Abstract
Classical bosonic systems may be tailored to support topological order and unidirectional edge transport exploiting gauge fields. Here, we theoretically explore how synthetic gauge fields may be used to induce higher-order topological phases and zero-energy boundary states. We demonstrate these principles in two types of three-dimensional topolectrical circuits with synthetic gauge fields threading through their reduced two-dimensional lattices, leading to a half-quantized quadrupole charge within a region of the momentum space. We theoretically show the emergence of nodal line rings and Weyl points in the bulk dispersion, whose projected surfaces and hinges support surface Fermi arcs and flat hinge Fermi arcs emanating from the nodal line ring and Weyl points, representing the spectral signature of higher-order topological semimetals. These analogs of higher-order semimetals realized in electric circuits using synthetic gauge fields may be extended to various photonic platforms and find applications in photonic crystals, nano-optics, and cold atom research.
Highlights
Topological matter, including topological insulators (TIs)[1,2,3,4] and topological semimetals,[5,6,7,8,9,10] has widely been investigated in the past two decades because of the elegant theoretical framework that describes its response and the inherent robustness of its response
To test whether the higher-order topolectrical semimetal can be experimentally implemented and whether it allows the coexistence of bulk states, surface Fermi arcs, and hinge Fermi arcs at the same frequency, we design the higher-order Weyl semimetal model in a circuit layout, as a finite topolectrical circuit array composed of 5 × 5 × 5 unit cells, and carry out full-wave simulations based on commercially available Advanced Design System (ADS)
We have introduced synthetic gauge fields in 3D topolectrical circuits to emulate the physics of higher-order semimetals, demonstrating higher-order topological phases induced by synthetic gauge fields
Summary
Topological matter, including topological insulators (TIs)[1,2,3,4] and topological semimetals,[5,6,7,8,9,10] has widely been investigated in the past two decades because of the elegant theoretical framework that describes its response and the inherent robustness of its response These concepts, born in the field of condensed matter physics and electronic materials, have been extended to classical wave systems,[11,12,13,14,15] where synthetic gauge fields play the essential role of endowing neutral particles with the dynamics of charged particles subject to real gauge fields, inducing topological order in photonics,[16–21] cold atoms,[22–24] mechanics,[25,26] and acoustics.[27–29]. The synthetic gauge field is induced by a negative coupling in one direction of the reduced 2D model By stacking such 2D lattices to form a 3D metamaterial and introducing complex hopping coefficients between layers, we construct a higherorder Weyl semimetal, which supports bulk Weyl points emanating both surface Fermi arcs and hinge Fermi arcs. The excitation of these circuits demonstrates the coexistence of bulk, surface, and hinge states propagating in one dimension in the same frequency range, consistent with the features of higher-order Weyl semimetals
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