Geometry-induced Exceptional Point Detached from Fermi Arcs

TL;DR

This paper demonstrates that geometry alone can induce exceptional points in non-Hermitian systems, independent of Fermi arcs, revealing new ways to engineer EPs and their associated band structures.

Contribution

It uncovers the fundamental role of geometry in inducing non-Bloch EPs, distinct from traditional boundary-driven mechanisms, supported by theoretical analysis and experimental validation.

Findings

Geometry induces non-Bloch EPs in a reciprocal Lieb lattice.

EPs correspond to saddle points, not branch points, and are detached from Fermi arcs.

Experimental measurements confirm the separation of geometry-induced EPs from Fermi arc branch points.

Abstract

Exceptional points (EPs), ubiquitous non-Hermitian degeneracies, are central features in band structures where non-Hermitian Fermi arcs connect EPs and eigenvalue knots encircle them. Under open boundary conditions (OBCs), non-Hermitian skin effects enforce complex momenta and yield non-Bloch band structures, introducing EPs unique to OBCs whose origins depend on boundary-driven mechanisms. Here, we reveal both theoretically and experimentally that geometry itself can induce such non-Bloch EPs in a reciprocal non-Hermitian Lieb lattice supporting geometry-dependent skin effects. By analyzing non-Bloch band structures, we find that geometry-induced EPs correspond to saddle points rather than branch points. Branch points, even while carrying OBC eigenenergies, do not yield EPs but manifest as Whitney cusps, a characteristic type of geometric singularity, and Fermi arcs connecting them remain crucial in determining eigenvalue knots. Our measurements of these knots confirm that geometry-induced EPs are detached from the branch points of Fermi arcs, contrasting with their unified counterparts in Bloch systems. Our results establish geometry as an additional degree of freedom for engineering EP-based devices and reveal its fundamental role in shaping non-Bloch band structures.