F. Grandi, M. A. Sentef, D. M. Kennes, and R. Thomale
Phys. Rev. B 110, 245138 (2024)
Starting from a low-energy continuum model for the band dispersion of the 2×2 charge-ordered phase of the kagome metals AV3Sb5 (A = K, Rb, Cs), we show that nematicity can develop in this state driven either by three inequivalent 1×4 charge fluctuations preemptive of a 1×4 charge order (CO), or by an actual zero-momentum d-wave charge Pomeranchuk instability (PI). We perform an analysis that starts from a Kohn-Luttinger theory in the particle-hole sector, which allows us to establish a criterion for the development of an attractive nematic channel near the onset of the 1×4 CO and near the d-wave charge PI, respectively. We derive an effective charge-fermion model for the d-wave PI with a nematic susceptibility given via a random phase approximation (RPA) summation. By contrast, for the finite momentum CO, the RPA scheme breaks down and needs to be improved upon by including Aslamazov-Larkin contributions to the nematic pairing vertex. We then move to the derivation of the Ginzburg-Landau potentials for the 1×4 CO and for the d-wave PI, and we obtain the corresponding analytical expression for the nematic susceptibility at the nematic transition temperature T ～ Tnem in both cases. The nematic response functions obtained in this way are interpreted starting from the two charge-fermion models, and we underline under which assumptions one recovers the Ginzburg-Landau result. Finally, we show an enhancement of the nematic character that is rooted in the coupling of the order parameters to elastic deformations. Our work establishes a relation between the nematicity observed in some of the iron-based superconductors, where the nematic phase might be driven by spin fluctuations, and the vanadium-based kagome metals, where charge fluctuations likely induce nematicity. The two microscopic mechanisms we propose for the stabilization of the nematic state in AV3Sb5, i.e., the zero-momentum d-wave PI and the fluctuations of the finite momentum CO, are distinguishable by diffusive scattering experiments, meaning that it is possible to gauge which of the two theories, if any, is the most likely to describe this phase. Both mechanisms might also be relevant for the recently discovered titanium-based family AV3Sb5, where nematicity has also been observed.
