Topological phonon modes in filamentary structures

Applied Physics Reviews

The topological phenomenon has been extensively studied in condensed matter physics and has attracted much attention in many different fields. Like electrons, phonons can also be studied using critical theorems and topology concepts, giving impetus to the birth of topological phonons. Among the topological phonons, the topological nodal line phonons in crystalline materials have emerged as a new area of rapid development in both experiment and theory. Researchers have been hunting for realistic materials with nodal line phonons for the last four years. To date, however, a timely review of recent advances in topological nodal line phonons, and especially their material realization, is still lacking. Considering the classification of the nodal line states, in this review, we will first review the identification of the materials hosting the nodal line phonons with different degeneracies, different types of dispersion, and different geometric shapes in theory. Moreover, we will review a...

Nature Communications, 2021

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 real materials. We have discovered 5014 TP materials and grouped them into two main classes of Weyl and nodal-line (ring) TPs. We have clarified the physical mechanism for the occurrence of single Weyl, high degenerate Weyl, individual nodal-line (ring), nodal-link, nodal-chain, and nodal-net TPs in various materials and their mutual correlations. Among the phononic systems, we have predicted the hourglass nodal net TPs in TeO3, as well as the clean and single type-I Weyl TPs between the acoustic and optical branches in half-Heusler LiCaAs. In addition, we found that different types of TPs can coexist in many ...

Recently, a novel biological principle, revealing specific electromagnetic (EM) radiation frequencies that sustain life, was presented by us on the basis of an evaluation of 175 biological articles concerning beneficial effects of electromagnetic waves on the state of living cells. This concept was also based on a very similar range of frequencies emitted by a clay-mineral catalyst of RNA synthesis that may have been instrumental in the evolutionary initiation of first life, and therefore was tentatively designated as "Algorithm of Life". The particular spectrum of frequency bands indicate that nature seems to employ discrete eigenfrequencies or standing waves that match precisely with an acoustic scale, with frequency ratios of 1:2, and closely approximated by 2:3, 3:4, 3:5, 4:5 and higher partials, allowing the discrete frequencies to be expressed in scalars. Our further studies clearly indicate now that this "life algorithm" pattern matches very well with the mathematical calculations of W. to compute eigenfrequencies of the sound induced geometric patterns. These have been earlier demonstrated through membrane vibration experiments of E. Chladni , as well as several follow up studies from 1970-2013. Our findings, therefore, touch upon the science of acoustics, also since we show that the discrete frequencies could be modeled by music torus geometry. We postulate that the spectrum of EM frequencies detected, exhibit a quantum ordering effect on life cells on the basis of induction of geometric wave patterns. These constitute phonon/photon and electron wave energies, and quantum oscillations at far-infrared frequencies, that are communicated through toroidal constructive interference into scalar wave information. This idea is supported through our identification of potential intrinsic toroidal eigenfrequencies and minimal energy levels. The particular torus topology for information processing may also provide quantum error correction and protection against decoherence. Finally, we propose a phonon guided organization of cells and integral brain function by three elementary processes: 1) A phonon mediated geometric organization of coherent arrangement of water molecules in cellular plasma, leading to instructive functional organization of cellular structures and metabolic processes and enabling the origination and sustainment of life processes. 2) Toroidal phonon/photon/electron coupling, protecting standing wave coherency of resonant cell components such as proteins and DNA. 3) A toroidal integration of electromagnetic and phononic fluxes of information into scalar standing waves, promoting quantum flux of informational excitons such as Ca2+-ions and electrons (polaron and polariton formation). Our brain, therefore, can be placed in a 4+1 geometry, supported by internal and external quantum states and makes use of geometrical defined information fluxes, that are converted to standing waves. The integration of these interrelated processes is considered to be instrumental in the creation of conscious perception and is proposed to be organized in a fractal, nested, 4-D toroidal geometry.

Physical Review B

Topological phononic crystals (PCs) are periodic artificial structures which can support nontrivial acoustic topological bands, and their topological properties are linked to the existence of topological edge modes. Most previous studies focused on the topological edge modes in Bragg gaps which are induced by lattice scatterings. While local resonant gaps would be of great use in subwavelength control of acoustic waves, whether it is possible to achieve topological interface states in local resonant gaps is a question. In this article, we study the topological bands near local resonant gaps in a time-reversal symmetric acoustic systems and elaborate the evolution of band structure using a spring-mass model. Our acoustic structure can produce three band gaps in subwavelength region: one originates from local resonance of unit cell and the other two stem from band folding. It is found that the topological interface states can only exist in the band folding induced band gaps but never appear in the local resonant band gap. The numerical simulation perfectly agrees with theoretical results. Our study provides an approach of localizing the subwavelength acoustic wave.

