Session: 01-02-01: Topological Phononics

Paper Number: 173297

Designing Topological Edge States in a Locally Resonant Bandgap 

Waves in phononic crystals are studied by dividing the frequency domain into passband and bandgap regions, where the waves propagate and attenuate, respectively. Of particular interest is the presence of localized boundary states — at edges or interfaces — in certain phononic crystals within the bandgap regions of their bulk spectra. These localized modes are especially important for applications in waveguiding and energy localization. Edge-states inside Bragg-scattering-based bandgaps have been extensively studied, for example in the prototypical one-dimensional stiffness dimer (mapped from the Su-Schrieffer-Heeger or the SSH model). These systems exhibit topological behaviour that is characterized by topological invariants such as the Zak phase, which is derived from the geometric phase accumulated over the Brillouin zone. Such invariants serve to classify bandgaps as topologically trivial or non-trivial. In the SSH model, a non-trivial Zak phase corresponds to the existence of edge states, thus demonstrating the bulk–edge correspondence (BEC) principle. 

 However, such Bragg-scattering-based bandgaps pose limitations in the low-frequency regimes, such as requiring large impractical length scales of lattice periodicity. Since the attenuation profiles of the bulk influences the localization profile of the edge states, these limitations of the bandgaps extend to the edge-states hosted within them. Local-resonance-based gaps have been used successfully in various low-frequency studies as they don’t rely on length scales of lattice periodicity to open a bandgap. However, edge-states within them remain relatively unexplored. A lack of band inversion phenomena necessary for phase transformation, that typically produces non-trivial edge-states in Bragg gaps, remains a key challenge in locally resonant bandgaps as they cannot be closed and reopened to enable such transitions. Although edge-states in local-resonance-based bandgaps have been demonstrated, the fundamental mechanisms that restrict or enable them need to be further explored. 

 In this work, we propose a novel chain by adding a hidden source of strain to the intracell couplings of an SSH system using local resonators that addresses these challenges. We call this system the effective SSH chain, as it replaces one of the coupling constants with an effective stiffness derived from the resonator dynamics. The nature of Zak phase in its two bandgaps —one Bragg-based and one locally resonant— is explored. Interplay between the two types of bandgaps in this system produces a non-trivial locally resonant bandgap: something not possible with a stand-alone locally resonant bandgap. A flatband is shown to serve a critical transition point in this process. In addition, we fully utilize the low-frequency applicability of local-resonance-based bandgaps by achieving this non-triviality in the lowest bandgap.  By analysing a finite effective SSH chain with fixed ends, we establish a BEC and demonstrate extreme localization in the edge-state profiles corresponding to the anti-resonance notch in the attenuation profile of the bulk spectra.

Presenting Author: Garigipati Sai Srikanth Indian Institute of Science

Presenting Author Biography: Garigipati Sai Srikanth — who simply goes by Srikanth — is a PhD scholar at the Indian Institute of Science (IISc), where he studies wave propagation in architected materials at the Laboratory for Engineered Materials and Structures (LEMS), under the guidance of Dr. Rajesh Chaunsali. His research covers areas such as topological insulators, dispersion dynamics, local resonators, inertial amplification, and low-frequency isolation — in short, figuring out how to make waves do interesting things.

He holds a Master’s in Structural Engineering from IIT Madras and a Bachelor’s in Civil Engineering from BITS Pilani. Srikanth enjoys combining creative thinking with mathematical structure to build intuitive insights into complex physical systems.

When he’s not trying to outsmart mechanical waves, he’s passionately supporting Arsenal (which has taught him a lot about resilience) and following cricket, often juggling simulations and score updates with equal enthusiasm.

Authors:

Garigipati Sai Srikanth Indian Institute of Science
Kai Qian University of California San Diego
Ian Frankel University of California San Diego
Georgios Theocharis Laboratoire d'Acoustique de l'Université du Maine
Nicholas Boechler University of California San Diego
Rajesh Chaunsali Indian Institute of Science