This paper summarises the theory and functionality behind Questaal, an open-source suite of codes for calculating the electronic structure and related properties of materials from first principles. The formalism of the linearised muffin-tin orbital (LMTO) method is revisited in detail and developed further by the introduction of short-ranged tight-binding basis functions for full-potential calculations. The LMTO method is presented in both Green's function and wave function formulations for bulk and layered systems. The suite's full-potential LMTO code uses a sophisticated basis and augmentation method that allows an efficient and precise solution to the band problem at different levels of theory, most importantly density functional theory, LDA+U, quasi-particle self-consistent GW and combinations of these with dynamical mean field theory. This paper details the technical and theoretical bases of these methods, their implementation in Questaal, and provides an overview of the code's design and capabilities. Program summary Program Title: Questaal Program Files doi: http://dx.doi.org/10.17632/35jxxtzpdn.1 Code Ocean Capsule: https://doi.org110.24433/CO.3778701.v1 Licensing provisions: GNU General Public License, version 3 Programming language: Fortran, C, Python, Shell Nature of problem: Highly accurate ab initio calculation of the electronic structure of periodic solids and of the resulting physical, spectroscopic and magnetic properties for diverse material classes with different strengths and kinds of electronic correlation. Solution method: The many electron problem is considered at different levels of theory: density functional theory, many body perturbation theory in the GW approximation with different degrees of self consistency (notably quasiparticle self-consistent GW) and dynamical mean field theory. The solution to the single-particle band problem is achieved in the framework of an extension to the linear muffin-tin orbital (LMTO) technique including a highly precise and efficient full-potential implementation. An advanced fully-relativistic, non-collinear implementation based on the atomic sphere approximation is used for calculating transport and magnetic properties. (C) 2019 The Author(s). Published by Elsevier B.V.

An electronic quantity, the correlation strength, is defined as a necessary step for understanding the properties and trends in strongly correlated electronic materials. As a test case, this is applied to the different phases of elemental Pu. Within the $\mathit{GW}$ approximation we have surprisingly found a ``universal'' scaling relationship, where the $f$-electron bandwidth reduction due to correlation effects is shown to depend only on the local density approximation bandwidth and is otherwise independent of crystal structure and lattice constant.

Received 18 November 2011DOI:https://doi.org/10.1103/PhysRevB.84.209902©2011 American Physical Society

Different approximations in calculations of electronic quasi‐particle states in semiconductors are compared and evaluated with respect to their validity in predictions of optical properties. The quasi‐particle self‐consistent GW (QSGW) approach yields values of the band gaps which are close to experiments and represents a significant improvement over “single‐shot” GW calculations using local density approximation (LDA) start wavefunctions. The QSGW approximation is compared to LDA bands for a wide‐gap material (CuAlO2) and materials with very small gaps, PbX (X = S, Se, and Te). For wide‐gap materials QSGW overestimates the gaps by 0.3–0.8 eV, an error which is ascribed to the omission of “vertex corrections.” This is confirmed by calculations of excitonic effects, by solving the Bethe‐Salpeter equation. The LDA error in predicting the binding energy of the Cu‐3d states is examined and the QSGW and LDA + U approximations are compared. For PbX the spin‐orbit coupling is included, and it is shown that although LDA gives a reasonable magnitude of the gap at L, only QSGW predicts the correct order of the ${\rm L}_{6}^{ + } $ and ${\rm L}_{6}^{{-} } $ states and thus the correct sign (negative) of the gap pressure coefficient. The pressure‐induced gap closure leads to linear (Dirac‐type) band dispersions around the L point.

The electronic structures of mercury chalcogenides in the zinc-blende structure have been calculated within the LDA, GW (G(0)W(0), "one-shot") and quasi-particle self-consistent GW (QSGW) approximations, including spin-orbit (SO) coupling. The slight tendency to overestimation of band gaps by QSGW is avoided by using a hybrid scheme (20% LDA and 80% QSGW). The details of the GW bands near the top of the valence bands differ significantly from the predictions obtained by calculations within the LDA. The results obtained by G(0)W(0) depend strongly on the starting wave functions and are thus quite different from those obtained from QSGW. Within QSGW, HgS is found to be a semiconductor, with a Gamma(6) s-like conduction-band minimum state above the valence top Gamma(7) and Gamma(8) ("negative" SO splitting). HgSe and HgTe have negative gaps (inverted band structures), but for HgTe the Gamma(7) state is below Gamma(6) due to the large Te SO splitting, in contrast to HgSe where Gamma(6) is below Gamma(7). There appears to be significant differences, in particular for HgSe and HgS, between the ordering of the band-edge states as obtained from experiments and theory.

The electronic band structures of InN, GaN, and a hypothetical ordered InGaN2 compound, all in the wurtzite crystal structure, are calculated using the quasiparticle self-consistent GW approximation. This approach leads to band gaps which are significantly improved compared to gaps calculated on the basis of the local approximation to density functional theory, although generally overestimated by 0.2-0.3 eV in comparison with experimental gap values. Details of the electronic energies and the effective masses including their pressure dependence are compared with available experimental information. The band gap of InGaN2 is considerably smaller than what would be expected by linear interpolation implying a significant band gap bowing in InGaN alloys.

We show that the band spin splitting caused by spin-orbit interaction in crystal structures with no inversion symmetry is strongly influenced by band anticrossing. The splitting is always enhanced for one of the anticrossing bands and suppressed for the other. There are two limiting cases. In the first, the spin splitting is completely suppressed for one of the bands and doubled for the other. In the second, the absolute value of the splitting is markedly enhanced for both bands approaching the magnitude of the hybridization gap. We demonstrate these effects in zinc-blende semiconductors with the help of first-principles GW calculations.

