Origin of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>π</mml:mi></mml:math>-shifted three-dimensional charge density waves in the kagomé metal <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mrow><mml:mi>A</mml:mi><mml:mi mathvariant="normal">V</mml:mi></mml:mrow><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> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>(</mml:mo><mml:mi>A</mml:mi><mml:mo>=</mml:mo><mml:mi>Cs</mml:mi><mml:mo>,</mml:mo><mml:mo> </mml:mo><mml:mi>Rb</mml:mi><mml:mo>,</mml:mo><mml:mo> </mml:mo><mml:mi mathvariant="normal">K</mml:mi><mml:mo>)</mml:mo></mml:math>
Heqiu Li, Xiaoyu Liu, Yong Baek Kim, Hae‐Young Kee
Abstract
Understanding the nature of charge density wave (CDW) and superconductivity in the kagom\'e metal ${A\mathrm{V}}_{3}{\mathrm{Sb}}_{5}$ $(A= \mathrm{Cs},\mathrm{Rb},\mathrm{K})$ is a recent subject of intensive study. Due to the presence of van Hove singularities, electron-electron interaction has been suggested to play an important role in the formation of such broken-symmetry states. Recent experiments show that the CDW order is three dimensional and it is staggered across different kagom\'e layers. However, the experimental interpretation for the precise structure of CDW varies in terms of whether it is the star of David (SD), inverse star of David (ISD), or the alternation of the two among neighboring layers. In this work, we show that the origin of these distinct CDW orders can be understood in a unified picture by considering intralayer and interlayer electron-electron interactions as well as the coupling between electrons and lattice distortions. Utilizing an effective nine-band model with V $d$ orbitals and out-of-plane Sb $p$ orbitals, it is demonstrated that the repulsive electron-electron interaction favors charge bond order which induces either SD or ISD upon including lattice distortions. As the interlayer interaction is introduced, $\ensuremath{\pi}$-shifted CDW develops with the staggered ordering along the $c$ axis. We also find that the phase with alternating SD and ISD can be stabilized as the ground state under strong interlayer interaction.