Spin susceptibility and electron-phonon coupling of two-dimensional materials by range-separated hybrid density functionals: Case study of LixZrNCl

We investigate the capability of density functional theory (DFT) to appropriately describe the spin susceptibility, χs, and the intervalley electron-phonon coupling in LixZrNCl. At low doping, LixZrNCl behaves as a two-dimensional two-valley electron gas, with parabolic bands. In such a system, χs increases with decreasing doping because of the electron-electron interaction. We show that DFT with local functionals (LDA/GGA) is not capable of reproducing this behavior. The use of exact exchange in Hartree-Fock (HF) or in DFT hybrid functionals enhances χs. HF, B3LYP, and PBE0 approaches overestimate χs, whereas the range-separated HSE06 functional leads to results similar to those obtained in the random phase approximation (RPA) applied to a two-valley two-spin electron gas. Within HF, LixZrNCl is even unstable towards a ferromagnetic state for x<0.16. The intervalley phonons induce an imbalance in the valley occupation that can be viewed as the effect of a pseudomagnetic field. Thus, similarly to what happens for χs, the electron-phonon coupling of intervalley phonons is enhanced by the electron-electron interaction. Only hybrid DFT functionals capture such an enhancement and the HSE06 functional reproduces the RPA results presented in M. Calandra et al. [Phys. Rev. Lett. 114, 077001 (2015)PRLTAO0031-900710.1103/PhysRevLett.114.077001]. These results imply that the description of the susceptibility and electron-phonon coupling with a range-separated hybrid functional would be important also in other two-dimensional weakly doped semiconductors, such as transition-metal dichalcogenides and graphene.