4D spinless topological insulator in a periodic electric circuit

Abstract

According to the mathematical classification of topological band structures, there exist a number of fascinating topological states in dimensions larger than three with exotic boundary phenomena and interesting topological responses. While these topological states are not accessible in condensed matter systems, recent works have shown that synthetic systems, such as photonic crystals or electric circuits, can realize higher-dimensional band structures. Here, we argue that the 4D spinless topological insulator, due to its symmetry properties, is particularly well suited to be implemented in these synthetic systems. We explicitly construct a 2D electric circuit lattice, whose resonance frequency spectrum simulate the 4D spinless topological insulator. We perform detailed numerical calculations of the circuit lattice and show that the resonance frequency spectrum exhibit pairs of 3D Weyl boundary states, a hallmark of the nontrivial topology. These pairs of 3D Weyl states with the same chirality are protected by classical time-reversal symmetry that squares to +1, which is inherent in the proposed circuit lattice. We also discuss how the simulated 4D topological band structure can be observed in experiments.

Four-dimensional topological lattices through connectivity

“…Since this proposal was put on arXiv, it has been experimentally implemented in electric circuits [59]. Theoretical proposals have also been made for electric circuits to realise a different spinless (Class AI) 4DQH model [60], to simulate nth-Chern-number insulators [61] and to image nodal boundary Seifert surfaces in 4D circuits [62].…”

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.…”

Observation of hybrid higher-order skin-topological effect in non-Hermitian topolectrical circuits

“…Electrical circuits are ideally suited for transcending the abovementioned challenges, since electronic components, which have benefitted from industrial refinement over the decades, can accommodate almost any desired features like arbitrary long-range connectivity, dimensionality, non-Hermiticity gain/loss as well as non-reciprocity. Recently, simulating topological states with electric circuits has attracted lots of interests based on the similarity between circuit Laplacian and lattice Hamiltonian [23][24][25][26][27][28][29][30]. Some topological states have been observed in circuit networks [31][32][33][34][35].…”