Hexagonal-to-base-centered-orthorhombic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>4</mml:mn><mml:mi>Q</mml:mi></mml:mrow></mml:math> charge density wave order in kagome metals <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>KV</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mi>Sb</mml:mi><mml:mn>5</mml:mn></mml:msub><mml:mo>,</mml:mo></mml:mrow></mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>RbV</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mi>Sb</mml:mi><mml:mn>5</mml:mn></mml:msub><mml:mo>,</mml:mo></mml:mrow></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>CsV</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mi>Sb</mml:mi><mml:mn>5</mml:mn></mml:msub></mml:mrow></mml:math>
Alaska Subedi
Abstract
The recently discovered kagome metals ${\mathrm{KV}}_{3}{\mathrm{Sb}}_{5}$, ${\mathrm{RbV}}_{3}{\mathrm{Sb}}_{5}$, and ${\mathrm{CsV}}_{3}{\mathrm{Sb}}_{5}$ exhibit a unique charge density wave state which hosts both superconductivity and a large anomalous Hall response. The microscopic mechanisms that underlie these phenomena have not been fully understood because the structure of the charge density wave order has not been completely determined. Previous theoretical results show that the parent $P6/mmm$ phase of these materials has phonon instabilities at the $M(\frac{1}{2},0,0)$ and $L(\frac{1}{2},0,\frac{1}{2})$ points in their Brillouin zone, but the energetics of all the low-symmetry phases that can arise due to the phonon instabilities was not investigated. Here, I perform such a search for the lowest-energy structure of these materials using first-principles calculations. Group-theoretical analysis shows that there are 17 different distortions that are possible due to the phonon instabilities. 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 ${M}_{1}^{+}(a,0,0)+{L}_{2}^{\ensuremath{-}}(0,b,b)$ 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 a doubly degenerate unstable phonon mode at the $A(0,0,\frac{1}{2})$ point in the parent $P6/mmm$ phase. The $A$ point has only one element in its star, and condensation of the instability at this point leads to a base-centered-orthorhombic structure with the space group $Cmcm$ and $4Q$ order parameter ${M}_{1}^{+}(a,0,0)+{L}_{2}^{\ensuremath{-}}(0,b,b)+{A}_{6}^{+}(\frac{1}{2}c,\frac{\ensuremath{-}\sqrt{3}}{2}c)$. A characteristic signature of this charge order is the absence of the mirror symmetry perpendicular to the $b$ axis in individual kagome layers, whose experimental observation below the structural transition temperature would be a strong indication that the $Cmcm$ structure describes the charge density wave state of these materials.