Successive orthorhombic distortions in kagome metals by molecular orbital formation

Abstract

The kagome lattice, with its inherent frustration, hosts a plethora of exotic phenomena, including the emergence of $3\mathbf{q}$ charge density wave order. The high rotational symmetry, required to realize such an unconventional charge order, is broken in many kagome materials by orthorhombic distortions at high temperature, the origin of which is much less discussed despite their ubiquity. In this study, synchrotron X-ray diffraction reveals a structural phase transition from a parent hexagonal phase to an orthorhombic ground state, mediated by a critical regime of diffuse scattering in the prototypical kagome metals $R$Ru$_3$Si$_2$ ($R$=rare-earth). Structural analysis uncovers an interlayer dimerization of kagome atoms in the low-temperature phase. Accordingly, a dimer model with one-dimensional disorder on kagome layers successfully reproduces the diffuse scattering. The observations point to molecular orbital formation between kagome $4d_{z^2}$ orbitals as the driving force behind the transition, consistent with \textit{ab initio} calculations. A framework based on electronegativity and atomic radii is proposed to evaluate the stability of the hexagonal phase in kagome metals, guiding the design of highly symmetric materials.