Emulating tightly bound electrons in crystalline solids using mechanical waves

TL;DR

This paper demonstrates a mechanical system that emulates tightly bound electrons in crystalline solids by using resonators connected through periodic couplers, replicating electronic band structure and localization phenomena.

Contribution

The authors create a mechanical analog of the tight-binding model using resonators and periodic couplers, enabling experimental study of electron-like localization and band structure.

Findings

Mechanical resonators mimic electron orbital localization.

Vibrational wave amplitude shows exponential decay similar to electronic wavefunctions.

Mechanical model exhibits band structure consistent with quantum tight-binding models.

Abstract

Solid state physics deals with systems composed of atoms with strongly bound electrons. The tunneling probability of each electron is determined by interactions that typically extend to neighboring sites, as their corresponding wave amplitudes decay rapidly away from an isolated atomic core. This kind of description is essential to material science, and it rules the electronic transport properties of metals, insulators and other condensed matter systems. The corresponding phenomenology is well captured by tight-binding models, where the electronic band structure emerges from atomic orbitals of isolated atoms plus their coupling to neighboring sites in a cristal. In this work, a mechanical system that emulates dynamically a tightly bound electron is built. This is done by connecting mechanical resonators via locally periodic aluminum bars acting as couplers. When the frequency of a particular resonator lies within the frequency gap of a coupler, the vibrational wave amplitude imitates a bound electron orbital. The localization of the wave at the resonator site and its exponential decay along the coupler are experimentally verified. The quantum dynamical tight-binding model and frequency measurements in mechanical structures show an excellent agreement.