Structural-Disorder-Induced Second-Order Topological Insulators in Three Dimensions

Topological Anderson phases in heat transport

Topological Anderson phases (TAPs) offer intriguing transitions from ordered to disordered systems in photonics and acoustics. However, achieving these transitions often involves cumbersome structural modifications to introduce disorders in parameters, leading to limitations in flexible tuning of topological properties and real-space control of TAPs. Here, we exploit disordered convective perturbations in a fixed heat transport system. Continuously tunable disorder-topology interactions are enabled in thermal dissipation through irregular convective lattices. In the presence of a weak convective disorder, the trivial diffusive system undergos TAP transition, characterized by the emergence of topologically protected corner modes. Further increasing the strength of convective perturbations, a second phase transition occurs converting from TAP to Anderson phase. Our work elucidates the pivotal role of disorders in topological heat transport and provides a novel recipe for manipulating thermal behaviors in diverse topological platforms.

Higher-order topological phases in crystalline and non-crystalline systems: a review

In recent years, higher-order topological phases have attracted great interest in various fields of physics. These phases have protected boundary states at lower-dimensional boundaries than the conventional first-order topological phases due to the higher-order bulk-boundary correspondence. In this review, we summarize current research progress on higher-order topological phases in both crystalline and non-crystalline systems. We firstly introduce prototypical models of higher-order topological phases in crystals and their topological characterizations. We then discuss effects of quenched disorder on higher-order topology and demonstrate disorder-induced higher-order topological insulators. We also review the theoretical studies on higher-order topological insulators in amorphous systems without any crystalline symmetry and higher-order topological phases in non-periodic lattices including quasicrystals, hyperbolic lattices, and fractals, which have no crystalline counterparts. We conclude the review by a summary of experimental realizations of higher-order topological phases and discussions on potential directions for future study.

Anderson critical metal phase in trivial states protected by average magnetic crystalline symmetry

Transitions between distinct obstructed atomic insulators (OAIs) protected by crystalline symmetries, where electrons form molecular orbitals centering away from the atom positions, must go through an intermediate metallic phase. In this work, we find that the intermediate metals will become a scale-invariant critical metal phase (CMP) under certain types of quenched disorder that respect the magnetic crystalline symmetries on average. We explicitly construct models respecting average C2zT, m, and C4zT and show their scale-invariance under chemical potential disorder by the finite-size scaling method. Conventional theories, such as weak anti-localization and topological phase transition, cannot explain the underlying mechanism. A quantitative mapping between lattice and network models shows that the CMP can be understood through a semi-classical percolation problem. Ultimately, we systematically classify all the OAI transitions protected by (magnetic) groups P m , P 2 ' , P 4 ' , and P 6 ' with and without spin-orbit coupling, most of which can support CMP.

Generation of higher-order topological insulators using periodic driving

Topological insulators (TIs) are a new class of materials that resemble ordinary band insulators in terms of a bulk band gap but exhibit protected metallic states on their boundaries. In this modern direction, higher-order TIs (HOTIs) are a new class of TIs in dimensionsd > 1. These HOTIs possess(d-1)-dimensional boundaries that, unlike those of conventional TIs, do not conduct via gapless states but are themselves TIs. Precisely, annth orderd-dimensional higher-order TI is characterized by the presence of boundary modes that reside on itsdc=(d-n)-dimensional boundary. For instance, a three-dimensional second (third) order TI hosts gapless (localized) modes on the hinges (corners), characterized bydc=1(0). Similarly, a second-order TI (SOTI) in two dimensions only has localized corner states (dc=0). These higher-order phases are protected by various crystalline as well as discrete symmetries. The non-equilibrium tunability of the topological phase has been a major academic challenge where periodic Floquet drive provides us golden opportunity to overcome that barrier. Here, we discuss different periodic driving protocols to generate Floquet HOTIs while starting from a non-topological or first-order topological phase. Furthermore, we emphasize that one can generate the dynamical anomalousπ-modes along with the concomitant 0-modes. The former can be realized only in a dynamical setup. We exemplify the Floquet higher-order topological modes in two and three dimensions in a systematic way. Especially, in two dimensions, we demonstrate a Floquet SOTI (FSOTI) hosting 0- andπcorner modes. Whereas a three-dimensional FSOTI and Floquet third-order TI manifest one- and zero-dimensional hinge and corner modes, respectively.

Observation of bulk quadrupole in topological heat transport

The quantized bulk quadrupole moment has so far revealed a non-trivial boundary state with lower-dimensional topological edge states and in-gap zero-dimensional corner modes. In contrast to photonic implementations, state-of-the-art strategies for topological thermal metamaterials struggle to achieve such higher-order hierarchical features. This is due to the absence of quantized bulk quadrupole moments in thermal diffusion fundamentally prohibiting possible band topology expansions. Here, we report a recipe for generating quantized bulk quadrupole moments in fluid heat transport and observe the quadrupole topological phases in non-Hermitian thermal systems. Our experiments show that both the real- and imaginary-valued bands exhibit the hierarchical features of bulk, gapped edge and in-gap corner states-in stark contrast to the higher-order states observed only on real-valued bands in classical wave fields. Our findings open up unique possibilities for diffusive metamaterial engineering and establish a playground for multipolar topological physics.

