An official website of the United States government
Abstract 2D topological insulators promise novel approaches towards electronic, spintronic, and quantum device applications. This is owing to unique features of their electronic band structure, in which bulk-boundary correspondences enforces the existence of 1D spin–momentum locked metallic edge states—both helical and chiral—surrounding an electrically insulating bulk. Forty years since the first discoveries of topological phases in condensed matter, the abstract concept of band topology has sprung into realization with several materials now available in which sizable bulk energy gaps—up to a few hundred meV—promise to enable topology for applications even at room-temperature. Further, the possibility of combining 2D TIs in heterostructures with functional materials such as multiferroics, ferromagnets, and superconductors, vastly extends the range of applicability beyond their intrinsic properties. While 2D TIs remain a unique testbed for questions of fundamental condensed matter physics, proposals seek to control the topologically protected bulk or boundary states electrically, or even induce topological phase transitions to engender switching functionality. Induction of superconducting pairing in 2D TIs strives to realize non-Abelian quasiparticles, promising avenues towards fault-tolerant topological quantum computing. This roadmap aims to present a status update of the field, reviewing recent advances and remaining challenges in theoretical understanding, materials synthesis, physical characterization and, ultimately, device perspectives.
more »
« less
This content will become publicly available on August 12, 2026
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 strategy capable of systematically and efficiently discovering metamaterials with desired topological state. Our approach builds on topological quantum chemistry, 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 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.
more »
« less
- Award ID(s):
- 2344257
- PAR ID:
- 10650564
- Publisher / Repository:
- arXiv
- Date Published:
- Journal Name:
- Proceedings of the National Academy of Sciences
- Volume:
- 122
- Issue:
- 32
- ISSN:
- 0027-8424
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract Flat band systems are currently under intense investigation in quantum materials, optical lattices, and metamaterials. These efforts are motivated by potential realization of strongly correlated phenomena enabled by frustration-induced flat band dispersions; identification of candidate platforms plays an important role in these efforts. Here, we develop a high-throughput materials search for bulk crystalline flat bands by automated construction of uniform-hopping near-neighbor tight-binding models. We show that this approach captures many of the essential features relevant to identifying flat band lattice motifs in candidate materials in a computationally inexpensive manner, and is of use to identify systems for further detailed investigation as well as theoretical and metamaterials studies of model systems. We apply this algorithm to 139,367 materials in the Materials Project database and identify 63,076 materials that host at least one flat band elemental sublattice. We further categorize these candidate systems into at least 31,635 unique flat band crystal nets and identify candidates of interest from both lattice and band structure perspectives. This work expands the number of known flat band lattices that exist in physically realizable crystal structures and classifies the majority of these systems by the underlying lattice, providing additional insights for familiar (e.g., kagome, pyrochlore, Lieb, and dice) as well as previously unknown motifs.more » « less
-
Abstract Band edges at the high symmetry points in reciprocal space of periodic structures hold special interest in materials engineering for their high density of states. In optical metamaterials, standing waves found at these points have facilitated lasing, bound‐states‐in‐the‐continuum, and Bose–Einstein condensation. However, because high symmetry points by definition are localized, properties associated with them are limited to specific energies and wavevectors. Conversely, quasi‐propagating modes along the high symmetry directions are predicted to enable similar phenomena over a continuum of energies and wavevectors. Here, quasi‐propagating modes in 2D nanoparticle lattices are shown to support lasing action over a continuous range of wavelengths and symmetry‐determined directions from a single device. Using lead halide perovskite nanocrystal films as gain materials, lasing is achieved from waveguide‐surface lattice resonance (W‐SLR) modes that can be decomposed into propagating waves along high symmetry directions, and standing waves in the orthogonal direction that provide optical feedback. The characteristics of the lasing beams are analyzed using an analytical 3D model that describes diffracted light in 2D lattices. Demonstrations of lasing across different wavelengths and lattice designs highlight how quasi‐propagating modes offer possibilities to engineer chromatic multibeam emission important in hyperspectral 3D sensing, high‐bandwidth Li‐Fi communication, and laser projection displays.more » « less
-
Abstract Topological mechanical metamaterials have been widely explored for their boundary states, which can be robustly isolated or transported in a controlled manner. However, such systems often require pre-configured design or complex active actuation for wave manipulation. Here, we present the possibility of in-situ transfer of topological boundary modes by leveraging the reconfigurability intrinsic in twisted origami lattices. In particular, we employ a dimer Kresling origami system consisting of unit cells with opposite chirality, which couples longitudinal and rotational degrees of freedom in elastic waves. The quasi-static twist imposed on the lattice alters the strain landscape of the lattice, thus significantly affecting the wave dispersion relations and the topology of the underlying bands. This in turn facilitates an efficient topological state transfer from one edge to the other. This simple and practical approach to energy transfer in origami-inspired lattices can thus inspire a new class of efficient energy manipulation devices.more » « less
-
Abstract Maxwell lattices possess distinct topological states that feature mechanically polarized edge behaviors and asymmetric dynamic responses protected by the topology of their phonon bands. Until now, demonstrations of non‐trivial topological behaviors from Maxwell lattices have been limited to fixed configurations or have achieved reconfigurability using mechanical linkages. Here, a monolithic transformable topological mechanical metamaterial is introduced in the form of a generalized kagome lattice made from a shape memory polymer (SMP). It is capable of reversibly exploring topologically distinct phases of the non‐trivial phase space via a kinematic strategy that converts sparse mechanical inputs at free edge pairs into a biaxial, global transformation that switches its topological state. All configurations are stable in the absence of confinement or a continuous mechanical input. Its topologically‐protected, polarized mechanical edge stiffness is robust against broken hinges or conformational defects. More importantly, it shows that the phase transition of SMPs that modulate chain mobility, can effectively shield a dynamic metamaterial's topological response from its own kinematic stress history, referred to as “stress caching”. This work provides a blueprint for monolithic transformable mechanical metamaterials with topological mechanical behavior that is robust against defects and disorder while circumventing their vulnerability to stored elastic energy, which will find applications in switchable acoustic diodes and tunable vibration dampers or isolators.more » « less
