Flat phonon soft modes and unconventional charge density wave formation in ScV6Sn6: Microscopic and effective theory

Kagome materials with flat bands exhibit wildly different physical properties depending on symmetry group and electron number. We analyze the case of the kagome 166 material ScV6Sn6 in symmetry group 191, with the Fermi level away from the flat bands. Experimentally, an ∼95 K charge density wave (CDW) at vector K̄=(13,13,13) exists, with no nesting or peaks in the electron susceptibility at K̄. We show that ScV6Sn6 has a collapsed phonon mode at H=(13,13,12) and an imaginary flat phonon band in the H vicinity. The soft phonon is supported on the triangular Sn (SnT) z-directed mirror-even vibration, which is faithfully described by a three-degree-of-freedom simple force constant model. We show that the phonon softening comes from the electron-phonon coupling between mirror-even electron orbitals at SnT and the mirror-even vibration of SnT atoms. We model it using a (Gaussian) approximation of the hopping parameter Yu, Nat. Phys. 20, 1262 (2024)10.1038/s41567-024-02486-0 and show that the resulting field-theoretical renormalization of the phonon frequency reproduces the collapse of the H phonon and induces small in-plane dispersion away from H. To explain the appearance of the K̄ CDW we build an effective model of two order parameters (OPs): one at the collapsed phonon H and one at the CDW K̄. Comparing our results with experimental data [Korshunov, Nat. Commun. 14, 6646 (2023)2041-172310.1038/s41467-023-42186-6], we show that the H OP undergoes a second-order phase transition; however, its flatness around H induces large fluctuations and stabilizes a K̄ CDW via a first-order transition. We construct CDW OPs in the electron and phonon fields that match the ab initio calculations. Our results not only explain the CDW in ScV6Sn6 but also show an unprecedented level of modeling of complex electronic systems that open different collaboration between ab initio calculations and analytics.