QS$G\hat{W}$: Quasiparticle Self consistent $GW$ with ladder diagrams in $W$

Abstract

We present an extension of the quasiparticle self-consistent $GW$ approximation (QS$GW$) [Phys. Rev. B, 76 165106 (2007)] to include vertex corrections in the screened Coulomb interaction $W$. This is achieved by solving the Bethe-Salpeter equation for the polarization matrix at all $k$-points in the Brillouin zone. We refer to this method as QS$G\hat{W}$. QS$GW$ yields a reasonable and consistent description of the electronic structure and optical response, but systematic errors in several properties appear, notably a tendency to overestimate insulating bandgaps, blue-shift plasmon peaks in the imaginary part of the dielectric function, and underestimate the dielectric constant ${\epsilon }_{\infty }$. A primary objective of this paper is to assess to what extent including ladder diagrams in $W$ ameliorates systematic errors for insulators in the QS$GW$ approximation. For benchmarking we consider about 40 well understood semiconductors, and also examine a variety of less well characterized nonmagnetic systems, six antiferromagnetic oxides, and the ferrimagnet Fe${}_3$O${}_4$. We find ladders ameliorate shortcomings in QS$GW$ to a remarkable degree in both the one-body Green's function and the dielectric function for a wide range of insulators. New discrepancies with experiment appear, and a key aim of this paper is to establish to what extent the errors are systematic and can be traced to diagrams missing from the theory. One key finding of this work is to establish a relation between the bandgap and the dielectric constant ${\epsilon }_{\infty }$. Good description of both properties together provides a much more robust benchmark than either alone. We show how this information can be used to improve our understanding of the one-particle spectral properties in materials systems such as SrTiO${}_3$ and FeO.

47 pages, 28 figures

References in corpus (21)

• Topological Insulators with Inversion Symmetry
• Continuous-time Monte Carlo methods for quantum impurity models
• Quasiparticle self-consistent $GW$ method; a basis for the independent-particle approximation
• Consistent set of band parameters for the group-III nitrides AlN, GaN, and InN
• Dynamical vertex approximation - a step beyond dynamical mean field theory
• Efficient implementation of the GW approximation within the all-electron FLAPW method
• Controlling orbital moment and spin orientation in CoO layers by strain
• Predominance of non-adiabatic effects in zero-point renormalization of the electronic band gap
• Many-body effects in iron pnictides and chalcogenides -- non-local vs dynamic origin of effective masses
• Role of electron-electron and electron-phonon interaction effect in the optical conductivity of VO2
• Bulk Band Structure of Bi${}_2$Te${}_3$
• Spin wave dispersion based on the quasiparticle self-consistent $GW$ method: NiO, MnO and $\alpha$-MnAs
• Quasiparticle self-consistent GW method based on the augmented plane-wave and muffin-tin orbital method
• All-electron quasi-particle self-consistent $GW$ band structures for SrTiO${}_3$ including lattice polarization corrections in different phase
• Electronic Structure of Chromium Trihalides beyond Density Functional Theory
• First-principles study of phase stability of Gd-doped EuO and EuS
• Lattice polarization effects on the screened Coulomb interaction $W$ of the GW approximation
• First principles vs second principles: Role of charge self-consistency in strongly correlated systems
• Full versus quasi-particle self consistency in vertex corrected GW approaches
• Electronic structure correspondence of singlet-triplet scale separation in strained Sr2RuO4
• Lifetime of quasi-particles in the nearly-free electron metal Sodium

Cited by in corpus (23)

• Magnon-mediated exciton-exciton interaction in a van der Waals antiferromagnet
• Giant exchange splitting in the electronic structure of A-type 2D antiferromagnet CrSBr
• Unconventional Spintronics from Chiral Perovskites
• Beyond quasi-particle self-consistent $GW$ for molecules with vertex corrections
• Distinct Magneto-Optical Response of Frenkel and Wannier Excitons in CrSBr
• Electronic correlations and long-range magnetic ordering in NiO tuned by pressure
• Dome structure in pressure dependence of superconducting transition temperature for HgBa${}_2$Ca${}_2$Cu${}_3$O${}_8$ -- Studies by $ab$ $initio$ low-energy effective Hamiltonian
• Many-body perturbation theory vs. density functional theory: A systematic benchmark for band gaps of solids
• Effective bands and band-like electron transport in amorphous solids
• Comparison of interband related optical transitions and excitons in ZnGeN${}_2$ and GaN
• Deconstruction of the anisotropic magnetic interactions from spin-entangled optical excitations in van der Waals antiferromagnets
• Spin-dependent interactions in orbital-density-dependent functionals: non-collinear Koopmans spectral functionals
• Self-consistent quasi-particle $GW$ and hybrid functional calculations for Al/InAs/Al heterojunctions: band offset and spin-orbit coupling effects
• Many body theory beyond GW : towards a complete description of 2-body correlated propagation
• Quasiparticle Description of Angle-Resolved Photoemission Spectroscopy for SrCuO2
• Possible realization of hyperbolic plasmons in a few-layered rhenium disulfide
• Optical absorption and luminescence of $\alpha$-LiV${}_2$O${}_5$ from the Bethe Salpeter Equation
• Many-body theory predictions of positron binding energies in five-membered heterocycles involving N, O, S and NH substituents
• Many-body description of two-dimensional van der Waals ferroelectric $\alpha -$In${}_2$Se${}_3$
• Self-consistent $GW$+Extended Dynamical Mean Field Theory for semiconductors and insulators
• Predicting the suitability of photocatalysts for water splitting using Koopmans spectral functionals: The case of TiO${}_2$ polymorphs
• All-electron Quasiparticle Self-consistent GW for Molecules and Periodic Systems within the Numerical Atomic Orbital Framework
• Electronic band structure and exciton properties of $Pna{2}_1$ CaSnN${}_2$