An anisotropic functional for two-dimensional material systems

TL;DR

Problem: standard density functional theory functionals fail for 2D materials due to isotropic screening and lack of derivative discontinuity, causing underestimation of band gaps and poor defect localization. Approach: propose an anisotropic screened-exchange functional that combines a bulk-style screened exchange $V^{X}(q)=\\epsilon^{-1}(q) V^{HF}(q)$ with a 2D macroscopic dielectric screening model, yielding an effective interaction characterized by a form factor $F(q)$ and dielectric $\\epsilon^{2D}_{eff}(q)$; parameters depend on layer thickness $h$ and surrounding dielectrics. Contributions: demonstrates implementation in VASP, reproduces $GW_0$ band gaps across several 2D semiconductors, achieves piecewise linear total energy with fractional occupation (e.g., $E(x)=b_0+b_1 x+b_2 x^2$ with $b_2\\approx 0.03$ eV for Ge_Ga in GaSe), and yields optical spectra in good agreement with $GW_0$+BSE and TDDFT Cassida kernel. Impact: provides an efficient, Koopmans-compliant framework for defect physics and optoelectronic properties in 2D materials.

Abstract

Density function theory is the workhorse of modern electronic structure theory. However, its accuracy in practical calculations is limited by the choice of the exchange-correlation potential. In this respect, 2D materials pose a special challenge, as all 2D materials and their heterostructures have a crucial similarity. The underlying atomic structures are strongly spatially inhomogeneous, implying that current exchange-correlation functionals, that in almost all cases are isotropic, are ill-prepared for an accurate description. We present an anisotropic screened-exchange potential, that remedies this problem and reproduces the band-gap of 2D materials as well as the piecewise linearity of the total energy with fractional occupation number.

Figures (5)

• Figure 1: Screening functions $\varepsilon(q)$ as defined in Eqs. \ref{['eqn:epsmodel']} for GaSe. For comparison the effective 2D and bulk dielectric functions are shown.
• Figure 2: Fundamental band gap E$_G^\text{Func}$ for a several 2D semiconductors, as calculated via the anisotropic screened exchange approach proposed. Depicted is the band gap resulting of our functional as a function of the reference GW$_0$ band gap E$_G^{Ref}$. The filled diamonds are a comparison to the results of the 3D screened exchange functional of Ref. Lorke20Koopmans. The inset shows effective layer thickness as a function of ionic thickness for the material.
• Figure 3: Band structure of GaSe, calculated with the GW$_0$ approach (lines) as well as with the screened exchange approach presented in this work (circles). The energy of the valence band maximum has been set to 0.
• Figure 4: Total energy of the $\text{Ge}_\text{Ga}$ substitutional defect in GaSe as a function of the fractional occupation number. The energy of the neutral defect has been set to 0.
• Figure 5: Optical absorption from GW$_0$+BSE and from a linear response TDDFT, i.e. the Cassida equation, with the functional presented here as Kernel. Shown are the spectra for (a) GaSe and (b) hBN.