Simple vertex correction improves GW band energies of bulk and two-dimensional crystals

Abstract

The GW self-energy method has long been recognized as the gold standard for quasiparticle (QP) calculations of solids in spite of the fact that the neglect of vertex corrections and the use of a DFT starting point lacks rigorous justification. In this work we remedy this situation by including a simple vertex correction that is consistent with an LDA starting point. We analyse the effect of the self-energy by splitting it into a short-range and long-range term which are shown to govern respectively the center and size of the band gap. The vertex mainly improves the short-range correlations and therefore has a small effect on the band gap, while it shifts the band gap center up in energy by around 0.5 eV in good agreement with experiments. Our analysis also explains how the relative importance of short- and long-range interactions in structures of different dimensionality is reflected in their QP energies. Inclusion of the vertex comes at practically no extra computational cost and even improves the basis set convergence compared to GW. The method thus provides an efficient and rigorous improvement over the GW approximation and sets a new standard for quasiparticle calculations of solids.

References in corpus (17)

• Observation of giant bandgap renormalization and excitonic effects in a monolayer transition metal dichalcogenide semiconductor
• The GW method
• Yambo: an \textit{ab initio} tool for excited state calculations
• Computational 2D Materials Database: Electronic Structure of Transition-Metal Dichalcogenides and Oxides
• First-principles GW calculations for fullerenes, porphyrins, phtalocyanine, and other molecules of interest for organic photovoltaic applications
• Probing excitonic states in ultraclean suspended two-dimensional semiconductors by photocurrent spectroscopy
• Fully selfconsistent GW calculations for molecules
• Quasiparticle GW calculations for solids, molecules and 2D materials
• All-electron GW approximation with the mixed basis expansion based on the full-potential LMTO method
• Self-consistent GW: All-electron implementation with localized basis functions
• Band Offsets at the Si/SiO${}_2$ Interface from Many-Body Perturbation Theory
• Dynamical and anharmonic effects on the electron-phonon coupling and the zero-point renormalization of the electronic structure
• Temperature dependent excitonic effects in the optical properties of single-layer MoS${}_2$
• Efficient many-body calculations of 2D materials using exact limits for the screened potential: Band gaps of MoS${}_2$, hBN, and phosphorene
• Extending the random-phase approximation for electronic correlation energies: The renormalized adiabatic local density approximation
• Adiabatic-connection fluctuation-dissipation DFT for the structural properties of solids-the renormalized ALDA and electron gas kernels
• Beyond the random phase approximation: Improved description of short range correlation by a renormalized adiabatic local density approximation

Cited by in corpus (16)

• The Computational 2D Materials Database: High-Throughput Modeling and Discovery of Atomically Thin Crystals
• The GW compendium: A practical guide to theoretical photoemission spectroscopy
• On The Relation Between Equation-of-Motion Coupled-Cluster Theory and the GW Approximation
• Representing individual electronic states for machine learning GW band structures of 2D materials
• Accurate ground state- and quasiparticle energies: beyond the RPA and GW methods with adiabatic exchange-correlation kernels
• Accurate electronic band gaps of two-dimensional materials from the local modified Becke-Johnson potential
• Vertex corrections to the polarizability do not improve the GW approximation for the ionization potential of molecules
• Towards fully automatized GW band structure calculations: What we can learn from 60.000 self-energy evaluations
• Excitons in Bulk and Layered Chromium Tri-Halides: From Frenkel to the Wannier-Mott Limit
• An Optimally-Tuned Starting Point for Single-Shot $GW$ Calculations of Solids
• Exploring the Statically Screened $G3W2$ Correction to the $GW$ Self-Energy: Charged Excitations and Total Energies of Finite Systems
• A Finite-field Approach for $GW$ Calculations Beyond the Random Phase Approximation
• Critical assessment of $G_0{W}_0$ calculations for 2D materials: the example of monolayer MoS${}_2$
• Combining the $\Delta$-Self-Consistent-Field and GW Methods for Predicting Core Electron Binding Energies in Periodic Solids
• Embedding vertex corrections in GW self-energy: theory, implementation, and outlook
• Bandgap of two-dimensional materials: Thorough assessment of modern exchange-correlation functionals