Layer-number parity induced topological phase transition

TL;DR

This paper reveals that the parity of the number of stacked layers can induce topological phase transitions, leading to protected boundary states and bound states in the continuum, confirmed analytically, numerically, and experimentally.

Contribution

It introduces the novel concept that layer-number parity acts as a topological switch, enabling topological phases in stacked trivial layers under symmetry constraints.

Findings

Odd-layer systems support topological bound states in the continuum.

Spectrum becomes gapless for an odd number of layers.

Experimental validation in stacked acoustic lattices.

Abstract

We demonstrate that stacking topologically trivial layers, under enforced symmetry restrictions, yields emergent topological phases with protected boundary states. Remarkably, the number of layers itself acts as a topological switch, enabling the system to host topological bound states in the continuum (BICs). We analytically show that the spectrum becomes gapless for an odd number of layers; combined with entanglement-spectrum calculations, this confirms that odd-layer systems indeed support topological BICs. We provide experimental confirmation of these phenomena in stacked acoustic lattices. Our findings establish a previously overlooked pathway to topology and demonstrate a readily applicable strategy for realizing exotic states in a wide range of artificial material systems.