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

Abstract

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)]. 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.

High- Tc superconductivity in weakly electron-doped HfNCl

“…However, in general, the effective mass of HfNCl is slightly larger than that of ZrNCl. Similarly, N (0) is larger in HfNCl than ZrNCl for all doping 26 .…”

“…In previous work, it has been shown that in 2D mul-tivalley semiconductors, at low doping, the electronelectron interaction enhances intervalley electron-phonon coupling, explaining the behavior of T c 25,26 . The enhancement of T c is linked to the enhancement of the spin susceptibility χ s .…”

“…The enhancement of T c is linked to the enhancement of the spin susceptibility χ s . Furthermore, a systematic study of the electronic, magnetic, and vibrational properties of Li x ZrNCl has been performed using density functional theory (DFT) with hybrid functionals with exact exchange and range separation, and this paper shows that the exact exchange component leads to a similar enhancement in spin susceptibility and electron-phonon interaction 26 . This effect on the enhancement of T c should be quite general as it only requires basic general ingredients such as a 2D multivalley (ideally two-valley) semiconductor and a large enough electron-gas parameter, r s = 1/a B √ πn with a B = ǫ M 2 /(m * e 2 ) where n is the electron density per unit area [linked to the doping per formula unit x per area Ω of 2 formula units (f.u.)…”

“…However, in the weakly doped regime of transition-metal chloronitrides, T c increases with decreasing doping 9,10,14 . This unexpected behavior resulted in a search for a theoretical understanding of the physics of superconductivity in 2D semiconductors [19][20][21][22][23][24][25][26] .…”

Quantum‐mechanical condensed matter simulations with CRYSTAL

“…Furthermore, it is now possible to force the total spin to assume noninteger values, which often happens to be the case for the ground state in magnetic metals. This also allows to compute the static spin susceptibility χ s = ∂M s / ∂B , where M s is the spin magnetization and B the magnetic field, by finite differences using the formula χ s = ( ∂ 2 E tot / ∂M s 2 ) −1 (Pamuk, Baima, Dovesi, Calandra, & Mauri, ).…”