Observation of D-class topology in an acoustic metamaterial.

Topological materials and metamaterials opened new paradigms to create and manipulate phases of matter with unconventional properties. Topological D-class phases (TDPs) are archetypes of the ten-fold classification of topological phases with particle-hole symmetry. In two dimensions, TDPs support propagating topological edge modes that simulate the elusive Majorana elementary particles.

Converging Periodic Boundary Conditions and Detection of Topological Gaps on Regular Hyperbolic Tessellations.

Tessellations of the hyperbolic spaces by regular polygons support discrete quantum and classical models with unique spectral and topological characteristics. Resolving the true bulk spectra and the thermodynamic response functions of these models requires converging periodic boundary conditions and our Letter delivers a practical and rigorous solution for this open problem on generic {p,q}-tessellations. This enables us to identify the true spectral gaps of bulk Hamiltonians and construct all but one topological models that deliver the topological gaps predicted by the K theory of the lattices.

Smart patterning for topological pumping of elastic surface waves.

Topological pumping allows waves to navigate a sample undisturbed by disorders and defects. We demonstrate this phenomenon with elastic surface waves by strategically patterning an elastic surface to create a synthetic dimension. The surface is decorated with arrays of resonating pillars that are connected by spatially slow-varying coupling bridges and support eigenmodes located below the sound cone.

Revealing topology in metals using experimental protocols inspired by K-theory.

Topological metals are conducting materials with gapless band structures and nontrivial edge-localized resonances. Their discovery has proven elusive because traditional topological classification methods require band gaps to define topological robustness. Inspired by recent theoretical developments that leverage techniques from the field of C-algebras to identify topological metals, here, we directly observe topological phenomena in gapless acoustic crystals and realize a general experimental technique to demonstrate their topology.

Creating synthetic spaces for higher-order topological sound transport.

Modern technological advances allow for the study of systems with additional synthetic dimensions. Higher-order topological insulators in topological states of matters have been pursued in lower physical dimensions by exploiting synthetic dimensions with phase transitions. While synthetic dimensions can be rendered in the photonics and cold atomic gases, little to no work has been succeeded in acoustics because acoustic wave-guides cannot be weakly coupled in a continuous fashion.

Experimental Demonstration of Dynamic Topological Pumping across Incommensurate Bilayered Acoustic Metamaterials.

A Thouless pump can be regarded as a dynamical version of the integer quantum Hall effect. In a finite-size configuration, such a topological pump displays edge modes that emerge dynamically from one bulk band and dive into the opposite bulk band, an effect that can be reproduced with both quantum and classical systems. Here, we report the first unassisted dynamic energy transfer across a metamaterial, via pumping of such topological edge modes.

Topological Braiding of Non-Abelian Midgap Defects in Classical Metamaterials.

Nontrivial braid-group representations appear as non-Abelian quantum statistics of emergent Majorana zero modes in one- and two-dimensional topological superconductors. Here, we generate such representations with topologically protected domain-wall modes in a classical analog of the Kitaev superconducting chain, with a particle-holelike symmetry and a Z_{2} topological invariant. The midgap modes are found to exhibit distinct fusion channels and rich non-Abelian braiding properties, which are investigated using a T-junction setup.

Observation of Topological Edge Modes in a Quasiperiodic Acoustic Waveguide.

Topological boundary and interface modes are generated in an acoustic waveguide by simple quasiperiodic patterning of the walls. The procedure opens many topological gaps in the resonant spectrum and qualitative as well as quantitative assessments of their topological character are supplied. In particular, computations of the bulk invariant for the continuum wave equation are performed.

Mapping the dispersion of water wave channels.

Large classes of electronic, photonic, and acoustic crystals and quasi-crystals have been predicted to support topological wave-modes. Some of these modes are stabilized by certain symmetries but others occur as pure wave phenomena, hence they can be observed in many other media that support wave propagation. Surface water-waves are mechanical in nature but very different from the elastic waves, hence they can provide a new platform for studying topological wave-modes.

Dynamical Majorana edge modes in a broad class of topological mechanical systems.

Mechanical systems can display topological characteristics similar to that of topological insulators. Here we report a large class of topological mechanical systems related to the BDI symmetry class. These are self-assembled chains of rigid bodies with an inversion centre and no reflection planes.

Topological criticality in the chiral-symmetric AIII class at strong disorder.

The chiral AIII symmetry class in the classification table of topological insulators contains topological phases classified by a winding number ν for each odd space dimension. An open problem for this class is the characterization of the phases and phase boundaries in the presence of strong disorder. In this work, we derive a covariant real-space formula for ν and, using an explicit one-dimensional disordered topological model, we show that ν remains quantized and nonfluctuating when disorder is turned on, even though the bulk energy spectrum is completely localized.

Quantum plasmonics: optical properties of a nanomatryushka.

