitian, $\\mathcal{PT}$-symmetric NH, and non-$\\mathcal{PT}$-symmetric NH configurations. Key findings show that the Hermitian Fibonacci ring yields only weak current responses, whereas non-Hermitian installations markedly amplify transport, circulating currents, and the induced magnetic field, with strong sensitivity to gain–loss sign and system size; parity of the Fibonacci sequence and hopping correlations drive unconventional size dependence in the non-$\\mathcal{PT}$-symmetric case. The results demonstrate that NH quasiperiodic rings can be engineered to achieve large, tunable current-driven magnetic responses, offering insights for designing nanoscale devices with enhanced magnetoelectric effects.

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.

Figures (11)

• Figure 1: (Color online). Schematic illustration of a quantum ring structure in which both the upper and lower arms are modulated by a Fibonacci quasiperiodic arrangement. Along the upper arm, the sites follow the sequence $\mathrm{A}\mathrm{B}\mathrm{A}\mathrm{A}\mathrm{B}\ldots$ as electrons propagate from the source to the drain, whereas the lower arm is characterized by the complementary sequence $\mathrm{B}\mathrm{A}\mathrm{B}\mathrm{B}\mathrm{A}\ldots$, again extending from the source to the drain. The two distinct lattice sites, $\mathrm{A}$ and $\mathrm{B}$, are represented by green and orange spheres, respectively. With the introduction of non-Hermitian contributions satisfying parity-time ($\mathcal{PT}$) symmetry, this configuration corresponds to a $\mathcal{PT}$-symmetric system. Subplot (a) corresponds to a system of size $L=10$, where each arm is characterized by the Fibonacci index $5$, whereas subplot (b) represents a larger system with $L=16$, with the Fibonacci index in each arm equal to $8$.
• Figure 2: (Color online). This schematic depicts a Fibonacci-modulated ring in which the lower arm is traversed in the reversed sequence, $\mathrm{B}\mathrm{A}\mathrm{B}\mathrm{B}\mathrm{A}\ldots$, from the drain to the source, while the upper arm retains the $\mathrm{A}\mathrm{B}\mathrm{A}\mathrm{A}\mathrm{B}\ldots$ ordering from source to drain. With the inclusion of non-Hermitian terms, this geometry realizes a non-$\mathcal{PT}$-symmetric configuration. The two subplots (a) and (b) correspond to $L=10$ and $L=16$, associated with Fibonacci indices $5$ and $8$ in each arm, respectively.
• Figure 3: (Color online). Transmission coefficient and junction current characteristics for Fibonacci rings of different sizes. Panels (a) and (b) show the energy-dependent transmission spectra for system sizes $N=16$ and $N=26$, respectively for $\lambda=0.2$, where red and green curves represent case 1 and case 2 configurations. Panels (c) and (d) display the corresponding junction current as a function of applied bias voltage.
• Figure 4: (Color online). Bond current density and circular current characteristics for Fibonacci rings. Panels (a) and (b) show the energy-dependent bond current density for system sizes $N=16$ and $N=26$, respectively for $\lambda=0.2$, while panels (c) and (d) depict the circular current as a function of applied bias voltage. Red and green curves correspond to case 1 and case 2 configurations, respectively.
• Figure 5: (Color online). Dependence of the maximum circular current and junction current on the potential strength $\lambda$ for Fibonacci rings of two different sizes ($N=16$ and $N=26$). Panels (a) and (b) show the variation of the maximum circular current with $\lambda$, while panels (c) and (d) present the corresponding junction currents. Red and blue curves denote case 1 and case 2 configurations, respectively, as discussed in the text. The induced magnetic field, derived from the circulating current, is plotted using twin-$y$ axes in panels (a) and (b), exhibiting peak values of approximately $0.5$ T and $0.4$ T for $N=16$ and $N=26$, respectively.