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A flatband material is a system characterized by energy bands with zero dispersion, allowing for the compact localization of wavefunctions in real space. This compact localization significantly enhances inter-particle correlations and light-matter interactions, leading to notable advancements such as fractional Chern insulators in condensed matter systems and flat-band lasers in photonics. Previous flatband platforms, including twisted bilayer graphene and artificial kagome/Lieb lattices, typically focused on nondegenerate flatbands, lacking access to the high degeneracy that can facilitate the localization of orbital angular momentum (OAM). Here, we propose a general framework to construct highly degenerate flatbands from bound states in the continuum (BICs)--a concept originating from quantum theory but significantly developed in photonics and acoustics in recent years. The degeneracy of flatbands is determined by the number of BICs within each unit cell in a lattice. We experimentally validate this approach in two-dimensional (2D) and three-dimensional (3D) acoustic crystals, demonstrating flatbands with 4-fold and 12-fold degeneracies, respectively. The high degeneracy provides sufficient internal degrees of freedom, enabling the selective excitation of localized OAM at any position in any direction. Our results pave the way for exploring BIC-constructed flatbands and their localization properties., Comment: 15 pages, 4 figures

Spin and valley are two fundamental properties of electrons in crystals. The similarity between them is well understood in valley-contrasting physics established decades ago in two-dimensional (2D) materials like graphene--with broken inversion symmetry, the two valleys in graphene exhibit opposite orbital magnetic moments, similar to the spin-1/2 behaviors of electrons, and opposite Berry curvature that leads to a half topological charge. However, valley-contrasting physics has never been explored in 3D crystals. Here, we develop a 3D acoustic crystal exhibiting 3D valley-contrasting physics. Unlike spin that is fundamentally binary, valley in 3D can take six different values, each carrying a vortex in a distinct direction. The topological valley transport is generalized from the edge states of 2D materials to the surface states of 3D materials, with interesting features including robust propagation, topological refraction, and valley-cavity localization. Our results open a new route for wave manipulation in 3D space., Comment: 8 pages, 5 figures

The interplay between disorder and topology leads to rich phenomena such as topological Anderson insulator phases, where disorder opens a topological bandgap and thereby enhances transport. With the recent advances in non-Hermitian topological physics, topological Anderson insulators have been generalized to systems with non-Hermitian disorder. However, achieving disorder-induced nontrivial point-gap topology, which is unique to non-Hermitian systems and is responsible for non-Hermitian skin effect, remains elusive. In this work, we experimentally realized non-Hermitian disorder-induced point-gap topology in a one-dimensional acoustic crystal. By controlling the gain factor of the amplifier in each basic unit, we obtained a series of disordered unidirectional hoppings with tunable strength. Using disordered acoustic crystals under open boundary conditions, we observed the emergence of non-Hermitian skin effect and the direction reversal of skin mode localization when the disorder strength is tuned. These results serve as hallmarks of point-gap topological phase transition induced by non-Hermitian disorder. Our work paves the way for exploring various disorder-induced phenomena in non-Hermitian acoustic systems., Comment: 7 pages, 4 figures

When electrons moving in two-dimensions (2D) are subjected to a strong uniform magnetic field, they form flat bands called Landau levels, which are the basis for the quantum Hall effect. Landau levels can also arise from pseudomagnetic fields (PMFs) induced by lattice distortions; for example, mechanically straining graphene causes its Dirac quasiparticles to form a characteristic set of unequally-spaced Landau levels, including a zeroth Landau level. In three-dimensional (3D) systems, there has thus far been no experimental demonstration of Landau levels or any other type of flat band. For instance, applying a uniform magnetic field to materials hosting Weyl quasiparticles, the 3D generalizations of Dirac quasiparticles, yields bands that are non-flat in the direction of the field. Here, we report on the experimental realization of a flat 3D Landau level in an acoustic crystal. Starting from a lattice whose bandstructure exhibits a nodal ring, we design an inhomogeneous distortion corresponding to a specific pseudomagnetic vector potential (PVP) that causes the nodal ring states to break up into Landau levels, with a zeroth Landau level that is flat along all three directions. These findings point to the possibility of using nodal ring materials to generate 3D flat bands, to access strong interactions and other interesting physical regimes in 3D.

