Valley and pseudospin-valley topologically protected edge states in symmetric pillared phononic crystals

TL;DR

This paper introduces symmetric pillared phononic crystals capable of emulating quantum spin and valley Hall effects, demonstrating topologically protected edge states, diverse refraction phenomena, and valley-dependent splitting in waveguides.

Contribution

It presents a novel phononic crystal platform that can realize both QSHE and QVHE effects through geometric perturbations, enabling control over topological edge states.

Findings

Realization of valley-protected and pseudospin-protected edge states.

Observation of positive, negative, and evanescent refraction phenomena.

Demonstration of valley-based splitting in a Y-junction waveguide.

Abstract

We present a symmetric double-sided pillared phononic crystals (PPnCs) that can emulate both quantum spin Hall effect (QSHE) and quantum valley Hall effect (QVHE) by solely imposing different geometric perturbations. Indeed, the Dirac cones can occur in the low (deep subwavelength) and high frequency regime by judiciously turning the parameters of the attached pillars and even a double Dirac cone can be achieved. We realize the valley-protected, the pseudospin-protected or the pseudospin-valley coupled edge states with the proposed platform. Besides, we show a variety of refraction phenomena (positive, negative and evanescent) of the valley-polarized edge state at the zigzag termination when emulating QVHE. Further, we illustrate the valley-dependent feature of the pseudospin-valley coupled edge state and demonstrate the valley based splitting of the pseudospin-protected edge states in a Y-junction wave guide.