Nodal Manifolds Bounded by Exceptional Points on Non-Hermitian Honeycomb Lattices and Electrical-Circuit Realizations

TL;DR

This paper explores non-Hermitian honeycomb lattices where exceptional points bound exotic nodal manifolds, revealing unique bulk-boundary relationships and proposing electrical circuit simulations to realize these phenomena.

Contribution

It demonstrates the realization of exotic nodal manifolds bounded by exceptional points in non-Hermitian honeycomb lattices and proposes electrical circuit implementations.

Findings

Exotic nodal lines and drumheads with exceptional boundaries can be realized in 2D and 3D honeycomb lattices.

Bulk-boundary correspondence is fundamentally altered for these non-Hermitian states under open boundary conditions.

Electrical circuit simulations can emulate these non-Hermitian topological states using operational amplifiers.

Abstract

Topological semimetals feature a diversity of nodal manifolds including nodal points, various nodal lines and surfaces, and recently novel quantum states in non-Hermitian systems have been arousing widespread research interests. In contrast to Hermitian systems whose bulk nodal points must form closed manifolds, it is fascinating to find that for non-Hermitian systems exotic nodal manifolds can be bounded by exceptional points in the bulk band structure. Such exceptional points, at which energy bands coalesce with band conservation violated, are iconic for non-Hermitian systems. In this work, we show that a variety of nodal lines and drumheads with exceptional boundary can be realized on 2D and 3D honeycomb lattices through natural and physically feasible non-Hermitian processes. The bulk nodal Fermi-arc and drumhead states, although is analogous to, but should be essentially distinguished from the surface counterpart of Weyl and nodal-line semimetals, respectively, for which surface nodal-manifold bands eventually sink into bulk bands. Then we rigorously examine the bulk-boundary correspondence of these exotic states with open boundary condition, and find that these exotic bulk states are thereby undermined, showing the essential importance of periodic boundary condition for the existence of these exotic states. As periodic boundary condition is non-realistic for real materials, we furthermore propose a practically feasible electrical-circuit simulation, with non-Hermitian devices implemented by ordinary operational amplifiers, to emulate these extraordinary states.