Ideal type-II Weyl points in topological circuits

Abstract

Weyl points (WPs), nodal degenerate points in three-dimensional (3D) momentum space, are said to be ‘ideal’ if they are symmetry-related and well-separated, and reside at the same energy and far from nontopological bands. Although type-II WPs have unique spectral characteristics compared with type-I counterparts, ideal type-II WPs have not yet been reported due to the lack of an experimental platform with enough flexibility to produce strongly tilted dispersion bands. Here we experimentally realize a topological circuit that hosts only topological bands with a minimal number of four ideal type-II WPs. By stacking two-dimensional (2D) layers of inductor-capacitor (LC) resonator dimers with the broken parity inversion symmetry (P), we achieve a strongly tilted band structure with two group velocities in the same direction, and topological surface states in an incomplete bandgap. Our results establish an ideal system for the further study of Weyl physics and other exotic topological phenomena.

Observation of Quadratic (Charge‐2) Weyl Point Splitting in Near‐Infrared Photonic Crystals

“…Weyl materials have drawn significant interest over the last decade for their ability to support Weyl points (WPs), which are topologically protected degeneracies in 3D periodic systems. They have been examined in a wide range of physical systems such as conventional solids, [ 1–7 ] photonic systems, [ 8–18 ] acoustic systems, [ 19–22 ] cold atoms, [ 23,24 ] electric circuits, [ 25 ] and coupled resonator arrays. [ 26,27 ] In photonics, WPs are sought for a range of applications such as designing large‐volume single‐mode lasers [ 28 ] and mediating long‐range interactions between quantum emitters, [ 29,30 ] and as such they have been realized in a variety of optical and photonic systems [ 8–18 ] spanning orders of magnitude in wavelength.…”

Probing Rotated Weyl Physics on Nonlinear Lithium Niobate-on-Insulator Chips

“…The most interesting property of these topological materials is the existence of topologically protected edge states or surface states, for example, the Fermi arc surface states in Weyl semimetals. At present, the Weyl point (WP) has been observed in condensed matters [7,8], photonic crystals [9,10], waveguide arrays [11], and metamaterials [12][13][14]. In addition, with the help of synthetic dimension, people can also obtain 3D WPs with lower dimensional structures [15,16].…”

“…In addition, with the help of synthetic dimension, people can also obtain 3D WPs with lower dimensional structures [15,16]. Although Weyl semimetals have been widely studied, most of the researches have focused on the single Weyl crystal [7][8][9][10][11][12][13][14][15][16]. Recently, rotating bilayer graphene has become a hot topic [17].…”

“…As the parameter space is not periodic, charge neutrality is not indispensable here [16,41]. Thus, unlike periodic systems [7][8][9][10][11][12][13][14][15][16], our system exhibits a single negative-charged WP (Supplemental Material, Sec. IV [40]).…”

Experimental realization of non-Abelian gauge potentials and topological Chern state in circuit system

“…A number of recent articles using circuit systems to study various topological states have appeared, including the design of topological insulators [31][32][33][34][35][36][37][38][39], Weyl states [33,[40][41][42], non-Hermitian systems [43,44], 4D TIs [45][46][47][48], topological Anderson insulator [49], and higher-order topological states [50][51][52][53]. Circuit systems have the unique advantage, that the properties of the circuit are independent of the shape of the system and only related to the topological geometry of the interconnections of the circuit devices.…”