Singular topological states, analog mechanical computers in electromechanical metamaterial

Abstract Analog mechanical computers (AMCs) are returning to the spotlight due to major breakthroughs in materials science, particularly metamaterials. This resurgence is driven by the increasing demand for efficient computational devices arising from the widespread adoption of artificial intelligence and related applications. As digital computers (DCs) approach their physical and energy limits, AMCs have emerged as a promising alternative enabled by advances in metamaterials and wave-based computing concepts. However, one of the critical challenges faced by AMCs is their high sensitivity to noise and defects. When implemented using phononic lattices, these systems are further restricted to high-frequency operation. Although locally resonant metamaterials (LRMMs) enable low-frequency functionality while maintaining compact size, they remain difficult to reconfigure for new arrangements, limiting their adaptability. In this work, we mitigate these challenges by leveraging electromechanical LRMMs. These systems consist of a uniform lattice incorporating piezoelectric materials shunted with resonant electrical circuits, where the resonators are electrical rather than mechanical. This approach provides improved accessibility, tunability, and reconfigurability. We consider a one-dimensional electromechanical LRMM lattice and apply spatial modulation to the electrical parameters, specifically the inductance, to reveal topological characteristics within the local resonator gap (LRG). As a result, singular topological edge state modes (STESMs) emerge, exhibiting strong topological protection and enabling robust functionality. We then investigate the topological features and dynamic behavior of the proposed system and demonstrate the practical use of these STESMs by solving a first-order differential equation as a proof-of-concept signal-processing task. Finally, we examine the robustness of the system against disorder and noise to confirm its resilience and address the sensitivity limitations of conventional AMCs. These results indicate that electromechanical LRMMs offer a promising pathway for designing advanced AMCs with topological protection, ease of reconfiguration, and flexible operation through electrical parameter tuning.