Tunable Aharonov-Bohm cages through anti-$\mathcal{PT}$-symmetric imaginary couplings

TL;DR

This paper introduces a tunable non-Hermitian Aharonov-Bohm cage using anti-$\mathcal{PT}$-symmetric imaginary couplings in a generalized Creutz ladder, enabling control over localization and dynamics.

Contribution

It presents a novel non-Hermitian AB cage with tunable flat-band energy via anti-$\mathcal{PT}$ symmetry, expanding localization manipulation in physics.

Findings

Non-Hermitian engineering affects localization probability distributions.

Increases the oscillation period of AB cage dynamics.

Demonstrates the general applicability of the approach.

Abstract

The Aharonov-Bohm (AB) cage enables localized confinement with nondiffractive propagation for arbitrary excitation. In this study, we introduce an anti-parity-time (anti-$\mathcal{PT}$) symmetric imaginary coupling in a generalized Creutz ladder to construct a non-Hermitian AB cage with tunable flat-band energy. We investigate compact localized states and complete localization dynamics, and show that non-Hermiticity affects the localization probability distributions and increases the oscillation period of the AB cage dynamics. Non-Hermitian engineering of the decoupled core of the AB cage is the essential point in our proposal. Our approach is widely applicable to a more general situation and can facilitate the manipulation of localization in physics.