Fig. 1. Unconventional Weyl exceptional contours in non-Hermitian anisotropic chiral plasma, parameterized by the in-plane permittivity. When the contour splits or not, the space is divided into the red part, the gray part, and the boundary in between, corresponding to the QWERs, two separated WERs, and the WECs. Underlined are three special cases that pinned in planes by pseudo-PT symmetries: in-plane QWERs, type I WECs with a single chain point, and type II WECs with two chain points.

Fig. 2. Quadratic Weyl point in Hermitian anisotropic chiral plasma. (a) Isofrequency contour at the plasma frequency in the k space, where QWP is at the k=0 point. (b) Quadratic in-plane dispersion. (c) Linear out-of-plane dispersion. (d) As χ<0, the accumulated Berry phase of the circle over the sphere that encloses QWP is +4π for the upper band (in red), indicating C=+2.

Fig. 3. Four typical cases evolving from the QWP. (a) Two WPs, where ε‖=[1,0.4;0.4,1]. (b) QWER, where ε‖=[1,0.4;−0.4,1]. (c) Type II WEC, where ε‖=[1,0.4i;0.4i,1]. (d) Type I WEC, where ε‖=[1,0.4;0,1]. For each case we plot the exceptional contour, the band diagrams in the slices indicated in the left panel, and the Wilson loop on a sphere covering the unconventional Weyl exceptional contours.

Fig. 4. Metamaterial designs to implement various unconventional Weyl exceptional contours. (a) Unit cell of metamaterial. The metallic structure (in gray) is designed to create in-plane resonance to introduce chirality. By switching the in-plane permittivity of the background material to [4.0,0.5;−0.5,4.0], [4.0,0.5i;0.5i,4.0], and [4.0,0.5;−0.06,4.0], respectively, the third and the fourth bands intersect as (b) the QWER, (c) the type II WEC, and (d) the type I WEC around 6.3 GHz in the vicinity of the Γ point, respectively. All exceptional contours are pinned inside one of the kα=0 planes by C2αT symmetries, where α=x,y,z. The gray area in the Brillouin zone in (b)–(d) covers the exceptional contour, where a detailed band plot is given to show the real and imaginary parts of the eigenfrequencies. kx and ky are normalized by π/px and π/py, respectively. For each case in (b)–(d), we fit the bulk bands by the continua model with effective constitutive parameters, plotted in dashed black curves in the vicinity of the Γ point. Note that in (d), in-plane permittivity is not rigorously upper-triangular due to the nonlocal effect.

Fig. 5. Evolution of Berry phases on the latitude circles of the spheres enclosing (a) QWP, (b) QWER, (c) type II WEC, and (d) type I WEC. As the polar angle varies from 0 to π, the accumulated phases imply the topological charge C=+2.

Fig. 6. ky-projected surface band structure along an ellipse enclosing the Γ point. (a) QWP, (b) QWER, (c) type II WEC, and (d) type I WEC. The red lines denote the Fermi arc surface states.

Table 1. Variants of QWP When Introducing Perturbations to the In-Plane Permittivity, Where ε and γ are Real Numbers^a