Non-Hermiticity induced exceptional points and skin effect in the Haldane model on a dice lattice

The interplay of topology and non-Hermiticity has led to diverse, exciting manifestations in a plethora of systems. In this work, we systematically investigate the role of non-Hermiticity in the Chern insulating Haldane model on a dice lattice. Due to the presence of a nondispersive flat band, the dice-Haldane model hosts a topologically rich phase diagram with the nontrivial phases accommodating Chern numbers +/- 2. We introduce non-Hermiticity into this model in two ways-through balanced non-Hermitian gain and loss, and by nonreciprocal hopping in one direction. Both these types of non-Hermiticity induce higher-order exceptional points of order three. Remarkably, the exceptional points at high-symmetry points occur at odd integer values root of the non-Hermiticity strength in the case of balanced gain and loss, and at odd integer multiples of 1/ 2 for nonreciprocal hopping. We substantiate the presence and the order of these higher-order exceptional points using the phase rigidity and its scaling. Furthermore, we construct a phase diagram to identify and locate the occurrence of these exceptional points in the parameter space. Non-Hermiticity has yet more interesting consequences on a finite-sized lattice. Unlike for balanced gain and loss, in the case of nonreciprocal hopping, the nearest-neighbor lattice system under periodic boundary conditions accommodates a finite, nonzero spectral area in the complex plane. This manifests as the non-Hermitian skin effect when open boundary conditions are invoked. In the more general case of the dice-Haldane lattice model, the non-Hermitian skin effect can be caused by both gain and loss or nonreciprocity. Fascinatingly, the direction of localization of the eigenstates depends on the nature and strength of the non-Hermiticity. We establish the occurrence of the skin effect using the local density of states, inverse participation ratio, and the edge probability and demonstrate its robustness to disorder. Our results place the dice-Haldane model as an exciting platform to explore non-Hermitian physics.

Automated summary

The role of non-Hermiticity in the Chern insulating Haldane model on a dice lattice is systematically investigated in this work. Two types of non-Hermiticity, balanced non-Hermitian gain and loss, and nonreciprocal hopping, induce higher-order exceptional points of order three. The finite-sized lattice under nonreciprocal hopping exhibits a non-Hermitian skin effect, while the balanced gain and loss case does not. The occurrence of the skin effect and its robustness to disorder are demonstrated using various techniques.