Observation of symmetry-protected zero modes in topolectrical circuits

Observation of antichiral edge states in a circuit lattice

“…Circuit metamaterials have been the subject of recent theoretical and experimental interest [28][29][30][31][32][33][34][35][36][37][38][39][40] due to the ease with which they can be designed and fabricated to realize different topological phases, as well as unusual lattice configurations that are hard to achieve on other platforms. Circuits have been used to demonstrate nonlinear topological boundary states [33,34], topological corner modes [35][36][37][38], and four-dimensional topological insulators [39,40]. Most notably, Jia et al [7] have shown how a Haldane-type Chern insulator phase can be accessed using a lattice of capacitors (C) and inductors (L) with braided interconnections.…”

“…Most notably, Jia et al [7] have shown how a Haldane-type Chern insulator phase can be accessed using a lattice of capacitors (C) and inductors (L) with braided interconnections. Although LC circuits are time-reversal symmetric, the braiding decomposes the spectrum into two degenerate decoupled sectors that are individually T-broken [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43], with the physical T symmetry mapping each sector to the other. Utilizing this idea, we design and fabricate a braided LC circuit lattice that realizes the modified Haldane model.…”

Topological phase transition and thermal Hall effect in kagome ferromagnets

“…, or diammonium quinuclidinium vanadium(III,IV) oxyfluoride (DQVOF), as well as the materials Li 2 In 1−x Sc x Mo 3 O 8 have opened an alternative route for the study of quantum spin liquids on the breathing kagome lattice in the absence of inversion symmetry [54][55][56][57][58][59][60]. Moreover, topological properties, especially on higher-order topological insulators, have been widely investigated on the breathing kagome lattice in electronics [61][62][63][64], photonics [65,66], acoustic metamaterials [67,68], electric circuits [69][70][71], magnetic solitons [72] and mechanical metamaterials [73]. More interestingly, a skyrmion crystal phase with large topological Hall effect was also experimentally observed in Gd 3 Ru 4 Al 12 with a Gd-based breathing kagome lattice [74].…”

Manipulating building blocks of matter

“…Subsequently, this idea was taken over in the previous sections and by Refs. [194][195][196][197][198][199].…”

“…In the first part of this chapter, the protection of these zero-energy corner states is explained within the framework of a generalized chiral symmetry, which relies on the fact that the Kagome lattice is tripartite. After the introduction of this framework [189], it has been used to explain the outcome of several experiments, including ours [194][195][196][197][198][199]. In the second part of this chapter, we revisit the generalized chiral symmetry, presenting a critical review of this model and show where it breaks down (see Sec.…”