The discovery of topological quantum states marks a new chapter in both condensed matter physics and materials sciences. By analogy to spin electronic system, topological concepts have been extended into phonons, boosting the birth of topological phononics (TPs). Here, we present a high-throughput screening and data-driven approach to compute and evaluate TPs among over 10,000 materials. We have clarified 5014 TP materials and classified them into single Weyl, high degenerate Weyl, and nodal-line (ring) TPs. Among them, three representative cases of TPs have been discussed in detail. Furthermore, we suggest 322 TP materials with potential clean nontrivial surface states, which are favorable for experimental characterizations. This work significantly increases the current library of TP materials, which enables an in-depth investigation of their structure-property relations and opens new avenues for future device design related to TPs.
Efficient control of phonons is crucial to energy-information technology, but limited by the lacking of tunable degrees of freedom like charge or spin. Here we suggest to utilize crystalline symmetry-protected pseudospins as new quantum degrees of freedom to manipulate phonons. Remarkably, we reveal a duality between phonon pseudospins and electron spins by presenting Kramers-like degeneracy and pseudospin counterparts of spin-orbit coupling, which lays the foundation for "pseudospin phononics". Furthermore, we report two types of three-dimensional phononic topological insulators, which give t…
A unified form of time-reversal symmetry (TRS) breaking terms in phononic crystals, leading to nontrivial phononic topology, has been proposed recently, but is contradicted by some other works which introduce gyroscopic effect as TRS-breaking. We re-study gyroscopic phononic crystals using Newtonian mechanical method, and find the correct TRS-breaking term in consistent with the unified form. Applying this term we calculate the basic topological phononics in a honeycomb lattice. Furthermore, we study nonlinear phonon-phonon scattering effect on topological phononic edge states by molecular dyn…
The quantum anomalous Hall effect, an exotic topological state first theoretically predicted by Haldane and recently experimentally observed, has attracted enormous interest for low-power-consumption electronics. In this work, we derived a Schr{ö}dinger-like equation of phonons, where topology-related quantities, time reversal symmetry and its breaking can be naturally introduced similar as for electrons. Furthermore, we proposed a phononic analog of the Haldane model, which gives the novel quantum (anomalous) Hall-like phonon states characterized by one-way gapless edge modes immune to scatte…
We report a new type of phononic crystals with topologically non-trivial bandgaps for both longitudinal and transverse polarizations, resulting in protected one-way elastic edge waves. In our design, gyroscopic inertial effects are used to break the time-reversal symmetry and realize the phononic analogue of the electronic quantum Hall effect. We investigate the response of both hexagonal and square gyroscopic lattices and observe bulk Chern number of 1 and 2, indicating that these structures support single and multi-mode edge elastic waves immune to back-scattering. These robust one-way phono…
Distinct from the phononic valley pseudo-spin, the real physical spin of elastic waves adds a novel tool-kit capable of envisaging the valley-spin physics of topological valley phononic crystals from a local viewpoint. Here, we report the observation of local elastic valley spin as well as the hidden elastic spin-valley locking mechanism overlooked before. We demonstrate that the selective one-way routing of valley phonon states along the topological interface can be reversed by imposing the elastic spin meta-source at different interface locations with opposite valley-spin correspondence. We …
Topological metamaterials have robust properties engineered from their macroscopic arrangement, rather than their microscopic constituency. They can be designed by starting from Dirac metamaterials with either symmetry-enforced or accidental degeneracy. The latter case provides greater flexibility in the design of topological switches, waveguides, and cloaking devices, because a large number of tuning parameters can be used to break the degeneracy and induce a topological phase. However, the design of a topological logic element--a switch that can be controlled by the output of a separate swit…