Anomalous topological waves in strongly amorphous scattering networks

Topological insulators are crystalline materials that have revolutionized our ability to control wave transport. They provide us with unidirectional channels that are immune to obstacles, defects, or local disorder and can even survive some random deformations of their crystalline structures. However, they always break down when the level of disorder or amorphism gets too large, transitioning to a topologically trivial Anderson insulating phase. We demonstrate a two-dimensional amorphous topological regime that survives arbitrarily strong levels of amorphism. We implement it for electromagnetic waves in a nonreciprocal scattering network and experimentally demonstrate the existence of unidirectional edge transport in the strong amorphous limit. This edge transport is shown to be mediated by an anomalous edge state whose topological origin is evidenced by direct topological invariant measurements. Our findings extend the reach of topological physics to a class of systems in which strong amorphism can induce, enhance, and guarantee the topological edge transport instead of impeding it.

Emerging Long-Range Order from a Freeform Disordered Metasurface

Recently, disordered metasurfaces have attracted considerable interest due to their potential applications in imaging, holography, and wavefront shaping. However, how to emerge long-range ordered phase distribution in disordered metasurfaces remains an outstanding problem. Here, a general framework is proposed to generate a spatially homogeneous in-plane phase distribution from a disordered metasurface, by engineering disorder parameters together with topology optimization. As a proof-of-concept demonstration, an all-dielectric disordered supercell metasurface with relatively homogeneous in-plane phase fluctuation is designed by disorder parameter engineering, manifesting as polarization conversion-dependent random scattering or unidirectional transmission. Then, a topology optimization approach is utilized to overcome the lattice coupling effect and to further improve the homogeneity of complex electric field fluctuation. In comparison with the initial supercell metasurface, both the phase fluctuation range and the relative efficiency of the topology-optimized freeform metasurface are significantly improved, leading to a long-range ordered electric field distribution. Moreover, three experimental realizations are performed, all of which agree well with the theoretical results. This methodology may inspire more exotic optical phenomena and find more promising applications in disordered metasurfaces and disordered optics.

Structural Amorphization-Induced Topological Order

Electronic properties of crystals are inherently pertained to crystalline symmetry, so that amorphization that lowers and breaks symmetry is detrimental. One important crystalline property is electron band topology which is known to be weakened and destroyed by structural disorder. Here, we report a counterintuitive theoretical discovery that atomic structural disorder by amorphization can in fact induce electronic order of topology in an otherwise topologically trivial crystal. The resulting nontrivial topology is characterized by a nonzero spin Bott index, associated with robust topological edge states and quantized conductance. The underlying topological phase transition (TPT) from a trivial crystal to a topological amorphous is analyzed by mapping out a phase diagram in the degree of structural disorder using an effective medium theory. The atomic disorder is revealed to induce topological order by renormalizing the spectral gap toward nontriviality near the phase boundary. As a concrete example, we further show such TPT in amorphous stanane by first-principles calculations. Our findings point to possible observation of an electronic ordering transition accompanied by a structural disorder transition.

Multiband topological states in non-Hermitian photonic crystals

Novel phenomena found in non-Hermitian systems and robust edge states have attracted much attention. When non-Hermitian parameters (gain and loss) are above a critical value, the non-Hermitian photonic crystal (PC) bandgaps close, leading to a mixture of the topological edge state (TES) and topological corner state (TCS) with the bulk state. Meanwhile, new bandgaps also open, in which new TES and TCS can appear. Thus, with appropriate non-Hermitian parameters, TES can emerge in both the original bandgaps and the newly opened bandgaps. The results described here will further enrich understanding of the topological properties of non-Hermitian systems.

Symmetry-Protected Topological Phases in a Rydberg Glass

Recent theoretical studies predict that structural disorder, serving as a bridge connecting a crystalline material to an amorphous material, can induce a topological insulator from a trivial phase. However, to experimentally observe such a topological phase transition is very challenging due to the difficulty in controlling structural disorder in a quantum material. Given experimental realization of randomly positioned Rydberg atoms, such a system is naturally suited to studying structural disorder induced topological phase transitions and topological amorphous phases. Motivated by the development, we study topological phases in an experimentally accessible one-dimensional amorphous Rydberg atom chain with random atom configurations. In the single-particle level, we find symmetry-protected topological amorphous insulators and a structural disorder induced topological phase transition, indicating that Rydberg atoms provide an ideal platform to experimentally observe the phenomenon using state-of-the-art technologies. Furthermore, we predict the existence of a gapless symmetry-protected topological phase of interacting bosons in the experimentally accessible system. The resultant many-body topological amorphous phase is characterized by a Z_{2} invariant.