Quantum mechanical effects can significantly reduce the plasmon-induced field enhancements around nanoparticles. Here we present a quantum mechanical investigation of the plasmon resonances in a nanomatryushka, which is a concentric core-shell nanoparticle consisting of a solid metallic core encapsulated in a thin metallic shell. We compute the optical response using the time-dependent density functional theory and compare the results with predictions based on the classical electromagnetic theory.

Topological phonon modes in filamentary structures.

This work describes a class of topological phonon modes, that is, mechanical vibrations localized at the edges of special structures that are robust against the deformations of the structures. A class of topological phonons was recently found in two-dimensional structures similar to that of microtubules. The present work introduces another class of topological phonons, this time occurring in quasi-one-dimensional filamentary structures with inversion symmetry.

Entanglement spectrum of a disordered topological Chern insulator.

We investigate the behavior of a topological Chern insulator in the presence of disorder, with a focus on its entanglement spectrum (EtS) constructed from the ground state. For systems with symmetries, the EtS was shown to contain explicit information about the topological universality class revealed by sorting the EtS against the conserved quantum numbers. In the absence of any symmetry, we demonstrate that statistical methods such as the level statistics of the EtS can be equally insightful, allowing us to distinguish when an insulator is in a topological or trivial phase and to map the boundary between the two phases.

Quantum plasmonics: optical properties and tunability of metallic nanorods.

The plasmon resonances in metallic nanorods are investigated using fully quantum mechanical time-dependent density functional theory. The computed optical absorption curves display well-defined longitudinal and transverse plasmon resonances whose energies depend on the aspect ratio of the rods, in excellent agreement with classical electromagnetic modeling. The field enhancements obtained from the quantum mechanical calculations, however, differ significantly from classical predictions for distances shorter than 0.

Topological phonon modes and their role in dynamic instability of microtubules.

Microtubules (MTs) are self-assembled hollow protein tubes playing important functions in live cells. Their building block is a protein called tubulin, which self-assembles in a particulate 2 dimensional lattice. We study the vibrational modes of this lattice and find Dirac points in the phonon spectrum.

Quantum description of the plasmon resonances of a nanoparticle dimer.

Using time-dependent density functional theory, we present a fully quantum mechanical investigation of the plasmon resonances in a nanoparticle dimer as a function of interparticle separation. We show that for dimer separations below 1 nm quantum mechanical effects, such as electron tunneling across the dimer junction and screening, significantly modify the optical response and drastically reduce the electromagnetic field enhancements relative to classical predictions. For larger separations, the dimer plasmons are well described by classical electromagnetic theory.

The dielectric response of spherical live cells in suspension: an analytic solution.

We develop a theoretical framework to describe the dielectric response of live cells in suspensions when placed in low external electric fields. The treatment takes into account the presence of the cell's membrane and of the charge movement at the membrane's surfaces. For spherical cells suspended in aqueous solutions, we give an analytic solution for the dielectric function, which is shown to account for the alpha- and beta-plateaus seen in many experimental data.

Tunneling conductance of amine-linked alkyl chains.

The tunneling transport theory developed in ref 9 (Phys. Rev. B 2007, 76, 115102) is applied to molecular devices made of alkyl chains linked to gold electrodes via amine groups.

Nearsightedness of electronic matter.

In an earlier paper, W. Kohn had qualitatively introduced the concept of "nearsightedness" of electrons in many-atom systems. It can be viewed as underlying such important ideas as Pauling's "chemical bond," "transferability," and Yang's computational principle of "divide and conquer.

Plasmon hybridization in spherical nanoparticles.

We show that the plasmon resonances in single metallic nanoshells and multiple concentric metallic shell particles can be understood in terms of interaction between the bare plasmon modes of the individual surfaces of the metallic shells. The interaction of these elementary plasmons results in hybridized plasmons whose energy can be tuned over a wide range of optical and infrared wavelengths. The approach can easily be generalized to more complex systems, such as dimers and small nanoparticle aggregates.

A hybridization model for the plasmon response of complex nanostructures.

We present a simple and intuitive picture, an electromagnetic analog of molecular orbital theory, that describes the plasmon response of complex nanostructures of arbitrary shape. Our model can be understood as the interaction or "hybridization" of elementary plasmons supported by nanostructures of elementary geometries. As an example, the approach is applied to the important case of a four-layer concentric nanoshell, where the hybridization of the plasmons of the inner and outer nanoshells determines the resonant frequencies of the multilayer nanostructure.

Time-correlated soliton tunneling in charge and spin density waves.

We consider a model in which an electric field induces quantum nucleation of kink-antikink pairs in a pinned charge or spin density wave. Pair nucleation events, prevented by Coulomb blockade below a pair creation threshold, become correlated in time above threshold. The model provides a natural explanation for the observed (i) small density wave polarization below threshold in NbSe (3), (ii) narrow band noise, (iii) coherent oscillations, and (iv) mode-locking at high drift frequencies.