The concept of topological energy bands and their manifestations have been demonstrated in condensed matter systems as a fantastic paradigm toward unprecedented physical phenomena and properties that are robust against disorders. Recent years, this paradigm was extended to phononic metamaterials (including mechanical and acoustic metamaterials), giving rise to the discovery of remarkable phenomena that were not observed elsewhere thanks to the extraordinary controllability and tunability of phononic metamaterials as well as versatile measuring techniques. These phenomena include, but not limit…
By means of first-principles calculations and modeling analysis, we have predicted that the traditional 2D-graphene hosts the topological phononic Weyl-like points (PWs) and phononic nodal line (PNL) in its phonon spectrum. The phonon dispersion of graphene hosts three type-I PWs (both PW1 and PW2 at the BZ corners \emph{K} and \emph{K}', and PW3 locating along the $Γ$-\emph{K} line), one type-II PW4 locating along the $Γ$-\emph{M} line, and one PNL surrounding the centered $Γ$ point in the $q_{x,y}$ plane. The calculations further reveal that Berry curvatures are vanishingly zero throughout t…
Topological phononic states, facilitating acoustic unique transports immunizing to defects and disorders, have significantly revolutionized our scientific cognition of acoustic wave systems. Up to now, the theoretical and experimental demonstrations of topologically protected one-way transports with pseudospin states in a phononic crystal beyond the graphene lattice with C6v symmetry are still unexploited. Furthermore, the tunable topological states, in form of robust reconfigurable acoustic pathways, have been evaded in the topological phononic insulators. Here, we realize a topological phase…
Dirac semimetals, the materials featured with discrete linearly crossing points (called Dirac points) between four bands, are critical states of topologically distinct phases. Such gapless topological states have been accomplished by a band-inversion mechanism, in which the Dirac points can be annihilated pairwise by perturbations without changing the symmetry of the system. Here, we report an experimental observation of Dirac points that are enforced completely by the crystal symmetry, using a nonsymmorphic three-dimensional phononic crystal. Intriguingly, our Dirac phononic crystal hosts fou…
The modern theory of charge polarization in solids is based on a generalization of Berry's phase. Its possible quantization lies at the heart of our understanding of all systems with topological band structures that were discovered over the last decades. While based on the concept of the "charge" polarization, the same theory can be used as an elegant tool to characterize the Bloch bands of neutral bosonic systems such as photonic or phononic crystals. Recently, the theory of this quantized polarization was extended from the dipole- to higher multipole-moments. In particular, a two-dimensional…
The discovery of Weyl semimetals opens the door for searching topological semimetals in physical science. The Weyl points are generally recognized as conventional, quadratic, spin-1, and those of high topological charges. Here we report the observation of the quadruple Weyl point of charge 4, the highest topological charge a twofold degenerate node can carry. Besides the quadruple Weyl point, the phononic semimetal also hosts conventional, quadratic, and spin-1 Weyl points, which stands as a system with yet the richest types of Weyl points. The quadruple-helicoid surface states, specific to th…
Two-dimensional (2D) Stiefel-Whitney (SW) insulator is a fragile topological state characterized by the second SW class in the presence of space-time inversion symmetry. So far, SWIs have been proposed in several electronic materials but seldom in phononic systems. Here we recognize that a large class of 2D buckled honeycomb crystals termed Xenes and their ligand-functionalized derivatives realize the nontrivial phononic SW topology. The phononic SWIs are identified by a nonzero second SW number $w_2=1$, associated with gaped edge states and robust topological corner modes. Despite the versati…
The field of topological mechanics has recently emerged due to the interest in robustly transporting various types of energy in a flaw and defect-insensitive fashion. While there have been a significant number of studies based on discovering and proposing topological materials and structures, very few have focused on tuning the resulting topological bandgaps, which is critical because the bandgap frequency is fixed once the structure has been fabricated. Here, we perform both lattice dynamical calculations and molecular dynamical simulations to investigate strain effects on the phononic topolo…
