Title:
Supporting Information: Role of Spin Currents on Electron-Electron Interaction in the Quantum Spin-Hall Phase
Year of Publication:
2022
Authors:
William P Comaskey, Filippo Bodo, Alessandro Erba, Jose L Mendoza-Cortes, Jacques K Desmarais
Abstract:
Our DFT and SCDFT calculations are performed with a developer’s version of the Crystal17 code, in which some of the present authors recently implemented a 2c-SCF procedure. S1–S6 The geometries of the bilayers are optimized at the SR 1c-SCF level, using analytical gradients for 2D periodic systems, and a quasi-Newton procedure, in the Broyden-Fletcher-Goldfarb-Shanno variant. S7–S10 The 1c/2c-SCF calculations employed a multiconfigurational Dirac-Hartree-Fock relativistic effective core potential (RECP), based on an adjustment to the Dirac-Coulomb-Breit Hamiltonian. S11 23 electrons (5s25p65d106s26p3) were treated in the valence space, employing a (10s6p6d)/[4s3p3d] basis set. S12 Diagonalization of the Fock matrix and calculation of the Fermi energy was achieved with a 20× 20 net in reciprocal space. A tolerance of 1× 10− 8 Eh was used as a criterion for convergence of the 1c/2c-SCF procedures. Truncation of the infinite Coulomb and exchange series was achieved with TOLINTEG parameters equal to 8 8 8 8 20 (see manual). Integration of the xc energy and construction of the xc matrix elements was performed on a direct space unpruned (uniform) grid with Gauss-Legendre radial and Lebedev angular point distributions, containing 75 radial points and 974 angular points (ie a Lebedev accuracy level of 16). S13–S15 Our GGA (hybrid-GGA) calculations were performed with the PBE functional (and a fraction of 1/n, with n= 10 of EXX). S16 The more common value of n= 4 was proposed by fourth-order Görling-Levy perturbation theory in tandem with the generalized Kohn-Sham scheme of Seidl and co-workers, and …
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