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Acoustic phonon in a crystalline solid is a well-known and ubiquitous example of elementary excitation with a triple degeneracy in the band structure. Because of the Nambu-Goldstone theorem, this triple degeneracy is always present in the phonon band structure. Here, we show that the triple degeneracy of acoustic phonons can be characterized by a topological charge $mathfrak{q}$ that is a property of three-band systems with $mathcal{PT}$ symmetry, where $mathcal{P}$ and $mathcal{T}$ are the inversion and the time-reversal symmetries, respectively. We therefore call triple points with nontrivial $mathfrak{q}$ the topological acoustic triple point (TATP). The topological charge $mathfrak{q}$ can equivalently be characterized by the skyrmion number of the longitudinal mode, or by the Euler number of the transverse modes, and this strongly constrains the nodal structure around the TATP. The TATP can also be symmetry-protected at high-symmetry momenta in the band structure of phonons and spinless electrons by the $O_h$ and the $T_h$ groups. The nontrivial wavefunction texture around the TATP can induce anomalous thermal transport in phononic systems and orbital Hall effect in electronic systems. Our theory demonstrates that the gapless points associated with the Nambu-Goldstone theorem are an avenue for discovering new classes of degeneracy points with distinct topological characteristics.
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We study a class of topological materials which in their momentum-space band structure exhibit three-fold degeneracies known as triple points. Focusing specifically on $mathcal{P}mathcal{T}$-symmetric crystalline solids with negligible spin-orbit coupling, we find that such triple points can be stabilized by little groups containing a three-, four- or six-fold rotation axis, and we develop a classification of all possible triple points as type-A vs. type-B according to the absence vs. presence of attached nodal-line arcs. Furthermore, by employing the recently discovered non-Abelian band topology, we argue that a rotation-symmetry-breaking strain transforms type-A triple points into multi-band nodal links. Although multi-band nodal-line compositions were previously theoretically conceived and related to topological monopole charges, a practical condensed-matter platform for their manipulation and inspection has hitherto been missing. By reviewing the known triple-point materials with weak spin-orbit coupling, and by performing first-principles calculations to predict new ones, we identify suitable candidates for the realization of multi-band nodal links in applied strain. In particular, we report that an ideal compound to study this phenomenon is Li$_2$NaN, in which the conversion of triple points to multi-band nodal links facilitates largely tunable density of states and optical conductivity with doping and strain, respectively.
Dislocations are ubiquitous in three-dimensional solid-state materials. The interplay of such real space topology with the emergent band topology defined in reciprocal space gives rise to gapless helical modes bound to the line defects. This is known as bulk-dislocation correspondence, in contrast to the conventional bulk-boundary correspondence featuring topological states at boundaries. However, to date rare compelling experimental evidences are presented for this intriguing topological observable, owing to the presence of various challenges in solid-state systems. Here, using a three-dimensional acoustic topological insulator with precisely controllable dislocations, we report an unambiguous experimental evidence for the long-desired bulk-dislocation correspondence, through directly measuring the gapless dispersion of the one-dimensional topological dislocation modes. Remarkably, as revealed in our further experiments, the pseudospin-locked dislocation modes can be unidirectionally guided in an arbitrarily-shaped dislocation path. The peculiar topological dislocation transport, expected in a variety of classical wave systems, can provide unprecedented controllability over wave propagations.
We analyze the band topology of acoustic phonons in 2D materials by considering the interplay of spatial and internal symmetries with additional constraints that arise from the physical context. These supplemental constraints trace back to the Nambu-Goldstone theorem and the requirements of structural stability. We show that this interplay can give rise to previously unaddressed non-trivial nodal charges that are associated with the crossing of the acoustic phonon branches at the center ($Gamma$-point) of the phononic Brillouin zone. We moreover apply our perspective to the concrete context of graphene, where we demonstrate that the phonon spectrum harbors these kinds of non-trivial nodal charges. Apart from its fundamental appeal, this analysis is physically consequential and dictates how the phonon dispersion is affected when graphene is grown on a substrate. Given the generality of our framework, we anticipate that our strategy that thrives on combining physical context with insights from topology should be widely applicable in characterizing systems beyond electronic band theory.
Inspired by concepts developed for fermionic systems in the framework of condensed matter physics, topology and topological states are recently being explored also in bosonic systems. The possibility of engineering systems with unidirectional wave propagation and protected against disorder is at the heart of this growing interest. Topogical acoustic effects have been observed in a variety of systems, most of them based on kHz-MHz sound waves, with typical wavelength of the order of the centimeter. Recently, some of these concepts have been successfully transferred to acoustic phonons in nanoscaled multilayered systems. The reported demonstration of confined topological phononic modes was based on Raman scattering spectroscopy, yet the resolution did not suffice to determine lifetimes and to identify other acoustic modes in the system. Here, we use time-resolved pump-probe measurements using an asynchronous optical sampling (ASOPS) technique to overcome these resolution limitations. By means of one-dimensional GaAs/AlAs distributed Bragg reflectors (DBRs) as building blocks, we engineer high frequency ($sim$ 200 GHz) topological acoustic interface states. We are able to clearly distinguish confined topological states from stationary band edge modes. The detection scheme reflects the symmetry of the modes directly through the selection rules, evidencing the topological nature of the measured confined state. These experiments enable a new tool in the study of the more complex topology-driven phonon dynamics such as phonon nonlinearities and optomechanical systems with simultaneous confinement of light and sound.
We report the evolution of the surface electronic structure and surface material properties of a topological crystalline insulator (TCI) Pb1-xSnxSe as a function of various material parameters including composition x, temperature T and crystal structure. Our spectroscopic data demonstrate the electronic groundstate condition for the saddle point singularity, the tunability of surface chemical potential, and the surface states response to circularly polarized light. Our results show that each material parameter can tune the system between trivial and topological phase in a distinct way unlike as seen in Bi2Se3 and related compounds, leading to a rich and unique topological phase diagram. Our systematic studies of the TCI Pb1-xSnxSe are valuable materials guide to realize new topological phenomena.
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