Tunable Topological Bandgaps and Frequencies in a Pre-Stressed Soft Phononic Crystal

B.H. Nguyen, X. Zhuang, H.S. Park and T. Rabczuk
Accepted for publication in Journal of Applied Physics 2019

Abstract

Topological insulators have recently received significant attention due to the promise of lossless transport of various types of energy. Despite this interest, one outstanding issue is that the topological bandgap and the frequencies that are topologically permitted are typically fixed once the topological structure has been designed and fabricated. Therefore, an open and unresolved question concerns the ability to actively tune both the bandgap magnitude, as well as the frequencies, for which the energy is topologically protected. In this work, we report a mechanically tunable phononic topological insulator (TI) using an acoustic analog of the Quantum valley Hall effect (QVHE). We propose a phononic crystal (PC) comprised of a soft, hyperelastic material where the phononic band structure is modulated through large deformation of the structure. In doing so, space-inversion symmetry (SIS) can be broken, which leads to a phase transition between two topologically-contrasted states and the emergence of topologically-protected interface modes according to bulk-edge correspondence. We further demonstrate the robustness of this topological protection of the edge state along the interface, which demonstrates that mechanical deformation can be used to effectively tailor and tune the topological properties of elastic structures.

Inverse Design of Quantum Spin Hall-Based Phononic Topological Insulators

S.S. Nanthakumar, X. Zhuang, H.S. Park, C. Nguyen, Y. Chen and T. Rabczuk
Journal of the Mechanics and Physics of Solids 2019; 125:550-571

Abstract

We propose a computational methodology to perform inverse design of quantum spin hall effect (QSHE)-based phononic topological insulators. We first obtain two-fold degeneracy, or a Dirac cone, in the band structure using a level set-based topology optimization approach. Subsequently, four-fold degeneracy, or a double Dirac cone, is obtained by using zone folding, after which breaking of translational symmetry, which mimics the effect of strong spin-orbit coupling and which breaks the four-fold degeneracy resulting in a bandgap, is applied. We use the approach to perform inverse design of hexagonal unit cells of C6 and C3 symmetry. The numerical examples show that a topological domain wall with two variations of the designed metamaterials exhibit topologically protected interfacial wave propagation, and also demonstrate that larger topologically-protected bandgaps may be obtained with unit cells based on C3 symmetry.

This paper is available in PDF form .


Strain Tunable Phononic Topological Bandgaps in Two-Dimensional Hexagonal Boron Nitride

J-W Jiang and H.S. Park
Journal of Applied Physics 2019; 125:082511 (Invited paper: Special Issue on Strain Engineering in Functional Materials)

Abstract

The field of topological mechanics has recently emerged due to the interest in robustly transporting various types of energy in a flaw and defect-insensitive fashion. While there have been a significant number of studies based on discovering and proposing topological materials and structures, very few have focused on tuning the resulting topological bandgaps, which is critical because the bandgap frequency is fixed once the structure has been fabricated. Here, we perform both lattice dynamical calculations and molecular dynamical simulations to investigate strain effects on the phononic topological bandgaps in two-dimensional monolayer hexagonal boron nitride. Our studies demonstrate that while the topologically protected phononic bandgaps are not closed even for severely deformed hexagonal boron nitride, and are relatively insensitive to uniaxial tension and shear strains, the position of the frequency gap can be efficiently tuned in a wide range through the application of biaxial strains. Overall, this work thus demonstrates that topological phonons are robust against the effects of mechanical strain engineering, and sheds light on the tunability of the topological bandgaps in nanomaterials.

This paper is available in PDF form .


Topologically Protected Interface Phonons in Two-Dimensional Nanomaterials: Hexagonal Boron Nitride and Silicon Carbide

J-W Jiang, B-S Wang and H.S. Park
Nanoscale 2018; 10:13913-13923

Abstract

We perform both lattice dynamics analysis and molecular dynamics simulations to demonstrate the existence of topologically protected phonon modes in two-dimensional, monolayer hexagonal boron nitride and silicon carbide sheets. The topological phonon modes are found to be localized at an in-plane interface that divides these systems into two regions of distinct valley Chern numbers. The dispersion of this topological phonon mode crosses over the frequency gap, which is opened through analogy with the quantum valley Hall effect by breaking inversion symmetry of the primitive unit cells. Consequently, vibrational energy with frequency within this gap is topologically protected, resulting in wave propagation that exhibits minimal backscattering, is robust with regards to structural defects such as sharp corners, and exhibits excellent temporal stability. Our findings open up the possibility of actuating and detecting topological phonons in two-dimensional nanomaterials.

This paper is available in PDF form .