All-electron fully relativistic Kohn-Sham theory for solids based on the Dirac-Coulomb Hamiltonian and Gaussian-type functions

Abstract

We present the first full-potential method that solves the fully relativistic 4-component Dirac-Kohn-Sham equation for materials in the solid state within the framework of atom-centered Gaussian-type orbitals (GTOs). Our GTO-based method treats one-, two-, and three-dimensional periodic systems on an equal footing, and allows for a seamless transition to the methodology commonly used in studies of molecules with heavy elements. The scalar relativistic effects and spin-orbit interaction are handled variationally. The full description of the electron-nuclear potential in the core region of heavy nuclei is straightforward due to the local nature of the GTOs and does not pose any computational difficulties. We show how the time-reversal symmetry and a quaternion algebra-based formalism can be exploited to significantly reduce the increased methodological complexity and computational cost associated with multiple wave-function components coupled by the spin-orbit interaction. We provide a description of how to employ the matrix form of the multipole expansion and an iterative renormalization procedure to evaluate the conditionally convergent lattice sums arising for periodic systems. We investigate the problem of inverse variational collapse that arises if the Dirac operator containing a repulsive periodic potential is expressed in a basis containing diffuse functions, and suggest a possible solution. We demonstrate the validity of the method on silver halide crystals with large relativistic effects, and two-dimensional honeycomb structures (silicene and germanene) exhibiting the spin-orbit-driven quantum spin Hall effect. Our results are well-converged with respect to the basis limit using standard bases developed for molecular calculations, and indicate that the rule of removing basis functions with small exponents should not be applied when transferring the molecular basis to solids.

arXiv comment24 pages, 2 figures

References in corpus (20)

• Topological Insulators
• Spintronics: Fundamentals and applications
• Quantum Spin Hall Effect in Graphene
• Quantum Spin Hall Effect in Silicene
• Universal Intrinsic Spin-Hall Effect
• High-throughput electronic band structure calculations: challenges and tools
• Topological quantum chemistry
• Graphene Spintronics
• Colloquium: Topological Band Theory
• Large-gap quantum spin Hall insulators in tin films
• Theory of electrical spin injection: Tunnel contacts as a solution of the conductivity mismatch problem
• Computational 2D Materials Database: Electronic Structure of Transition-Metal Dichalcogenides and Oxides
• Band-structure topologies of graphene: spin-orbit coupling effects from first principles
• Dual kinetic balance approach to basis set expansions for the Dirac equation
• Calculated spin-orbit splitting of all diamond-like and zinc-blende semiconductors: Effects of p1/2 local orbitals and chemical trends
• 103-Compound Band Structure Benchmark of Post-SCF Spin-Orbit Coupling Treatments in Density-Functional Theory
• Relativity and the lead-acid battery
• First Principles LCGO Calculation of the Magneto-optical Properties of Nickel and Iron
• Scalar-relativistic effects in solids in the framework of a Douglas-Kroll transformed Dirac-Coulomb Hamiltonian
• New quantum number for the many-electron Dirac-Coulomb Hamiltonian

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