A quantized microwave quadrupole insulator with topologically protected corner states

Abstract

The theory of electric polarization in crystals defines the dipole moment of an insulator in terms of a Berry phase (geometric phase) associated with its electronic ground state. This concept not only solves the long-standing puzzle of how to calculate dipole moments in crystals, but also explains topological band structures in insulators and superconductors, including the quantum anomalous Hall insulator and the quantum spin Hall insulator, as well as quantized adiabatic pumping processes. A recent theoretical study has extended the Berry phase framework to also account for higher electric multipole moments, revealing the existence of higher-order topological phases that have not previously been observed. Here we demonstrate experimentally a member of this predicted class of materials-a quantized quadrupole topological insulator-produced using a gigahertz-frequency reconfigurable microwave circuit. We confirm the non-trivial topological phase using spectroscopic measurements and by identifying corner states that result from the bulk topology. In addition, we test the critical prediction that these corner states are protected by the topology of the bulk, and are not due to surface artefacts, by deforming the edges of the crystal lattice from the topological to the trivial regime. Our results provide conclusive evidence of a unique form of robustness against disorder and deformation, which is characteristic of higher-order topological insulators.

Higher‐Order Topological States in Surface‐Wave Photonic Crystals

“…The quest for topological 0D cavity modes in 2D electromagnetic‐wave systems, which could serve as an important ingredient to build‐up of robust electromagnetic‐wave/photonic devices, was unsuccessful until very recently . Such an achievement was realized using the higher‐order topological insulators .…”

“…The quest for topological 0D cavity modes in 2D electromagnetic‐wave systems, which could serve as an important ingredient to build‐up of robust electromagnetic‐wave/photonic devices, was unsuccessful until very recently . Such an achievement was realized using the higher‐order topological insulators . Unlike the conventional D ‐dimensional topological insulators which have ( D −1)‐dimensional topological gapless boundary states, a D ‐dimensional higher‐order topological insulator gives rise to ( D − 2)‐dimensional (or even lower‐dimensional) topological gappless boundary states, in addition to the ( D − 1)‐dimensional gapped boundary states, offering a paradigm beyond the conventional bulk‐boundary correspondence.…”

Topological Insulators Turn a Corner

“…Combined with the unique prospect of isolated Majorana bound states (for two-dimensional second-order topological superconductors) or onedimensional chiral modes and a quantized Hall effect (for three-dimensional second-order TIs), higher-order TIs are a promising addition to the topological materials family. Very recently, some early experimental realizations of second-order topological insulators appeared [47][48][49][50], where Ref. [47] uses the bismuth nanowire which was previously shown to support edge states [51].…”

Deep‐Subwavelength Holey Acoustic Second‐Order Topological Insulators

“…To date, HOTIs have been theoretically predicted and experimentally realized in elastics, [34,35] microwaves, [36] electric circuits, [37] photonics, [38][39][40] and acoustic systems. To date, HOTIs have been theoretically predicted and experimentally realized in elastics, [34,35] microwaves, [36] electric circuits, [37] photonics, [38][39][40] and acoustic systems.…”