Persistent current in a non-Hermitian Hatano-Nelson ring: Disorder-induced amplification

Abstract: Non-reciprocal hopping induces a synthetic magnetic flux which leads to the non-Hermitian Aharonov-Bohm effect. Since non-Hermitian Hamiltonians possess both real and imaginary eigenvalues, this effect allows the observation of real and imaginary persistent currents in a ring threaded by the synthetic flux. Motivated by this, we investigate the behavior of persistent currents in a disordered Hatano-Nelson ring with anti-Hermitian intradimer hopping. The disorder is diagonal and we explore three distinct models, namely the Aubry-Andr\'{e}-Harper model, the Fibonacci model, both representing correlated disorder, and an uncorrelated (random) model. We conduct a detailed analysis of the energy spectrum and examine the real and imaginary parts of the persistent current under various conditions such as different ring sizes and filling factors. Interestingly, we find that real and imaginary persistent currents exhibit amplification in the presence of correlated disorder. This amplification is also observed in certain individual random configurations but vanishes after configuration averaging. Additionally, we observe both diamagnetic and paramagnetic responses in the current behavior and investigate aspects of persistent currents in the absence of disorder that have not been previously explored. Interestingly, we find that the intradimer bonds host only imaginary currents, while the interdimer bonds carry only real currents. The bulk-boundary correspondence is investigated by analyzing the existence of localized edge states under the open boundary condition.