Band topology of materials describes the extent Bloch wavefunctions are twisted in momentum space. Such descriptions rely on a set of topological invariants, generally referred to as topological charges, which form a characteristic class in the mathematical structure of fiber bundles associated with the Bloch wavefunctions. For example, the celebrated Chern number and its variants belong to the Chern class, characterizing topological charges for complex Bloch wavefunctions. Nevertheless, under the space-time inversion symmetry, Bloch wavefunctions can be purely real in the entire momentum space; consequently, their topological classification does not fall into the Chern class, but requires another characteristic class known as the Stiefel-Whitney class. Here, in a three-dimensional acoustic crystal, we demonstrate a topological nodal-line semimetal that is characterized by a doublet of topological charges, the first and second Stiefel-Whitney numbers, simultaneously. Such a doubly charged nodal line gives rise to a doubled bulk-boundary correspondence: while the first Stiefel-Whitney number induces ordinary drumhead states of the nodal line, the second Stiefel-Whitney number supports hinge Fermi arc states at odd inversion-related pairs of hinges. These results establish the Stiefel-Whitney topological charges as intrinsic topological invariants for topological materials, with their unique bulk-boundary correspondence beyond the conventional framework of topological band theory., Comment: 12 pages, 10 figures

Topological phases of matter have remained an active area of research in the last few decades. Periodic driving is known to be a powerful tool for enriching such exotic phases, which leads to various phenomena with no static analogs. One such phenomenon is the emergence of the elusive $pi/2$ modes, i.e., a type of topological boundary state pinned at a quarter of the driving frequency. The latter may lead to the formation of Floquet parafermions in the presence of interaction, which is known to support more computational power than Majorana particles. In this work, we experimentally verify the signature of $\pi/2$ modes in an acoustic waveguide array, which is designed to simulate a square-root periodically driven Su-Schrieffer-Heeger model. This is accomplished by confirming the $4T$-periodicity ($T$ being the driving period) profile of an initial-boundary excitation, which we also show theoretically to be the smoking gun evidence of $\pi/2$ modes. Our findings are expected to motivate further studies of $\pi/2$ modes in quantum systems for potential technological applications., Comment: 6 pages, 3 figure. Comments are welcome

Symmetry plays a key role in modern physics, as manifested in the revolutionary topological classification of matter in the past decade. So far, we seem to have a complete theory of topological phases from internal symmetries as well as crystallographic symmetry groups. However, an intrinsic element, i.e., the gauge symmetry in physical systems, has been overlooked in the current framework. Here, we show that the algebraic structure of crystal symmetries can be projectively enriched due to the gauge symmetry, which subsequently gives rise to new topological physics never witnessed under ordinary symmetries. We demonstrate the idea by theoretical analysis, numerical simulation, and experimental realization of a topological acoustic lattice with projective translation symmetries under a $Z_2$ gauge field, which exhibits unique features of rich topologies, including a single Dirac point, M\"{o}bius topological insulator and graphene-like semimetal phases on a rectangular lattice. Our work reveals the impact when gauge and crystal symmetries meet together with topology, and opens the door to a vast unexplored land of topological states by projective symmetries., Comment: 7 pages, 4 figures

The topological band theory predicts that bulk materials with nontrivial topological phases support topological edge states. This phenomenon is universal for various wave systems and has been widely observed for electromagnetic and acoustic waves. Here, we extend the notion of band topology from wave to diffusion dynamics. Unlike the wave systems that are usually Hermitian, the diffusion systems are anti-Hermitian with purely imaginary eigenvalues corresponding to decay rates. Via direct probe of the temperature diffusion, we experimentally retrieve the Hamiltonian of a thermal lattice, and observe the emergence of topological edge decays within the gap of bulk decays. Our results show that such edge states exhibit robust decay rates, which are topologically protected against disorders. This work constitutes a thermal analogue of topological insulators and paves the way to exploring defect-immune heat dissipation.