Impact of Sb degrees of freedom on the charge density wave phase diagram of the kagome metal CsV${}_3$Sb${}_5$

Abstract

Elucidating the microscopic mechanisms responsible for the charge density wave (CDW) instability of the AV${}_3$Sb${}_5$ (A=Cs, K, Rb) family of kagome metals is critical for understanding their unique properties, including superconductivity. In these compounds, distinct CDW phases with wave-vectors at the $M$ and $L$ points are energetically favorable, opening the possibility of tuning the type of CDW order by appropriate external parameters. Here, we shed light on the CDW landscape of CsV${}_3$Sb${}_5$ via a combination of first-principles calculations and phenomenology, which consists of extracting the coefficients of the CDW Landau free-energy expansion from density functional theory. We find that while the main structural distortions of the kagome lattice in the staggered tri-hexagonal CDW phase are along the nearest-neighbor V-V bonds, distortions associated with the Sb ions play a defining role in the energy gain in this and all other CDW states. Moreover, the coupling between ionic displacements from different unit cells is small, thus explaining the existence of multiple CDW instabilities with different modulations along the c-axis. We also investigate how pressure and temperature impact the CDW phase of CsV${}_3$Sb${}_5$. Increasing pressure does not change the staggered tri-hexagonal CDW ground state, even though the $M$-point CDW instability disappears before the $L$-point one, a behavior that we attribute to the large nonlinear coupling between the order parameters. Upon changing the temperature, we find a narrow regime in which another transition can take place, toward a tri-hexagonal Star-of-David CDW phase. We discuss the implications of our results by comparing them with experiments on this compound.

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• AV${}_3$Sb${}_5$ Kagome Superconductors: Progress and Future Directions
• Intertwined van-Hove Singularities as a Mechanism for Loop Current Order in Kagome Metals
• Evidence chain for time-reversal symmetry-breaking kagome superconductivity
• Origin and stability of the charge density wave in ScV${}_6$Sn${}_6$
• Charge order above room-temperature in a prototypical kagome superconductor La(Ru${}_{1-x}$Fe${}_x$)${}_3$Si${}_2$
• Origin of $\pi$-shifted three-dimensional charge density waves in kagome metal AV${}_3$Sb${}_5$
• Kagome metals
• Dynamical decoding of the competition between charge density waves in a kagome superconductor
• Kagome KMn${}_3$Sb${}_5$ metal: Magnetism, lattice dynamics, and anomalous Hall conductivity
• Noncollinear Magnetic Multipoles in Collinear Altermagnets
• Coherent Phonon Pairs and Rotational Symmetry Breaking of Charge Density Wave Order in the Kagome Superconductor CsV${}_3$Sb${}_5$
• Inversion and Tunability of Van Hove Singularities in $A$V${}_3$Sb${}_5$ ($A$ = K, Rb, and Cs) kagome metals
• Beyond kagome: $p$-bands in kagome metals
• Inter-Layer Correlation of Loop Current Charge Density Wave on the Bilayer Kagomé Lattice
• Electronic and structural properties of Rh- and Pd-based kagome layered shandites from first principles