Hexagonal-to-base-centered-orthorhombic $4Q$ charge density wave order in kagome metals KV$_3$Sb$_5$, RbV$_3$Sb$_5$, and CsV$_3$Sb$_5$

TL;DR

This study uses first principles calculations to identify a specific 4Q charge density wave order in kagome metals KV3Sb5, RbV3Sb5, and CsV3Sb5, revealing a transition from a high-symmetry phase to a lower-symmetry orthorhombic structure.

Contribution

The paper predicts a novel 4Q charge density wave order and structural transition in kagome metals using group-theoretical analysis and first principles calculations.

Findings

Identified the lowest energy structure as Fmmm with specific distortions.

Discovered a dynamical instability leading to a Cmcm orthorhombic phase.

Proposed a 4Q order parameter involving multiple distortions.

Abstract

I search for the ground state structures of the kagome metals KV$_3$Sb$_5$, RbV$_3$Sb$_5$, and CsV$_3$Sb$_5$ using first principles calculations. Group-theoretical analysis shows that there are seventeen different distortions that are possible due to the phonon instabilities at the $M$ $(\frac{1}{2},0,0)$ and $L$ $(\frac{1}{2},0,\frac{1}{2})$ points in the Brilouin zone of the parent $P6/mmm$ phase of these materials. I generated these structures for the three compounds and performed full structural relaxations that minimize the atomic forces and lattice stresses. I find that the $Fmmm$ phase with the order parameter $M_1^+$ $(a,0,0)$ $+$ $L_2^-$ $(0,b,b)$ has the lowest energy among these possibilities in all three compounds. However, the $Fmmm$ exhibits a dynamical instability at its $Z$ $(0,0,1)$ point, which corresponds to the $A$ $(0,0,\frac{1}{2})$ point in the parent $P6/mmm$ phase. Condensation of this instability leads to a base-centered orthorhombic structure with the space group $Cmcm$ and $4Q$ order parameter $M_1^+$ $(a,0,0)$ $+$ $L_2^-$ $(0,b,b)$ $+$ $A_6^+$ $(\frac{1}{2}c,\frac{-\sqrt{3}}{2}c)$.