Weyl semimetals are extraordinary systems where exotic phenomena such as Fermi arcs, pseudo-gauge fields and quantum anomalies arise from topological band degeneracy in crystalline solids for electrons and metamaterials for photons and phonons. On the other hand, higher-order topological insulators unveil intriguing multidimensional topological physics beyond the conventional bulk-edge correspondences. However, it is unclear whether higher-order topology can emerge in Weyl semimetals. Here, we report the experimental discovery of higher-order Weyl semimetals in its phononic analog which exhibi…
Phonons as collective excitations of lattice vibrations are the main heat carriers in solids. Tremendous effort has been devoted to investigate phonons and related properties, giving rise to an intriguing field of phononics, which is of great importance to many practical applications, including heat dissipation, thermal barrier coating, thermoelectrics and thermal control devices. Meanwhile, the research of topology-related physics, awarded the 2016 Nobel Prize in Physics, has led to discoveries of various exotic quantum states of matter, including the quantum (anomalous/spin) Hall [Q(A/S)H] e…
Topological defects (including disclinations and dislocations) which commonly exist in various materials have shown an amazing ability to produce excellent mechanical and physical properties of matters. In this paper, disclinations and dislocations are firstly introduced into the valley-polarized elastic phononic plate. Deformation of the lattice yields the interface expressing as the topologically protected wave guiding, due to the valley-polarized phase transition of phononic crystals (PnCs) across the interface. Then, disclinations are introduced into the Wannier-type elastic phononic plate…
National Laboratory of Solid State Microstructures, Nanjing University（南京大学固体微结构物理国家重点实验室）；School of Advanced Manufacturing Engineering, Nanjing University（南京工程学院（注：原文为Nanjing University，但通常Suzhou校区对应苏州大学或南京大学苏州研究院，此处严格按原文翻译）南京大学先进制造工程学院）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences（中国科学院金属研究所沈阳材料科学国家研究中心）；New Cornerstone Science Laboratory, Department of Physics, The University of Hong Kong（香港大学新基石科学学院物理学系）；School of Physical Science and Technology, Soochow University（苏州大学物理科学与技术学院）；School of Physical Sciences, University of Science and Technology of China（中国科学技术大学物理学院）；School of Physics Science and Engineering, Tongji University（同济大学物理科学与工程学院）；Suzhou Institute for Advanced Research, University of Science and Technology of China（中国科学技术大学苏州高等研究院）；National Laboratory of Solid State Microstructures and Department of Materials Science and Engineering, Nanjing University（南京大学固体微结构物理国家重点实验室和材料科学与工程系）
Reflection and refraction occur at interface between two different media. These two fundamental phenomena form the basis of fabricating various wave components. Specifically, refraction, dubbed positive refraction nowadays, appears in the opposite side of the interface normal with respect to the incidence. Negative refraction, emerging in the same side by contrast, has been observed in artificial materials1-5 following a prediction by Veslago6, which has stimulated many fascinating applications such as super-resolution imaging7. Here we report the first discovery of negative refraction of the …
Higher-order topological insulators have attracted great research interest recently. Different from conventional topological insulators, higher-order topological insulators do not necessarily require spin-orbit coupling, which makes it possible to realize them in spinless systems. Here, we study phonons in 2D graphyne family materials. By using first-principle calculations and topology/symmetry analysis, we find that phonons in both graphdiyne and $γ$-graphyne exhibit a second-order topology, which belongs to the specific case known as real Chern insulator. We identify the nontrivial phononic …
While condensed matter systems host both Fermionic and Bosonic quasi-particles, reliably predicting and empirically verifying topological states is only mature for Fermionic electronic structures, leaving topological Bosonic excitations sporadically explored. This is unfortunate, as Bosonic systems such a phonons offer the opportunity to assess spinless band structures where nodal lines can be realized without invoking special additional symetries to protect against spin-orbit coupling. Here we combine first-principles calculations and meV-resolution inelastic x-ray scattering to demonstrate t…
Topological phononic insulators are the counterpart of three-dimensional quantum spin Hall insulators in phononic systems and, as such, their topological surfaces are characterized by Dirac cone-shaped gapless edge states arising as a consequence of a bulk-boundary correspondence. We propose a theoretical framework for the possible superconducting phase in these materials, where the attractive interaction between electrons is mediated by topological phonons in nontrivial boundary modes. Within the BCS limit, we develop a self-consistent two-band gap equation, whose solutions show that the supe…
