arXiv subjects

Pegah Azizi

Publications and source records attributed to Pegah Azizi.

5 recordsLinked to original sources

arXiv2026

Boosting lattice polarization Mixing the perspectives of geometry optimization and cell-augmentation

Topologically polarized mechanical metamaterials enjoy a special built-in asymmetry that manifests as a preferred localization of edge states on selected edges. While this property has been shown for a few ideal Maxwell lattices, we currently lack systematic criteria to design families of structural systems exhibiting polarization. Here, we propose a framework to design polarized structural configurations enabled by topology optimization (TO), using both band and mode morphological properties as drivers of the optimization algorithm. Through the lens of TO, we are able to tap into a vast design space, unlocking geometric freedom far beyond what is achievable with canonical lattice architectures. At the same time, we elucidate important criteria that need to be satisfied, beyond the optimization outcome, to ensure robustness of the achieved polarization against perturbations of the edge morphology. These results provide the inspiration to loop back into the realm of ideal lattices in search of new configurations characterized by extreme polarization. The peculiar shape and connectivity of the TO-generated lattice offer a blueprint for identifying a new family of Maxwell trusses based on augmented kagome geometry. We demonstrate the achievement of strong polarization signatures up to a three-count edge state mismatch. For all the cases studied, we show agreement between theory, simulations, and experiments, which include laser vibrometry wave measurements on a waterjet-cut specimen and static tests on a 3D-printed prototype.

cond-mat.mtrl-sci↗

arXiv2025

Lattice Materials with Topological States Optimized On-Demand

Topological states of matter, first discovered in quantum systems, have opened new avenues for wave manipulation beyond the quantum realm. In elastic media, realizing these topological effects requires identifying lattices that support the corresponding topological bands. However, among the vast number of theoretically predicted topological states, only a small fraction has been physically realized. To close this gap, we present a new strategy capable of systematically and efficiently discovering metamaterials with any desired topological state. Our approach builds on topological quantum chemistry (TQC), which systematically classifies topological states by analyzing symmetry properties at selected wavevectors. Because this method condenses the topological character into mathematical information at a small set of wavevectors, it encodes a clear and computationally efficient objective for topology optimization algorithms. We demonstrate that, for certain lattice symmetries, this classification can be further reduced to intuitive morphological features of the phonon band structure. By incorporating these band morphology constraints into topology optimization algorithms and further fabricating obtained designs, we enable the automated discovery and physical realization of metamaterials with targeted topological properties. This methodology establishes a new paradigm for engineering topological elastic lattices on demand, addressing the bottleneck in material realization and paving the way for a comprehensive database of topological metamaterial configurations.

cond-mat.mtrl-sci↗

arXiv2024

Non-local twist sequences in floppy kagome chains

The twisted kagome family comprises a spectrum of configurations that can be realized through the sweep of a single configurational degree of freedom known as a twist angle. Recently, it was shown that certain pairs of configurations along this sweep were linked by duality transformations and displayed matching phonon spectra. In this work, we introduce an intercell-connection system that spreads the lattice in the dimension orthogonal to the tessellation plane. The resulting three-dimensional character of the lattice allows us to sweep the entirety of the twist-angle spectrum, including all the compact configurations featuring overlapping triangles that, in a strictly two-dimensional space, are forbidden. Duality provides precious guidance for interpreting the availability of floppy mechanisms arising in the compact configurations through the one-to-one correspondence with their expanded counterparts. Our focus is on the compact configuration corresponding to a null twist angle, where the lattice degenerates to a chain. From the perspective of the chain, several of the local connections between neighboring lattice cells play the role of nonlocal long-range interactions between cells of the chain. We demonstrate experimentally some peculiar behavior that results from such nonlocality, including a selective activation of floppy sequences that is informed by the direction of loading.

cond-mat.mtrl-sci↗

arXiv2023

Omnidirectional domain wall modes protected by fragile topological states

So-called fragile topological states of matter challenge our conventional notion of topology by lacking the robustness typically associated with topological protection, thereby displaying elusive manifestations that are difficult to harness for wave control. In this Letter, we leverage the recent discovery of fragile topological states in special classes of structural kagome lattices to document the availability of domain wall elastic wave modes that are directly traceable to fragile topology and, yet, exhibit remarkably strong signatures that support omni-directionality. We design twisted kagome bi-domains comprising two topologically distinct sublattices - one trivial and the other fragile topological - sharing a common bandgap and meeting at a domain wall. The two phases are achieved via carefully engineered surface cut patterns that modify the band landscape of the underlying lattices in complementary fashions, leading to dichotomous irreps landscapes. Under these circumstances, a domain wall-bound mode emerges within the shared bandgap and displays remarkable stability against domain wall orientation and introduced defects. We corroborate these findings via $\mathbf{k}\cdot\mathbf{p}$ Hamiltonian and Jackiw-Rabbi analysis and validate them experimentally through laser vibrometry tests on a prototype endowed with water jet-induced perforation patterns.

cond-mat.mtrl-sci↗

arXiv2022

Dynamics of self-dual kagome metamaterials and the emergence of fragile topology

Recent years have seen the discovery of systems featuring fragile topological states. These states of matter lack certain protection attributes typically associated with topology and are therefore characterized by weaker signatures that make them elusive to observe. Moreover, they are typically confined to special symmetry classes and, in general, rarely studied in the context of phononic media. In this Letter, we theoretically predict the emergence of fragile topological bands in the spectrum of a twisted kagome elastic lattice with three-fold rotational symmetry, in the so-called self-dual configuration. A necessary requirement is that the lattice is a structural metamaterial, in which the role of the hinges is played by elastic finite-thickness ligaments. The interplay between the edge modes appearing in the bandgaps bounding the fragile topological states is also responsible for the emergence of corner modes at selected corners of a finite hexagonal domain, which qualifies the lattice as a second-order topological insulator. We demonstrate our findings through a series of experiments via 3D Scanning Laser Doppler Vibrometry conducted on a physical prototype. The selected configuration stands out for its remarkable geometric simplicity and ease of physical implementation in the panorama of dynamical systems exhibiting fragile topology.

cond-mat.mtrl-sci↗