Mechanical Graphene

TL;DR

This paper introduces a mechanical model mimicking graphene's electronic spectrum using elastic point masses and tri-bonds, revealing topological phases and edge modes, and proposes a physical realization for experimental exploration.

Contribution

The work presents a tunable mechanical lattice model with graphene-like spectra, including topological features, and suggests a feasible physical implementation for experimental studies.

Findings

Model reproduces graphene's vibrational spectrum

Identifies topological phases with Weyl points and edge modes

Proposes a physical tri-bond implementation

Abstract

We present a model of a mechanical system with a vibrational mode spectrum identical to the spectrum of electronic excitations in a tight-binding model of graphene. The model consists of point masses connected by elastic couplings, called "tri-bonds," that implement certain three-body interactions, which can be tuned by varying parameters that correspond to the relative hopping amplitudes on the different bond directions in graphene. In the mechanical model, this is accomplished by varying the location of a pivot point that determines the allowed rigid rotations of a single tri-bond. The infinite system constitutes a Maxwell lattice, with the number of degrees of freedom equal to the number of constraints imposed by the tri-bonds. We construct the equilibrium and compatibility matrices and analyze the model's phase diagram, which includes spectra with Weyl points for some placements of the pivot and topologically polarized phases for others. We then discuss the edge modes and associated states of self stress for strips cut from the periodic lattice. Finally, we suggest a physical realization of the tri-bond, which allows access to parameter regimes not available to experiments on (strained) graphene and may be used to create other two-dimensional mechanical metamaterials with different spectral features.