An international team of researchers has discovered that the quantum particles responsible for the vibrations of materials—which influence their stability and various other properties—can be classified through topology. Phonons, the collective vibrational modes of atoms within a crystal lattice, generate disturbances that propagate like waves through neighboring atoms. These phonons are vital for many properties of solid-state systems, including thermal and electrical conductivity, neutron scattering, and quantum phases like charge density waves and superconductivity.
The spectrum of phonons—essentially the energy as a function of momentum—and their wave functions, which represent their probability distribution in real space, can be computed using ab initio first principle codes. However, these calculations have so far lacked a unifying principle. "For the quantum behavior of electrons, topology—a branch of mathematics—has successfully classified the electronic bands in materials. This classification shows that materials, which might seem different, are actually very similar. We already have catalogues of electronic topological behaviors, akin to a periodic table of compounds. Naturally, this led us to question: Can topology also characterize phonons?" explained B. Andrei Bernevig, a professor of physics at Princeton University, visiting professor at DIPC, and one of the study's authors.
In a study published in the journal Science, an international team from Princeton University, Zhejiang University, DIPC, ENS-CNRS, Max Planck Institute, and the University of the Basque Country uncovered that a wide range of materials could host topological phonons. Topology, the study of properties preserved through continuous deformations, is used to characterize manifolds. For instance, a Mobius strip is distinguished from a regular strip by a twist, and a doughnut differs from a sphere by a hole; these cannot be transformed into each other without cutting the manifold. "We first computed the phonon bands of thousands of quantum materials, identifying their wavefunctions and characterizing them by their symmetries, which provide a sort of local structure of the phonons," said Yuanfeng Xu, the first author of the study and a professor at Zhejiang University. "After completing this step, we employed topology to classify the global behavior of the phonon bands," he added.
Several phonon structure databases have been meticulously analyzed, revealing that at least half of the materials exhibit at least one non-atomic cumulative phononic band set. The team employed a formalism similar to that developed for characterizing electronic bands, as outlined in their previous work on Topological Quantum Chemistry (TQC).
An international team of scientists from the Princeton University, Donostia International Physics Center (DIPC), the University of the Basque Country (UPV/EHU), the Max Planck Institute, l'Ecole Normale Supérieure, the CNRS, and Zhejiang University have scanned several phonon databases and predict the existence of topological phonons in approximately 5000 materials.
