Double-bowl state in photonic Dirac nodal line semimetal

Abstract

The past decade has seen a proliferation of topological materials for both insulators and semimetals in electronic systems and classical waves. Topological semimetals exhibit topologically protected band degeneracies, such as nodal points and nodal lines. Dirac nodal line semimetals (DNLS), which own four-fold line degeneracy, have drawn particular attention. DNLSs have been studied in electronic systems but there is no photonic DNLS. Here in this work, we provide a new mechanism, which is unique for photonic systems to investigate a stringent photonic DNLS. When truncated, the photonic DNLS exhibits double-bowl states (DBS), which comprise two sets of perpendicularly polarized surface states. In sharp contrast to nondegenerate surface states in other photonic systems, here the two sets of surface states are almost degenerate over the whole-spectrum range. The DBS and the bulk Dirac nodal ring (DNR) dispersion along the relevant directions, are experimentally resolved.

Photonic Dirac nodal-line semimetals realized by a hypercrystal

“…DNLSs can be described by four-band Hamiltonian, which is expanded in Dirac gamma matrices. Considering the form of tensor product of two Pauli matrices 𝜏 𝑖 and 𝜎 𝑖 (𝑖 = 𝑥, 𝑦, 𝑧) acting on two isospin degrees of freedom, the effective Hamiltonian of photonic DNLSs can be written as [19]…”

“…In particular, the co-dimension of nodal points [7][8][9][10][11], nodal lines and nodal surfaces [42][43][44] is 3, 2 and 1 respectively, which corresponding to the degrees of freedom of parameters that tuned to encounter a band degeneracy [45]. Interestingly, nodal lines in topological semimetals can even form some complicated configurations, including helices [12], rings [13][14][15][16][17][18][19], links [20,21], chains [22][23][24], gyroscopes [18,[25][26][27], nexus [28][29][30][31][32], knots [33][34][35][36], nets [37][38][39][40], etc. So far, more and more topological semimetals have been proposed theoretically and verified experimentally in the electronic [7][8], optical [11,19,24,32], and acoustic systems …”

“…Interestingly, nodal lines in topological semimetals can even form some complicated configurations, including helices [12], rings [13][14][15][16][17][18][19], links [20,21], chains [22][23][24], gyroscopes [18,[25][26][27], nexus [28][29][30][31][32], knots [33][34][35][36], nets [37][38][39][40], etc. So far, more and more topological semimetals have been proposed theoretically and verified experimentally in the electronic [7][8], optical [11,19,24,32], and acoustic systems [23,[39][40][41]. As a result, a finer classification of topological phases is supported by band structure of semimetals.…”

“…As a result, a finer classification of topological phases is supported by band structure of semimetals. A rapidly growing frontier in this field is to emulate relativistic quasi-particles like two-fold Weyl fermions [8,41] and four-fold Dirac fermions [10,19], which have linear dispersion with novel transport properties like delocalization [46], Zitterbewegung [11,[47][48], and Klein tunneling [11,[49][50]. In addition, topological semimetal phases can be further divided into type-I [51][52], type-II [53][54], and type-III [55][56][57] based on the tilt angles of the Dirac/Weyl cones.…”

“…Photonic crystals (PCs) provide a powerful platform for manipulating the lightmatter interactions [62][63][64][65][66]. In 2021, Hu et al, uncover that double-bowl state in photonic Dirac nodal line semimetal in the one-dimensional (1D) PCs [19]. This pioneering work provides a new mechanism to realize a photonic type-II Dirac nodal line semimetal (DNLS).…”