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Register a new userDemonstrating an in-situ topological band transition in cylindrical granular chains
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We numerically investigate and experimentally demonstrate an in-situ topological band transition in a highly tunable mechanical system made of cylindrical granular particles. This system allows us to tune its inter-particle stiffness in a controllable way, simply by changing the contact angles between the cylinders. The spatial variation of particles stiffness results in an in-situ transition of the systems topology. This manifests as the emergence of a boundary mode in the finite system, which we observe experimentally via laser Doppler vibrometry. When two topologically different systems are placed adjacently, we analytically predict and computationally and experimentally demonstrate the existence of a finite-frequency topologically protected mode at their interface.
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We study ``nanoptera, which are non-localized solitary waves with exponentially small but non-decaying oscillations, in two singularly-perturbed Hertzian chains with precompression. These two systems are woodpile chains (which we model as systems of Hertzian particles and springs) and diatomic Hertzian chains with alternating masses. We demonstrate that nanoptera arise from Stokes phenomena and appear as special curves, called Stokes curves, are crossed in the complex plane. We use techniques from exponential asymptotics to obtain approximations of the oscillation amplitudes. Our analysis demonstrates that traveling waves in a singularly perturbed woodpile chain have a single Stokes curve, across which oscillations appear. Comparing these asymptotic predictions with numerical simulations reveals that this accurately describes the non-decaying oscillatory behavior in a woodpile chain. We perform a similar analysis of a diatomic Hertzian chain, that the nanpteron solution has two distinct exponentially small oscillatory contributions. We demonstrate that there exists a set of mass ratios for which these two contributions cancel to produce localized solitary waves. This result builds on prior experimental and numerical observations that there exist mass ratios that support localized solitary waves in diatomic Hertzian chains without precompression. Comparing asymptotic and numerical results in a diatomic Hertzian chain with precompression reveals that our exponential asymptotic approach accurately predicts the oscillation amplitude for a wide range of system parameters, but it fails to identify several values of the mass ratio that correspond to localized solitary-wave solutions.
This article explores the excitation of different vibrational states in a spatially extended dynamical system through theory and experiment. As a prototypical example, we consider a one-dimensional packing of spherical particles (a so-called granular chain) that is subject to harmonic boundary excitation. The combination of the multi-modal nature of the system and the strong coupling between the particles due to the nonlinear Hertzian contact force leads to broad regions in frequency where different vibrational states are possible. In certain parametric regions, we demonstrate that the Nonlinear Schrodinger (NLS) equation predicts the corresponding modes fairly well. We propose that nonlinear multi-modal systems can be useful in vibration energy harvest- ing and discuss a prototypical framework for its realization. The electromechanical model we derive predicts accurately the conversion from mechanical to electrical energy observed in the experiments.
Nonlinear vibrations in strained monoatomic carbon chains are studied with the aid of ab initio methods based on the density functional theory. An unexpected phenomenon of structural transformation at the atomic level above a certain value of the strain was revealed in cumulene chain (carbyne-{beta}). This phenomenon is a consequence of stability loss of the old equilibrium atomic positions that occur at small strain, and appearance of two new stable equilibrium positions near each of them. The aforementioned restructuring gives rise to a softening of {pi}-mode whose frequency tends to zero in a certain region of amplitudes when carbon atoms begin to vibrate near new equilibrium positions. This resembles the concept of soft mode whose freezing is postulated in the theory of phase transitions in crystals to explain the transitions of displacement type. The dynamical modeling of mass point chains whose particles interact via Lennard-Jones potential can approximate our ab initio results well enough. In particular, this study demonstrates an essential role of dipole-dipole interactions between carbon atoms in formation of their new equilibrium positions in the cumulene chain. We believe that computer studying of Lennard-Jones chains enables to predict properties of various dynamical objects in carbon chains (different nonlinear normal modes and their bushes, discrete breathers etc.) which then can be verified by ab initio methods.
We consider longitudinal nonlinear atomic vibrations in uniformly strained carbon chains with the cumulene structure ($=C=C=)_{n}$. With the aid of ab initio simulations, based on the density functional theory, we have revealed the phenomenon of the $pi$-mode softening in a certain range of its amplitude for the strain above the critical value $eta_{c}approx 11,{%}$. Condensation of this soft mode induces the structural transformation of the carbon chain with doubling of its unit cell. This is the Peierls phase transition in the strained cumulene, which was previously revealed in [Nano Lett. 14, 4224 (2014)]. The Peierls transition leads to appearance of the energy gap in the electron spectrum of the strained carbyne, and this material transforms from the conducting state to semiconducting or insulating states. The authors of the above paper emphasize that such phenomenon can be used for construction of various nanodevices. The $pi$-mode softening occurs because the old equilibrium positions (EQPs), around which carbon atoms vibrate at small strains, lose their stability and these atoms begin to vibrate in the new potential wells located near old EQPs. We study the stability of the new EQPs, as well as stability of vibrations in their vicinity. In previous paper [Physica D 203, 121(2005)], we proved that only three symmetry-determined Rosenberg nonlinear normal modes can exist in monoatomic chains with arbitrary interparticle interactions. They are the above-discussed $pi$-mode and two other modes, which we call $sigma$-mode and $tau$-mode. These modes correspond to the multiplication of the unit cell of the vibrational state by two, three or four times compared to that of the equilibrium state. We study properties of these modes in the chain model with arbitrary pair potential of interparticle interactions.
Granular conductors form an artificially engineered class of solid state materials wherein the microstructure can be tuned to mimic a wide range of otherwise inaccessible physical systems. At the same time, topological insulators (TIs) have become a cornerstone of modern condensed matter physics as materials hosting metallic states on the surface and insulating in the bulk. However it remains to be understood how granularity affects this new and exotic phase of matter. We perform electrical transport experiments on highly granular topological insulator thin films of Bi$_2$Se$_3$ and reveal remarkable properties. We observe clear signatures of topological surface states despite granularity with distinctly different properties from conventional bulk TI systems including sharp surface state coupling-decoupling transitions, large surface state penetration depths and exotic Berry phase effects. We present a model which explains these results. Our findings illustrate that granularity can be used to engineer designer TIs, at the same time allowing easy access to the Dirac-fermion physics that is inaccessible in single crystal systems.
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