We present a method for calculating the electronic structure of correlated materials based on a truly first-principles LDA+U scheme. Recently we suggested how to calculate U from first-principles, using a method which we named constrained RPA (cRPA).
The input is simply the Kohn-Sham eigenfunctions and eigenvalues obtained within the LDA. In our proposed self-consistent LDA+U scheme, we calculate the LDA+U eigenfunctions and eigenvalues and use these to extract U. The updated U is then used in the next iteration to obtain a new set of eigenfunctions and eigenvalues and the iteration is continued until convergence is achieved. The most significant result is that our numerical approach is indeed stable: it is possible to find the effective exchange and correlation interaction matrix in a self-consistent way, resulting in a significant improvement over the LDA results, regarding both the bandgap in NiO and the f-band exchange spin-splitting in Gd, but some discrepancies still remain.
The outstanding discrepancy between the measured and calculated (local-density approximation) Fermi surfaces in the well-characterized, paramagnetic Fermi liquid Sr2RhO4 is resolved by including the spin-orbit coupling and Coulomb repulsion. This res
ults in an effective spin-orbit coupling constant enhanced 2.15 times over the bare value. A simple formalism allows discussion of other systems. For Sr2RhO4, the experimental specific-heat and mass enhancements are found to be 2.2.
Using a combined local density functional theory (LDA-DFT) and quantum Monte Carlo (QMC) dynamic cluster approximation approach, the parameter dependence of the superconducting transition temperature Tc of several single-layer hole-doped cuprate supe
rconductors with experimentally very different Tcmax is investigated. The parameters of two different three-band Hubbard models are obtained using the LDA and the downfolding Nth-order muffin-tin orbital technique with N=0 and 1 respectively. QMC calculations on 4-site clusters show that the d-wave transition temperature Tc depends sensitively on the parameters. While the N=1 MTO basis set which reproduces all three $pdsigma$ bands leads to a d-wave transition, the N=0 set which merely reproduces the LDA Fermi surface and velocities does not.
Due to the orthorhombic distortion of the lattice, the electronic hopping integrals along the $a$ and $b$ diagonals, the orthorhombic directions, are slightly different. We calculate their difference in the LDA and find $t_{a}^{prime}-t_{b}^{prime}ap
prox 8 $meV. We argue that electron correlations in the insulating phase of La$_{2-x}$Sr$_{x}$CuO$_{4}$, i. e. at doping $xleq 0.055,$ dramatically enhance the $(t_{a}^{prime}-t_{b}^{prime}) $-splitting between the $a$- and $b$-hole valleys. In particular, we predict that the intensity of both angle-resolved photoemission and of optical absorption is very different for the $a$ and $b$ nodal points.
