Existence of Corner Modes in Elastic Twisted Kagome Lattices

TL;DR

This paper demonstrates the existence of corner modes in elastic twisted Kagome lattices at a critical twist angle, showing their shape-independent localization and relation to charge accumulation, with implications for boundary phenomena.

Contribution

It reveals the presence of shape-independent corner modes at the self-dual point in elastic twisted Kagome lattices and links them to charge accumulation phenomena.

Findings

Corner modes exist at a critical twist angle.

Modes are localized at specific corners regardless of shape.

Charge accumulation at boundaries is confirmed.

Abstract

This Letter investigates the emergence of corner modes in elastic twisted Kagome lattices at a critical twist angle, known as self-dual point. We show that a special type of corner modes exist and they are localized at a very specific type of corners independent of the overall shape of the finite lattice. Moreover, these modes appear even in the perturbed lattice at the corners with mirror planes. By exploring its counterpart in electronic system, we attribute such corner modes to charge accumulation at the boundary, which is confirmed by the plot of charge distribution in a finite lattice.