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The past decade has witnessed a surge of interest in exploring emergent particles in condensed matter systems. Novel particles, emerged as excitations around exotic band degeneracy points, continue to be reported in real materials and artificially engineered systems, but so far, we do not have a complete picture on all possible types of particles that can be achieved. Here, via systematic symmetry analysis and modeling, we accomplish a complete list of all possible particles in time reversal-invariant systems. This includes both spinful particles such as electron quasiparticles in solids, and spinless particles such as phonons or even excitations in electric-circuit and mechanical networks. We establish detailed correspondence between the particle, the symmetry condition, the effective model, and the topological character. This obtained encyclopedia concludes the search for novel emergent particles and provides concrete guidance to achieve them in physical systems.
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Recently, the very first large-gap Kane-Mele quantum spin Hall insulator was predicted to be monolayer jacutingaite (Pt$_2$HgSe$_3$), a naturally-occurring exfoliable mineral discovered in Brazil in 2008. The stacking of quantum spin Hall monolayers into a van-der-Waals layered crystal typically leads to a (0;001) weak topological phase, which does not protect the existence of surface states on the (001) surface. Unexpectedly, recent angle-resolved photoemission spectroscopy experiments revealed the presence of surface states dispersing over large areas of the 001-surface Brillouin zone of jacutingaite single crystals. The 001-surface states have been shown to be topologically protected by a mirror Chern number $C_M=-2$, associated with a nodal line gapped by spin-orbit interactions. Here, we extend the two-dimensional Kane-Mele model to bulk jacutingaite and unveil the microscopic origin of the gapped nodal line and the emerging crystalline topological order. By using maximally-localized Wannier functions, we identify a large non-trivial second nearest-layer hopping term that breaks the standard paradigm of weak topological insulators. Complemented by this term, the predictions of the Kane-Mele model are in remarkable agreement with recent experiments and first-principles simulations, providing an appealing conceptual framework also relevant for other layered materials made of stacked honeycomb lattices.
The successful isolation of graphene ten years ago has evoked a rapidly growing scientific interest in the nature of two-dimensional (2D) crystals. A number of different 2D crystals has been produced since then, with properties ranging from superconductivity to insulating behavior. Here, we predict the possibility for realizing ferromagnetic 2D crystals by exfoliating atomically thin films of K2CuF4. From a first-principles theoretical analysis, we find that single layers of K2CuF4 form exactly 2D Kosterlitz-Thouless systems. The 2D crystal can form a free-standing membrane, and exhibits an experimentally accessible transition temperature and robust magnetic moments of 1 Bohr magneton per formula unit. 2D K2CuF4 unites ferromagnetic and insulating properties and is a demonstration of principles for nanoelectronics such as novel 2D-based heterostructures.
Topological phases of matter have been extensively studied for their intriguing bulk and edge properties. Recently, higher-order topological insulators with boundary states that are two or more dimensions lower than the bulk states, have been proposed and investigated as novel states of matter. Previous implementations of higher-order topological insulators were based on two-dimensional (2D) systems in which 1D gapped edge states and 0D localized corner states were observed. Here we theoretically design and experimentally realize a 3D higher-order topological insulator in a sonic crystal with a large topological band gap. We observe the coexistence of third-, second- and first-order topological boundary states with codimension three, two and one, respectively, indicating a dimensional hierarchy of higher-order topological phenomena in 3D crystals. Our acoustic metamaterial goes beyond the descriptions of tight-binding model and possesses a band structure which automatically breaks the chiral symmetry, leading to the separation of bulk, surface, hinge and corner states. Our study opens a new route toward higher-order topological phenomena in three-dimensions and paves the way for topological wave trapping and manipulation in a hierarchy of dimensions in a single system.
The dispersion properties of exciton polaritons in multiple-quantum-well based resonant photonic crystals are studied. In the case of structures with an elementary cell possessing a mirror symmetry with respect to its center, a powerful analytical method for deriving and analyzing dispersion laws of the respective normal modes is developed. The method is used to analyze band structure and dispersion properties of several types of resonant photonic crystals, which would not submit to analytical treatment by other approaches. These systems include multiple quantum well structures with an arbitrary periodic modulation of the dielectric function and structures with a complex elementary cell. Special attention was paid to determining conditions for superradiance (Bragg resonance) in these structures, and to the properties of the polariton stop band in the case when this condition is fulfilled (Bragg structures). The dependence of the band structure on the angle of propagation, the polarization of the wave, and the effects due to exciton homogeneous and inhomogeneous broadenings are considered, as well as dispersion properties of excitations in near-Bragg structures.
We investigate, within the framework of linear elasticity theory, edge Rayleigh waves of a two-dimensional elastic solid with broken time-reversal and parity symmetries due to a Berry term. As our prime example, we study the elastic edge wave traveling along the boundary of a two-dimensional skyrmion lattice hosted inside a thin-film chiral magnet. We find that the direction of propagation of the Rayleigh modes is determined not only by the chirality of the thin-film, but also by the Poisson ratio of the crystal. We discover three qualitatively different regions distinguished by the chirality of the low-frequency edge waves, and study their properties. To illustrate the Rayleigh edge waves in real time, we have carried out finite-difference simulations of the model. Apart from skyrmion crystals, our results are also applicable to edge waves of gyroelastic media and screened Wigner crystals in magnetic fields. Our work opens a pathway towards controlled manipulation of elastic signals along boundaries of crystals with broken time-reversal symmetry.
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