Efficient tight-binding approach for the study of strongly correlated systems

In this work, we present results from self-consistent charge density functional based tight-binding (DFTB) calculational scheme, including local-density approximation $+U$ (LDA$+U$) and simplified self-interaction-corrected-like potentials for the simulation of systems with localized strongly correlated electrons. This approach attempts to combine the efficiency of tight binding with the accuracy of more sophisticated ab initio methods and allows treatment of highly correlated electrons for very large systems. This is particularly interesting for the case of rare earths in GaN, where dilute amount of rare earth ions is used. In this work, we show the results of test calculations on bulk ErN and on the substitutional ${\mathrm{Er}}_{\mathrm{Ga}}$ in wurtzite GaN, which we choose as representatives of bulk and point defects in solids with strongly correlated electrons. We find that ErN is a half metal in the ferromagnetic phase and that the substitutional ${\mathrm{Er}}_{\mathrm{Ga}}$ in wurtzite GaN has $C_{3v}$ symmetry. These examples show that the DFTB approach reproduces well the results of more demanding calculation schemes with a very low computational cost, making it suitable for the study of extended systems beyond the capabilities of density functional theory.

Figure 1

(Color online) Spin-resolved band structure of rocksalt ErN calculated with the SDFTB (first row) and $\mathrm{SDFTB}+U$ FLL and $\mathrm{SDFTB}+U$ AMF (second and third rows) approaches.

Figure 2

Volume slice of the magnetization density in the (100) plane of rocksalt ErN in the ferromagnetic phase. The axis labels are expressed in Å and the hue (in arbitrary units) the electronic density. The unpaired electrons are localized on the Er atoms.

Figure 3

The substitutional ${\mathrm{Er}}_{\mathrm{Ga}}$ in wurtzite GaN. Spin-resolved ([(a) and (c)] spin up and [(b) an (d)] spin down) energy band structure calculated with [(a) and (b)] LDA/DFTB and $\mathrm{LSDA}+U$ [(c) and (d)] calculated with a value of $(U-J)$ of $7.6\mathrm{eV}$. In the first row, reported are the DFTB calculations, and in the second, WIEN2K calculations (with the same computational parameters) are reported for comparison.

Figure 4

${\mathrm{Er}}_{\mathrm{Ga}}$ in the neutral charge state in wurtzite GaN. Spin-resolved DOS calculated with the different approaches implemented in DFTB (upper box) and with LDA and $\mathrm{LSDA}+U$ as implemented in WIEN2K (lower box). The arrows show the position of the $f$-related peaks. We only show the spin down electrons, as the spin up are occupied and included in the valence band. In the $\mathrm{LDA}+U$ and pSIC calculations, the $f$-related peak visible in the band gap is split into two parts, and the rest of the structure remains almost untouched. The valence band maximum was chosen in each case as zero of the energy scale.