ATK教程：旋轨耦合导致硅的能带劈裂.pdfVIP

10/15/15, 9:30 AMSpin-orbit splitting of the silicon band structure — QuantumWise 0.1.1 documentation Page 1 of 14/tutorials/spin_orbit_silicon.html Docs ? Tutorials ? Spintronics ? Spin-orbit splitting of the silicon band structure Spin-orbit splitting of the silicon band structure This tutorial will teach you how to take spin-orbit coupling into account in ATK- DFT calculations. Outline: We start off with a short introduction to relativistic effetcs in electronic structure theory, including spin-orbit (SO) coupling. You will then study how spin-orbit coupling splits the electronic bands around the silicon -point, leading to the so-called “split-off” valence band and bands with “heavy” and “light” holes. Lastly, you will employ a SO+MGGA method to get not only the correct band splits but also a reliable estimate of the indirect band gap. ! Note Spin-orbit calculations are more expensive than standard LDA or GGA methods and will often require more SCF iterations to converge. Usually, it is therefore more efficient to first do a spin-polarized LDA or GGA ground state calculation, and then use this ground state as an initial guess for the spin- orbit calculation. This procedure reduces the number of spin-orbit SCF steps and significantly reduces the overall computational time. !Warning Not all pseudopotentials can be used for spin-orbit calculations. The OMX potentials supplied with ATK contains the required SO terms, while the FHI potentials do not. ATK also offers spin-orbit editions of the SG15 pseudopotentials. However, in this tutorial we use the OMX potentials. Γ 10/15/15, 9:30 AMSpin-orbit splitting of the silicon band structure — QuantumWise 0.1.1 documentation Page 2 of 14/tutorials/spin_orbit_silicon.html ! Note Please remember that OMX pseudopotentials have in general more valence electrons in the cores than the FHI potentials do. Therefore, the OMX potentials usually require good basis sets and higher density-mesh cutoff energies (e.g. 200 Hartree). Rel