Structural evolution of the kagome superconductors AV3Sb5 (A = K, Rb, and Cs) through charge density wave order

Abstract

The kagome superconductors ${\mathrm{KV}}_{3}{\mathrm{Sb}}_{5}$, ${\mathrm{RbV}}_{3}{\mathrm{Sb}}_{5}$, and ${\mathrm{CsV}}_{3}{\mathrm{Sb}}_{5}$ are known to display charge density wave (CDW) order which impacts the topological characteristics of their electronic structure. Details of their structural ground states and how they evolve with temperature are revealed here using single crystal x-ray crystallographic refinements as a function of temperature, carried out with synchrotron radiation. The compounds ${\mathrm{KV}}_{3}{\mathrm{Sb}}_{5}$ and ${\mathrm{RbV}}_{3}{\mathrm{Sb}}_{5}$ present $2\ifmmode\times\else\texttimes\fi{}2\ifmmode\times\else\texttimes\fi{}2$ superstructures in the $Fmmm$ space group with a staggered trihexagonal deformation of vanadium layers. ${\mathrm{CsV}}_{3}{\mathrm{Sb}}_{5}$ displays more complex structural evolution, whose details have been unravelled by applying machine learning methods to the scattering data. Upon cooling through the CDW transition, ${\mathrm{CsV}}_{3}{\mathrm{Sb}}_{5}$ displays a staged progression of ordering from a $2\ifmmode\times\else\texttimes\fi{}2\ifmmode\times\else\texttimes\fi{}1$ supercell and a $2\ifmmode\times\else\texttimes\fi{}2\ifmmode\times\else\texttimes\fi{}2$ supercell into a final $2\ifmmode\times\else\texttimes\fi{}2\ifmmode\times\else\texttimes\fi{}4$ supercell that persists to $T=11$ K and exhibits an average structure where vanadium layers display both trihexagonal and Star of David patterns of deformations. Diffraction from ${\mathrm{CsV}}_{3}{\mathrm{Sb}}_{5}$ under pulsed magnetic fields up to ${\ensuremath{\mu}}_{0}H=28$ T suggest the real component of the CDW state is insensitive to external magnetic fields.