Phononic topological insulators based on six-petal holey silicon structures

Abstract

Since the discovery of the Quantum Spin Hall Effect, electronic and photonic topological insulators have made substantial progress, but phononic topological insulators in solids have received relatively little attention due to challenges in realizing topological states without spin-like degrees of freedom and with transverse phonon polarizations. Here we present a holey silicon-based topological insulator design, in which simple geometric control enables topologically protected in-plane elastic wave propagation up to GHz ranges with a submicron periodicity. By integrating a hexagonal lattice of six small holes with one central large hole and by creating a hexagonal lattice by themselves, our design induces zone folding to form a double Dirac cone. Based on the hole dimensions, breaking the discrete translational symmetry allows the six-petal holey silicon to achieve the topological phase transition, yielding two topologically distinct phononic crystals. Our numerical simulations confirm inverted band structures and demonstrate backscattering-immune elastic wave transmissions through defects including a cavity, a disorder, and sharp bends. Our design also offers robustness against geometric errors and potential fabrication issues, which shows up to 90% transmission of elastic waves even with 6% under-sized or 11% over-sized holes. These findings provide a detailed understanding of the relationship between geometry and topological properties and pave the way for developing future phononic circuits.

Topological flat band, Dirac fermions and quantum spin Hall phase in 2D Archimedean lattices

“…Therefore, our results can be directly interpreted in different quasiparticle systems, e.g. photonic 28 , phononic 37,38 , magnonic 39 . Moreover, including the intrinsic spin-orbit coupling to the model, we explore the quantum spin Hall phases in electronic systems.…”

Excitation and detection of acoustic phonons in nanoscale systems

“…[320][321][322] GHz applications have been demonstrated in one dimensional multilayer systems 237,323 while two dimensional systems have been mainly limited to theory. 319,324,325 Nevertheless, as the acoustic problems are scale-invariant, sooner or later, macroscopic phononic crystals will be replicated at the nanoscale. At the nanoscale, the principal existing challenge is the selective excitation and detection of acoustic waves that possess these special aforementioned properties.…”

Topological sound in two dimensions

“…The relative simplicity of this protocol has motivated a plethora of studies of various platforms, ranging from soda can metamaterials 130 and macroscopic phononic crystals [131][132][133][134][135][136][137][138][139][140][141][142][143] (Figure 5E) to on-chip systems, [144][145][146][147][148] whose reconfigurability opens the door to practical devices. 141,142 Moreover, Lamb waves in thin plates and their intrinsic polarization provide another handle to realize a pseudospin Hall effect and implement helical edge states.…”