Winding Topology of Multifold Exceptional Points

Abstract

Despite their ubiquity, a systematic classification of multifold exceptional points, $n$-fold spectral degeneracies (EP$n$s), remains a significant unsolved problem. In this article, we characterize the Abelian eigenvalue topology of generic EP$n$s and symmetry-protected EP$n$s for arbitrary $n$. The former and the latter emerge in a $(2n-2)$- and $(n-1)$-dimensional parameter space, respectively. By introducing topological invariants called resultant winding numbers, we elucidate that these EP$n$s are stable due to topology of a map from a base space (momentum or parameter space) to a sphere defined by resultants. In a $D$-dimensional parameter space ($D\ge c$), the resultant winding number topologically characterize a $(D-c)$-dimensional manifold of generic [symmetry-protected] EP$n$s whose codimension is $c=2n-2$ [$c=n-1$]. Our framework implies fundamental doubling theorems for both generic EP$n$s and symmetry-protected EP$n$s in $n$-band models.

10pages, 2 figures

References in corpus (26)

• The physics of exceptional points
• Topological Origin of Non-Hermitian Skin Effects
• Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
• Multiple types of topological fermions in transition metal silicides
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• Large Fermi Arcs in Unconventional Weyl Semimetal RhSi
• Topological Weyl semimetals in the chiral antiferromagnetic materials Mn3Ge and Mn3Sn
• Non-Hermitian topological phenomena: A review
• Discovery of topological chiral crystals with helicoid arc states
• New classes of chiral topological nodes with non-contractible surface Fermi arcs in CoSi
• Topological Non-Hermitian skin effect
• Flat Band in Disorder Driven Non-Hermitian Weyl Semimetals
• Exceptional points of the Lindblad operator of a two-level system
• Linear optical conductivity of chiral multifold fermions
• Realization and Topological Properties of Third-Order Exceptional Lines Embedded in Exceptional Surfaces
• Homotopy, Symmetry, and Non-Hermitian Band Topology
• Experimental Simulation of Symmetry-Protected Higher-Order Exceptional Points with Single Photons
• Topological Fermi arcs in superfluid ${}^3$He
• Braid Protected Topological Band Structures with Unpaired Exceptional Points
• Intrinsic negative magnetoresistance from the chiral anomaly of multifold fermions
• Fourth-Order Exceptional Points in Correlated Quantum Many-Body Systems
• Symmetry-protected exceptional and nodal points in non-Hermitian systems
• Revisiting the hierarchical construction of higher-order exceptional points
• Enhanced eigenvector sensitivity and algebraic classification of sublattice-symmetric exceptional points
• Symmetry-induced higher-order exceptional points in two dimensions
• Nonlinear photoconductivities and quantum geometry of chiral multifold fermions

Cited by in corpus (3)

• An exceptional surface and its topology
• The analytically tractable zoo of similarity-induced exceptional structures
• Exceptional topology on nonorientable manifolds