Based on first-principles calculations, we predict that the superconducting MgB$_2$ with a AlB$_2$-type centrosymmetric lattice host the so-called phononic topological Weyl nodal lines (PTWNLs) on its bulk phonon spectrum. These PTWNLs can be viewed as countless Weyl points (WPs) closely aligned along the straight lines in the $-$H-K-H direction within the three-dimensional Brillouin zone (BZ). Their topological non-trivial natures are confirmed by the calculated Berry curvature distributions on the planes perpendicular to these lines. These lines are highly unique, because they exactly locate…
Higher-order topological insulators (HOTIs) are described by symmetric exponentially decayed Wannier functions at some $necessary$ unoccupied Wyckoff positions and classified as obstructed atomic insulators (OAIs) in the topological quantum chemistry (TQC) theory. The boundary states in HOTIs reported so far are often fragile, manifested as strongly depending on crystalline symmetries and cleavage terminations in the disk or cylinder geometry. Here, using the TQC theory, we present an intuitive argument about the connection between the obstructed Wannier charge centers of OAIs and the emergenc…
Topological semimetal states which are constrained by symmetries and give birth to innovative excitations are the frontiers of topological quantum matter. Nodal chains in which two nodal rings connect at one point were first discovered in non-symmorphic electronic systems and then generalized to symmorphic phononic systems. In this work, we identify a new class of planar nodal chains in non-symmorphic phononic systems, where the connecting rings lie in the same plane. The constituting nodal rings are protected by mirror symmetry, their intersection is guaranteed by the combination of time-reve…
Berry curvature (BC) governs topological phases of matter and generates anomalous transport. When a magnetic field is applied, phonons can acquire BC indirectly through spin-lattice coupling, leading to a linear phonon Hall effect. Here, we show that polar lattice distortion directly couples to a phonon BC dipole, which causes a switchable non-linear phonon Hall effect. In a SnS monolayer, the in-plane ferroelectricity induces a phonon BC and leads to the phononic version of the non-volatile BC memory effect. As a new type of ferroelectricity-phonon coupling, the phonon Rashba effect emerges a…
Topological materials discovery has evolved at a rapid pace over the past 15 years following the identification of the first nonmagnetic topological insulators (TIs), topological crystalline insulators (TCIs), and 3D topological semimetals (TSMs). Most recently, through complete analyses of symmetry-allowed band structures - including the theory of Topological Quantum Chemistry (TQC) - researchers have determined crystal-symmetry-enhanced Wilson-loop and complete symmetry-based indicators for nonmagnetic topological phases, leading to the discovery of higher-order TCIs and TSMs. The recent app…
Following the emergence of many novel two-dimensional (2-D) materials beyond graphene, interest has grown in exploring implications for fundamental physics and practical applications, ranging from electronics, photonics, phononics, to thermal management and energy storage. In this Colloquium, we first summarize and compare the phonon properties, such as phonon dispersion and relaxation time, of pristine 2-D materials with single layer graphene to understand the role of crystal structure and dimension on thermal conductivity. We then compare the phonon properties, contrasting idealized 2-D crys…
Two-dimensional (2D) topological materials (TMs) have attracted tremendous attention due to the promise of revolutionary devices with non-dissipative electric or spin currents. Unfortunately, the scarcity of 2D TMs holds back the experimental realization of such devices. In this work, based on our recently developed, highly efficient TM discovery algorithm using symmetry indicators, we explore the possible 2D TMs in all non-magnetic compounds in four recently proposed materials databases for possible 2D materials. We identify hundreds of 2D TM candidates, including 205 topological (crystalline…
Topologically protected one-way transportation of sound, mimicking the topological properties of the condensed matter, has received greatly attentions. Thus far, the topological phases and the topological edge states of sound are yielded in the vicinity of the Dirac cones fixed at the high symmetric points of the Brillouin zone. Here, we present a new type of the phononic topological insulator in the square lattice with position-variational Dirac cones along the high symmetric lines. The emergence of such Dirac cones, characterized by the vortex structure in a momentum space, is attributed to …
