二维材料自旋极化率和电子-声子耦合的距离分离杂化密度泛函研究：Li $_x$ ZrNCl的实例研究
Spin susceptibility and electron-phonon coupling of two-dimensional materials by range-separated hybrid density functionals: Case study of Li$_x$ZrNCl
摘要：
我们研究了密度泛函理论（DFT）对Li $_x$ ZrNCl的自旋极化率、$χ_s$和谷间电子-声子耦合的描述能力。在低掺杂时，Li $_x$ ZrNCl表现为二维双谷电子气，具有抛物线带。在这样的系统中，由于电子-电子相互作用，$χ_s$随着掺杂的减少而增加。我们发现，DFT与局部泛函（LDA/GGA）是不能够再现这种行为。在Hartree-Fock（HF）或DFT混合泛函中使用精确交换增强了$χ_s$。HF，B3 LYP和PBE 0方法高估了$χ_s$，而范围分离的HSE 06功能导致的结果类似的随机相位近似（RPA）中获得的应用到一个两谷两自旋电子气。在HF中，Li $_x$ ZrNCl甚至不稳定，朝向$x<0.16$的铁磁状态。谷间声子引起的不平衡的山谷占领，可以被看作是一个伪磁场的效果。因此，与$χ_s$的情况类似，谷间声子的电子-声子耦合通过电子-电子相互作用而增强。只有混合DFT泛函捕获这样的增强和HSE06泛函再现的RPA结果在M。Calandra {\it等} [Phys. Rev. Lett. {\bf 114}，077001（2015）]。这些结果意味着，在其他二维弱杂质半导体中，如过渡金属二硫属化物和石墨烯，用距离分离的杂化泛函描述磁化率和电子-声子耦合也是重要的。
英文摘要：
We investigate the capability of density functional theory (DFT) to appropriately describe the spin susceptibility, $χ_s$, and the intervalley electron-phonon coupling in Li$_x$ZrNCl. At low doping, Li$_x$ZrNCl behaves as a two-dimensional two-valley electron gas, with parabolic bands. In such a system, $χ_s$ 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 $χ_s$. HF, B3LYP, and PBE0 approaches overestimate $χ_s$, 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, Li$_x$ZrNCl 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 $χ_s$, 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 {\it et al.} [Phys. Rev. Lett. {\bf 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.
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