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Register a new userSignatures of Topological Phonons in Superisostatic Lattices
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Soft topological surface phonons in idealized ball-and-spring lattices with coordination number $z=2d$ in $d$ dimensions become finite-frequency surface phonons in physically realizable superisostatic lattices with $z>2d$. We study these finite-frequency modes in model lattices with added next-nearest-neighbor springs or bending forces at nodes with an eye to signatures of the topological surface modes that are retained in the physical lattices. Our results apply to metamaterial lattices, prepared with modern printing techniques, that closely approach isostaticity.
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Simulations in which a globular ring polymer with delocalized knots is separated in two interacting loops by a slipping link, or in two non-interacting globuli by a wall with a hole, show how the minimal crossing number of the knots controls the equilibrium statistics. With slipping link the ring length is divided between the loops according to a simple law, but with unexpectedly large fluctuations. These are suppressed only for unknotted loops, whose length distribution shows always a fast power law decay. We also discover and explain a topological effect interfering with that of surface tension in the globule translocation through a membrane nanopore.
Topological mechanics and phononics have recently emerged as an exciting field of study. Here we introduce and study generalizations of the three-dimensional pyrochlore lattice that have topologically protected edge states and Weyl lines in their bulk phonon spectra, which lead to zero surface modes that flip from one edge to the opposite as a function of surface wavenumber.
The paper studies the modes of vibrations of a lattice with rod-like particles, in a continuum model where the sites of the lattice are the connections among strings and rigid rods. In these structures then, translational and rotational degrees of freedom are strongly coupled. We will discuss in particular two-dimensional lattices with auxetic-like behaviour. Auxetics are materials with a negative Poisson elastic parameter, meaning that they have a lateral extension, instead to shrink, when they are stretched. We assume as auxetic-like two-dimensional structures, structures which do not collapse, when stretched in one of the in-plane directions. The presence of rigid rod-like particles in the lattice prevents the shrinking of the membrane. Complete bandgaps between acoustic and optical modes are observed in analogy with the behaviour of crystalline materials.
Recent progress in topological mechanics have revealed a family of Maxwell lattices that exhibit topologically protected floppy edge modes. These modes lead to a strongly asymmetric elastic wave response. In this paper, we show how topological Maxwell lattices can be used to realize non-reciprocal transmission of elastic waves. Our design leverages the asymmetry associated with the availability of topological floppy edge modes and the geometric nonlinearity built in the mechanical systems response to achieve the desired non-reciprocal behavior, which can be further turned into strongly one-way phonon transport via the addition of on-site pinning potentials. Moreover, we show that the non-reciprocal wave transmission can be switched on and off via topological phase transitions, paving the way to the design of cellular metamaterials that can serve as tunable topologically protected phonon diodes.
The discovery of superconductivity at 203K in SH$_3$ is an important step toward higher values of $T_c$. Predictions based on state-of-the-art DFT for the electronic structure, including one preceding experimental confirmation, showed the mechanism to be the electron-phonon interaction. This was confirmed in optical spectroscopy measurements. For photon energies between $sim 450$ and 600 meV in SH$_3$, the reflectance in the superconducting state is below that in its normal state. This difference decreases as $T$ approaches $T_c$. Decreasing absorption with increasing $T$ is opposite to what is expected in ordinary metals. Such an anomalous behavior can be traced back to the energy dependence of the superconducting density of states which is highly peaked at the energy gap value $Delta$ but decays back to the constant normal state value as energy is increased, on a scale of a few $Delta$, or by increasing $T$ towards $T=T_c$. The process of phonon-assisted optical absorption is encoded with a knowledge of the $T$-dependence of $Delta$, the order parameter of the superconducting state. Should the energy of the phonon involved be very large, of order 200 meV or more, this process offers the possibility of observing the closing of the superconducting order parameter with $T$ at correspondingly very large energies. The very recent experimental observation of a $T_csimeq 250$ K in LaH$_{10}$ has further heightened interest in the hydrides. We compare the relevant phonon structure seen in optics with related features in the real and imaginary part of the frequency dependent gap, quasiparticle density of states, reflectance, absorption, and optical scattering rate. The phonon structures all carry information on the $T_c$ value and the $T$-dependence of the order parameter, and can be used to confirm that the mechanism involved in superconductivity is the electron-phonon interaction.
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