First-principles calculations, within the framework of density functional theory, have been performed on the well-studied 2H and the less explored 1T$^{\prime}$ phase of single-layer MoS$_{2}$. We have addressed the strain-induced tunability of the electronic and phononic properties of both phases, and compared their stability against the applied strain. By considering a large number of strain profiles for both tensile and compressive stress, we have found that the electronic properties of both 2H and 1T$^{\prime}$ phases are sensitive to the direction of the applied strain and can be tuned in…
Recent studies on different topological materials in condensed matter physics have provided the evidence of topological nature for bosonic particle like phonons by performing various theoretical calculations and experimental observations. Here, the topological behaviours of phonons of SnS, SnSe and SnTe materials in rock-salt structure are investigated using $ab$-$initio$ methodology. For all these materials, the tilted linear band touching is observed along with the presence of band inversion in direction X-W. The topological point in phonon dispersion curve along X-W direction is found to be…
Both SnS and SnSe have been experimentally and theoretically confirmed as topological crystalline insulators in native rocksalt structure. Here, phononic structure, thermodynamical properties and temperature dependent electron-phonon interaction (EPI) have investigated for both the materials in rocksalt phase. Previously performed theoretical studies have predicted the phase instability of SnS in this crystal structure at ambient condition. But, after a detailed study performing on the phonon calculation of SnS, we have predicted the phase stability of SnS with considering the Sn 4$p$ orbitals…
Critical couplings in topological-insulator waveguide-resonator systems observed in elastic waves
National Laboratory of Solid State Microstructures & Department of Materials Science and Engineering, Nanjing University（南京大学固态微结构实验室与材料科学与工程系）；Jiangsu Key Laboratory of Artificial Functional Materials, Nanjing University（南京大学江苏省人工功能材料重点实验室）
In parallel to electronic systems, the concept of topology has been extended to phonons, which has led to the birth of topological phonons. Very recently, nodal point phonons, nodal line phonons, and nodal surface phonons have been proposed, and a handful of candidate materials have been predicted in solid-state materials. In this work, based on symmetry analysis and first-principles calculations, we propose that hourglass Weyl nodal line (HWNL) phonons and Dirac nodal line (DNL) phonons coexist in the phonon dispersion of a single material, KCuS, with a $Pnma$-type structure. The HWNLs and DN…
Topological materials in crystal solids, including topological insulators (TIs), topological crystalline insulators (TCIs), topological Dirac semimetals (DSMs), topological Weyl semimetals (WSMs), topological Dirac or Weyl nodal line semimetals (NLSMs) and beyond, are mainly featured with topological, protected non-trivial surface states, and their bulk phases are insulators or semimetals with the proper presence of Dirac cones, Weyl nodes or Dirac nodal lines around the Fermi level. The author suggests a two-step computational screening strategy of 3D topological materials by mixing chemistry…
Topological insulators constitute one of the most intriguing phenomena in modern condensed matter theory. The unique and exotic properties of topological states of matter allow for unidirectional gapless electron transport and extremely accurate measurements of the Hall conductivity. Recently, new topological effects occurring at Dirac/Weyl points have been better understood and demonstrated using artificial materials such as photonic and phononic crystals, metamaterials and electrical circuits. In comparison, the topological properties of nodal lines, which are one-dimensional degeneracies in…
Phonons play a key role in the physical properties of materials, and have long been a topic of study in physics. While the effects of phonons had historically been considered to be a hindrance, modern research has shown that phonons can be exploited due to their ability to couple to other excitations and consequently affect the thermal, dielectric, and electronic properties of solid state systems, greatly motivating the engineering of phononic structures. Advances in nanofabrication have allowed for structuring and phonon confinement even down to the nanoscale, drastically changing material pr…
