Chiral phonons in a square lattice

TL;DR

This paper explores the existence and properties of chiral phonons in square and tetragonal lattices, expanding the understanding beyond hexagonal systems and highlighting their potential for experimental detection and applications.

Contribution

It identifies symmetry conditions for chiral phonons in 2D square and 3D tetragonal lattices, including the need for time-reversal symmetry breaking in 2D, and demonstrates their presence through model and first-principles calculations.

Findings

Chiral phonons can exist in 2D square lattices with broken time-reversal symmetry.

Chiral phonons are present in 3D tetragonal lattices along C4-invariant paths.

Potential for easier experimental detection due to coupling with optical transitions.

Abstract

Chiral phonons were initially proposed and further verified experimentally in two-dimensional (2D) hexagonal crystal lattices. Many intriguing features brought about by chiral phonons are attributed to the pseudo-angular momenta which are associated with the threefold rotational symmetry of hexagonal lattices. Here, we go beyond the hexagonal crystals and investigate the chiral phonons in systems with fourfold rotational symmetry. We clarify the symmetry requirements for the emergence of chiral phonons in both 2D square lattices and 3D tetragonal lattices. For 2D, the realization of $C_4$ chiral phonons requires the breaking of time-reversal symmetry; while for 3D, they can exist on the $C_4$-invariant path in a chiral tetragonal lattice. These phonons have the advantage that they can be more readily coupled with optical transitions, which facilitates their experimental detection. We demonstrate our idea via model analysis and first-principles calculations of concrete materials, including the MnAs monolayer and the $\alpha$-cristobalite. Our work reveals chiral phonons beyond the hexagonal lattices and paves the way for further exploration of chiral phonon physics in square/tetragonal materials and metamaterials.