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Register a new userComputation and data driven discovery of topological phononic materials
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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.
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We present a review of topological electronic materials discovery in crystalline solids from the prediction of the first 2D and 3D topological insulators (TIs) through the recently introduced methods that have facilitated large-scale searches for topological materials. We first briefly review the concepts of band theory and topology, as well as the experimental methods used to demonstrate nontrivial topology in solid-state materials. We then review the past 15 years of topological materials discovery, including the identification of the first nonmagnetic TIs, topological crystalline insulators (TCIs), and 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. Lastly, we discuss the recent application of TQC and related methods to high-throughput materials discovery, which revealed that over half of all of the known stoichiometric, solid-state, nonmagnetic materials are topological at the Fermi level, over 85% of the known stoichiometric materials host energetically isolated topological bands, and that just under $2/3$ of the energetically isolated bands in known materials carry the stable topology of a TI or TCI. We conclude by discussing future venues for the identification and manipulation of solid-state topological phases, including charge-density-wave compounds, magnetic materials, and 2D few-layer devices.
The modern theory of charge polarization in solids is based on a generalization of Berrys 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 quantized quadrupole insulator is predicted to have gapped yet topological one-dimensional edge-modes, which in turn stabilize zero-dimensional in-gap corner states. However, such a state of matter has not been observed experimentally. Here, we provide the first measurements of a phononic quadrupole insulator. We experimentally characterize the bulk, edge, and corner physics of a mechanical metamaterial and find the predicted gapped edge and in-gap corner states. We further corroborate our findings by comparing the mechanical properties of a topologically non-trivial system to samples in other phases predicted by the quadrupole theory. From an application point of view, these topological corner states are an important stepping stone on the way to topologically protected wave-guides in higher dimensions and thereby open a new design path for metamaterials.
We present a short pedagogical introduction to the physics of Dirac materials, restricted to graphene and two- dimensional topological insulators. We start with a brief reminder of the Dirac and Weyl equations in the particle physics context. Turning to condensed matter systems, semimetallic graphene and various Dirac insulators are introduced, including the Haldane and the Kane-Mele topological insulators. We also discuss briefly experimental realizations in materials with strong spin-orbit coupling.
Regression machine learning is widely applied to predict various materials. However, insufficient materials data usually leads to a poor performance. Here, we develop a new voting data-driven method that could generally improve the performance of regression learning model for accurately predicting properties of materials. We apply it to investigate a large family (2135) of two-dimensional hexagonal binary compounds focusing on ferroelectric properties and find that the performance of the model for electric polarization is indeed greatly improved, where 38 stable ferroelectrics with out-of-plane polarization including 31 metals and 7 semiconductors are screened out. By an unsupervised learning, actionable information such as how the number and orbital radius of valence electrons, ionic polarizability, and electronegativity of constituent atoms affect polarization was extracted. Our voting data-driven method not only reduces the size of materials data for constructing a reliable learning model but also enables to make precise predictions for targeted functional materials.
The realization of Dirac and Weyl physics in solids has made topological materials one of the main focuses of condensed matter physics. Recently, the topic of topological nodal line semimetals, materials in which Dirac or Weyl-like crossings along special lines in momentum space create either a closed ring or line of degeneracies, rather than discrete points, has become a hot topic in topological quantum matter. Here we review the experimentally confirmed and theoretically predicted topological nodal line semimetals, focusing in particular on the symmetry protection mechanisms of the nodal lines in various materials. Three different mechanisms: a combination of inversion and time-reversal symmetry, mirror reflection symmetry, and non-symmorphic symmetry, and their robustness under the effect of spin orbit coupling are discussed. We also present a new Weyl nodal line material, the Te-square net compound KCu$_2$EuTe$_4$, which has several Weyl nodal lines including one extremely close to the Fermi level ($<$30 meV below E$_F$). Finally, we discuss potential experimental signatures for observing exotic properties of nodal line physics.
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