“…Metamaterials with negative refraction [1][2][3][4][5][6][7] have attracted broad interest because of their potential applications, including perfect lenses [2,8], fingerprint identification in forensic science [9], simulating condensed matter phenomena and reversed Doppler effect [10,11], controlling light polarization [12], and electromagnetic cloaking [13][14][15]. In order to realize metamaterials, a number of routes have been proposed, including (molecular) split-ring resonators [3,16,17], chiral approaches [18], hyperbolic dispersion [19][20][21][22], dark-state mechanism [23][24][25][26][27], and topological routes [28][29][30]. However, none of these can effectively overcome the difficulty of realizing broad-band negative refraction.…”