2018

Topological metamaterials have robust properties engineered from their macroscopic arrangement, rather than their microscopic constituency. They can be designed by starting from Dirac metamaterials with either symmetry-enforced or accidental degeneracy. The latter case provides greater flexibility in the design of topological switches, waveguides, and cloaking devices, because a large number of tuning parameters can be used to break the degeneracy and induce a topological phase. However, the design of a topological logic element-a switch that can be controlled by the output of a separate switch-remains elusive. Here we numerically demonstrate a topological logic gate for ultrasound by exploiting the large phase space of accidental degeneracies in a honeycomb lattice. We find that a degeneracy can be broken by six physical parameters, and we show how to tune these parameters to create a phononic switch that transitions between a topological waveguide and a trivial insulator by ultrasonic heating. Our design scheme is directly applicable to photonic crystals and may guide the design of future electronic topological transistors.

Journal of Physics: Condensed Matter, 2019

We theoretically analyze the spectrum of phonons of a one-dimensional quasiperiodic lattice. We simulate the quasicrystal from the classic system of spring-bound atoms with a force constant modulated by the Aubry-Andr model, so that its value is slightly different in each site of the lattice. From the equations of motion, we obtained the equivalent phonon spectrum of the Hofstadter butterfly, characterizing a multifractal. In this spectrum, we obtained the extended, critical and localized regimes, and we observed that the multifractal characteristic is sensitive to the number of atoms and the λ parameter of our model. We also verified the presence of border states for phonons, where some modes in the system boundaries present vibrations. Through the measurement of localization of the individual displacements in each site, we verify the presence of a phase transition through the Inverse Participation Rate (IPR) for λ = 1.0, where the system changes from extended to localized.

European Biophysics Journal, 2005

Parameters characterizing elastic properties of microtubules, measured in several recent experiments, reflect an anisotropic character. We describe the microscopic dynamical properties of microtubules using a discrete model based on an appropriate lattice of dimers. Adopting a harmonic approximation for the dimer-dimer interactions and estimating the lattice elastic constants, we make predictions regarding vibration dispersion relations and vibration propagation velocities. Vibration frequencies and velocities are expressed as functions of the elastic constants and of the geometrical characteristics of the microtubules. We show that vibrations which propagate along the protofilament do so significantly faster than those along the helix.

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. The particle-hole symmetry characteristic to the BDI symmetry class stems from the distinct behaviour of the translational and rotational degrees of freedom under inversion. This and other generic properties led us to the remarkable conclusion that, by adjusting the gyration radius of the bodies, one can always simultaneously open a gap in the phonon spectrum, lock-in all the characteristic symmetries and generate a non-trivial topological invariant. The particle-hole symmetry occurs around a finite frequency, and hence we can witness a dynamical topological Majorana edge mode. Contrasting a floppy mode occurring at zero frequency, a dynamical edge mode can absorb and store mechanical energy, potentially opening new applications of topological mechanics.

Underdamped terahertz-frequency delocalized phonon-like modes have long been suggested to play a role in the biological function of DNA. Such phonon modes involve the collective motion of many atoms and are prerequisite to understanding the molecular nature of macroscopic conformational changes and related biochemical phenomena. Initial predictions were based on simple theoretical models of DNA. However, such models do not take into account strong interactions with the surrounding water, which is likely to cause phonon modes to be heavily damped and localized. Here we apply state-of-the-art femtosecond optical Kerr effect spectroscopy, which is currently the only technique capable of taking low-frequency (GHz to THz) vibrational spectra in solution. We are able to demonstrate that phonon modes involving the hydrogen bond network between the strands exist in DNA at physiologically relevant conditions. In addition, the dynamics of the solvating water molecules is slowed down by about a factor of 20 compared with the bulk.

Nature

The fundamental topology of cellular structures-the location, number and connectivity of nodes and compartments-can profoundly affect their acoustic 1-4 , electrical 5 , chemical 6,7 , mechanical 8-10 and optical 11 properties, as well as heat 1,12 , fluid 13,14 and particle transport 15. Approaches that harness swelling 16-18 , electromagnetic actuation 19,20 and mechanical instabilities 21-23 in cellular materials have enabled a variety of interesting wall deformations and compartment shape alterations, but the resulting structures generally preserve the defining connectivity features of the initial topology. Achieving topological transformation presents a distinct challenge for existing strategies: it requires complex reorganization, repacking, and coordinated bending, stretching and folding, particularly around each node, where elastic resistance is highest owing to connectivity. Here we introduce a two-tiered dynamic strategy that achieves systematic reversible transformations of the fundamental topology of cellular microstructures, which can be applied to a wide range of materials and geometries. Our approach requires only exposing the structure to a selected liquid that is able to first infiltrate and plasticize the material at the molecular scale, and then, upon evaporation, form a network of localized capillary forces at the architectural scale that 'zip' the edges of the softened lattice into a new topological structure, which subsequently restiffens and remains kinetically trapped. Reversibility is induced by applying a mixture of liquids that act separately at the molecular and architectural scales (thus offering modular temporal control over the softening-evaporation-stiffening sequence) to restore the original topology or provide access to intermediate modes. Guided by a generalized theoretical model that connects cellular geometries, material stiffness and capillary forces, we demonstrate programmed reversible topological transformations of various lattice geometries and responsive materials that undergo fast global or localized deformations. We then harness dynamic topologies to develop active surfaces with information encryption, selective particle trapping and bubble release, as well as tunable mechanical, chemical and acoustic properties.