Mechanical Analogue of a Majorana Bound State

Abstract

The discovery of topologically nontrivial electronic systems has opened a new age in condensed matter research. From topological insulators to topological superconductors and Weyl semimetals, it is now understood that some of the most remarkable and robust phases in electronic systems (e.g., quantum Hall or anomalous quantum Hall) are the result of topological protection. These powerful ideas have recently begun to be explored also in bosonic systems. Topologically protected acoustic, mechanical, and optical edge states have been demonstrated in a number of systems that recreate the requisite topological conditions. Such states that propagate without backscattering could find important applications in communications and energy technologies. Here, a topologically bound mechanical state, a different class of nonpropagating protected state that cannot be destroyed by local perturbations, is demonstrated. It is in particular a mechanical analogue of the well‐known Majorana bound states (MBSs) of electronic topological superconductor systems. The topological binding is implemented by creating a Kekulé distortion vortex on a 2D mechanical honeycomb superlattice that can be mapped to a magnetic flux vortex in a topological superconductor.

Dirac-vortex topological photonic crystal fibre

“…In this article, we introduce the topological photonic crystal fibre (PCF) whose invariant cross-section resembles the recent Dirac-vortex topological cavity 6 in two-dimensional photonic crystals. Such a topological bound state can be traced back to the Jackiw-Rossi zero mode in the two-dimensional (2D) Dirac equation 7 and has been realised in honeycomb lattices 8 , 9 in a couple of systems 10 – 13 . This Dirac-vortex silica fibre can support an arbitrary number of nearly degenerate guiding modes by varying the winding number ( w ) of the spatial vortex.…”

Topological Sound Pumping of Zero‐Dimensional Bound States

“…[ 33 ] Latest experimental implementations of the Jackiw–Rossi vortex employ a Kekulé texture to artificially decorated lattices that embody a winding process. [ 26,27 ] Here, we show that the binding mechanism indeed can be presented in terms of a pumping process encompassing the polar paramaters of the Kekulé modulation, which leads to a sonic spectral flow during the adiabatic structural tuning. Surprisingly, we find that the 0D states in finite crystals evolving from the adiabatic pumping process incorporate corner states that spectrally flow in the form of the coveted Majorana‐like zero modes.…”

“…[ 23–25 ] Recently, a wealth of experimental efforts has sparked curiosity among phononic and photonic researchers in the pursuit of a classical analogy. [ 26–29 ] Based on a so‐called Kekulé binding mechanism in artificially man‐made macroscopic lattices, equivalent zero modes of vibrations, sound, or light have shown intriguing properties for topological robust single‐mode wave control and confinement. Interestingly, it has been shown that such classical implementations of the Jackiw–Rossi binding mechanism facilitate particle‐hole symmetry counterparts, however, in the absence of the peculiar Majorana self‐conjugation relation.…”

Braiding flux-tubes in topological quantum and classical lattice models from class-D

“…With the platform of magnetically coupled spinners introduced in [25], layering has been already achieved and variable couplings can be implemented by replacing the permanent magnets by electro-magnets whose strength can be programmed at will. While this were still in the planning, the exciting work [38] appeared, showing an experimental demonstration and characterization of mechanical Majorana-like modes. In fact, our community is rapidly learning that classical topological meta-materials can be used quite effectively for information processing (see e.g.…”