Order-by-disorder charge density wave condensation at $\mathbf{\textit{q} =(\frac{1}{3},\frac{1}{3},\frac{1}{3})}$ in kagome metal ScV$_6$Sn$_6$

TL;DR

This study investigates the charge density wave order in kagome metal ScV6Sn6, revealing that entropy-driven order-by-disorder condensation at wave vector P is likely, despite a lower energy gain compared to other phonon instabilities.

Contribution

It demonstrates that the charge density wave at P is stabilized through an order-by-disorder mechanism, highlighting the role of entropy and structural multiplicity in this kagome metal.

Findings

Charge density wave at P involves multiple nearly degenerate structures.

Order-by-disorder mechanism favors P despite lower energy gain.

Distortions at H and L have larger energy gains but fewer configurations.

Abstract

The recent discovery of a charge density wave order at the wave vector $P$ $(\frac{1}{3},\frac{1}{3},\frac{1}{3})$ in the kagome metal ScV$_6$Sn$_6$ has created a mystery because subsequent theoretical and experimental studies show a dominant phonon instability instead at another wave vector $H$ $(\frac{1}{3},\frac{1}{3},\frac{1}{2})$. In this paper, I use first principles total energy calculations to map out the landscape of the structural distortions due to the unstable phonon modes at $H$, $L$ $(\frac{1}{2},0,\frac{1}{2})$, and $P$ present in this material. In agreement with previous results, I find that the distortions due to the $H$ instability cause the largest gain in energy relative to the parent structure, followed in order by the $L$ and $P$ instabilities. However, only two distinct structure occur due to this instability, which are separated by 6 meV/f.u. The instability at $L$ results in three distinct structures separated in energy by 5 meV/f.u. In contrast, six different distorted structures are stabilized due to the instability at $P$, and they all lie within 2 meV/f.u.\ of each other. Hence, despite a lower energy gain, the condensation at $P$ could be favorable due to a larger entropy gain associated with the fluctuations within a manifold with larger multiplicity via the order-by-disorder mechanism.