Cascade of pressure induced competing CDWs in the kagome metal FeGe

Electronic ordering is prevalent in correlated systems, which commonly exhibit competing interactions. Here, we use x-ray diffraction to demonstrate a cascade of pressure induced order-disorder transformations, with propagation vectors $\mathbf{q}_\mathrm{CDW}$= $\left(\frac{1}{2}\ 0\ \frac{1}{2}\right)$, $\mathbf{q}^*$=$\left(\frac{1}{3}\ \frac{1}{3}\ \frac{1}{2}\right)$ and $\mathbf{q}^\dagger$=$\left(\frac{1}{3}\ \frac{1}{3}\ \frac{1}{3}\right)$, in the kagome metal FeGe. In the pressure interval between 4$<p<$10 GPa, $\mathbf{q}_\mathrm{CDW}$ and $\mathbf{q}^*$ coexist and the spatial extent of the $\sqrt{3}\times\sqrt{3}$ order is nearly long-range at $\sim$15 GPa, $\sim$30 unit cells. Above $\sim$25 GPa, the periodic lattice distortion has a propagation wavevector of $\mathbf{q}^\dagger$=$\left(\frac{1}{3}\ \frac{1}{3}\ \frac{1}{3}\right)$ at room temperature. The cascade of phase transitions are captured by the Ising model of frustrated triangular lattices and modeled by Monte Carlo simulations based on the dimerization of trigonal Ge$_1$. The pressure dependence of the integrated intensities and correlation lengths of $\mathbf{q}_\mathrm{CDW}$, $\mathbf{q}^*$ and $\mathbf{q}^\dagger$ demonstrate a competition between the 2$\times$2 and $\sqrt{3}\times\sqrt{3}$ phases prove the tunability of order-disorder phase transitions under pressure and the rich landscape of metastable/fragile phases of FeGe.