Tidal surface states as fingerprints of non-Hermitian nodal knot metals

Abstract

The paradigm of metals has undergone a revision and diversification from the viewpoint of topology. Non-Hermitian nodal knot metals (NKMs) constitute a class of matter without Hermitian analog, where the intricate structure of complex-valued energy bands gives rise to knotted lines of exceptional points and new topological surface state phenomena. We introduce a formalism that connects the algebraic, geometric, and topological aspects of these surface states with their underlying parent knots, and complement our results by an optimized constructive ansatz that provides tight-binding models for non-Hermitian NKMs of arbitrary knot complexity and minimal hybridization range. In particular, we identify the surface state boundaries as ``tidal' intersections of the complex band structure in a marine landscape analogy. We further find these tidal surface states to be intimately connected to the band vorticity and the layer structure of their dual Seifert surface, and as such provide a fingerprint for non-Hermitian NKMs.

Non-Hermitian semi-Dirac semi-metals

“…which leads to four roots, β i (i = 1, 2, 3, 4). These four roots satisfy the same condition as we get from equation (46) in the main text: β 1 + β 2 + β 3 + β 4 = 0 and β 1 β 2 β 3 β 4 = 1. For a sufficiently long chain, |β 2 | = |β 3 | = β, and the model does not exhibit a non-Hermitian skin effect as the product of four roots is unity.…”

“…The research in this field has rapidly accelerated by considering the interplay between non-Hermiticity and topology [26][27][28][29][30][31][32][33][34]. Several non-Hermitian non-trivial topological phases have been proposed, including one-dimensional Su-Schrieffer-Heeger chains [35][36][37], knot semimetals [38,39], nodal line semimetals, nodal ring semimetals [40,41], Hopf link semimetals [42][43][44][45][46], and Weyl semimetals [47], to name just a few. One of the features of non-Hermitian topological systems is the existence of exceptional points (EPs).…”

Geometric Response and Disclination-Induced Skin Effects in Non-Hermitian Systems

“…Recently, there has been a growing interest in the interplay between non-Hermiticity and topological phases. The synergy of these two concepts has resulted in fruitful results that are distinct from Hermitian topological physics, such as new transport and dynamical features [20][21][22][23][24][25][26][27], new forms of bulk-boundary correspondence [28][29][30][31][32][33][34][35], and non-Hermitian analogy of topological insulators [36][37][38][39][40][41][42][43][44] and semimetals [45][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60].…”

Non-Hermitian semi-Dirac semi-metals

“…The research in this field has rapidly accelerated by considering the interplay between non-Hermiticity and topology [25][26][27][28] . Several non-Hermitian non-trivial topological phases have been proposed, including one-dimensional Su-Schrieffer-Heeger chains [29][30][31] , knot semimetals 32,33 , nodal line semimetals, nodal ring semimetals 68 , Hopf link semimetals [34][35][36][37][38] , and Weyl semimetals 35,79 , to name just a few. One of the features of non-Hermitian topological systems is the existence of exceptional points (EPs).…”