The spin-orbit interaction generally leads to spin splitting (SS) of electron and hole energy states in solids, a splitting that is characterized by a scaling with the wave vector k. Whereas for 3D bulk zinc blende solids the electron (heavy-hole) SS exhibits a cubic (linear) scaling with k, in 2D quantum wells, the electron (heavy-hole) SS is currently believed to have a mostly linear (cubic) scaling. Such expectations are based on using a small 3D envelope function basis set to describe 2D physics. By treating instead the 2D system explicitly as a system in its own right, we discover a large linear scaling of hole states in 2D. This scaling emerges from coupling of hole bands that would be unsuspected by the standard model that judges coupling by energy proximity. This discovery of a linear Dresselhaus k scaling for holes in 2D implies a different understanding of hole physics in low dimensions.

The electronic band structures of PbS, PbSe, and PbTe in the rocksalt structure are calculated with the quasiparticle self-consistent GW (QSGW) approach with spin-orbit coupling included. The semiconducting gaps and their deformation potentials as well as the effective masses are obtained. The GW approximation provides a correct description of the electronic structure around the gap, in contrast to the local-density approximation, which leads to inverted gaps in the lead chalcogenides. The QSGW calculations are in good quantitative agreement with experimental values of the gaps and masses. At moderate hole doping a complex filamental Fermi-surface structure develops with ensuing large density of states. The pressure-induced gap closure leads to linear (Dirac-type) band dispersions around the L point.

The pressure variation in the structural parameters, u and c/a, of the delafossite CuAlO2 is calculated within the local-density approximation (LDA). Further, the electronic structures as obtained by different approximations are compared: LDA, LDA+U, and a recently developed "quasiparticle self-consistent GW" (QSGW) approximation. The structural parameters obtained by the LDA agree very well with experiments but, as expected, gaps in the formal band structure are underestimated as compared to optical experiments. The (in LDA too high lying) Cu 3d states can be down shifted by LDA+U. The magnitude of the electric field gradient (EFG) as obtained within the LDA is far too small. It can be "fitted" to experiments in LDA+U but a simultaneous adjustment of the EFG and the gap cannot be obtained with a single U value. QSGW yields reasonable values for both quantities. LDA and QSGW yield significantly different values for some of the band-gap deformation potentials but calculations within both approximations predict that 3R-CuAlO2 remains an indirect-gap semiconductor at all pressures in its stability range 0-36 GPa, although the smallest direct gap has a negative pressure coefficient.

Using Fe/GaAs Schottky tunnel barriers as electrical spin detectors, we show that the magnitude and the sign of their spin-detection sensitivities can be widely tuned with the voltage bias applied across the Fe/GaAs interface. Experiments and theory establish that this tunability derives not just simply from the bias dependence of the tunneling conductances G(up arrow,down arrow) (a property of the interface), but also from the bias dependence of electric fields in the semiconductor which can dramatically enhance or suppress spin-detection sensitivities. Electrons in GaAs with fixed polarization can therefore be made to induce either positive or negative voltage changes at spin detectors, and some detector sensitivities can be enhanced over tenfold compared to the usual case of zero-bias spin detection.

Results of theoretical studies of electronic and optical properties of III–V nitride compound semiconductors under pressure are presented. As representatives InN and AlN have been chosen, and for InN the pressure effects on the fundamental gap as well as the role of conduction‐band filling are examined. Both the fundamental gap and the electron effective mass increase with pressure, but due to the strong non‐parabolicity of the conduction band, the pressure coefficient of the mass decreases with electron concentration. Particular attention is paid to the electronic states in the gap region. The “local‐density gap error” is avoided by performing Quasi Particle self‐consistent GW calculations, which produce slightly too large gaps. Including in addition the missing electron–hole excitonic states and the gap renormalization due to electron–phonon interaction a gap reduction is obtained. The e–h correlations are deduced from solutions of the Bethe‐Salpeter equation. These are further used to study excitonic states in the gap of AlN under pressure, and for the rocksalt phase a pressure induced delocalized → localized transition is predicted. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

We present results for the electronic structure of plutonium by using a recently developed quasiparticle self-consistent GW method (QSGW). We consider a paramagnetic solution without spin-orbit interaction as a function of volume for the face-centred cubic (fcc) unit cell. We span unit-cell volumes ranging from 10% greater than the equilibrium volume of the δ phase to 90% of the equivalent for the α phase of Pu. The self-consistent GW quasiparticle energies are compared to those obtained within the Local Density Approximation (LDA). The goal of the calculations is to understand systematic trends in the effects of electronic correlations on the quasiparticle energy bands of Pu as a function of the localisation of the f orbitals. We show that correlation effects narrow the f bands in two significantly different ways. Besides the expected narrowing of individual f bands (flatter dispersion), we find that an even more significant effect on the f bands is a decrease in the crystal-field splitting of the different bands.

We focus on inelastic neutron scattering in $URu_2Si_2$ and argue that observed gap in the fermion spectrum naturally leads to the spin feature observed at energies $\omega_{res} = 4-6 meV$ at momenta at $\bQ^* = (1\pm 0.4, 0,0)$. We discuss how spin features seen in $URu_2Si_2$ can indeed be thought of in terms of {\em spin resonance} that develops in HO state and is {\em not related} to superconducting transition at 1.5K. In our analysis we assume that the HO gap is due to a particle-hole condensate that connects nested parts of the Fermi surface with nesting vector $\bf{Q}^* $. Within this approach we can predicted the behavior of the spin susceptibility at $\bQ^*$ and find it to be is strikingly similar to the phenomenology of resonance peaks in high-T$_c$ and heavy fermion superconductors. The energy of the resonance peak scales with $T_{HO}$ $\omega_{res} \simeq 4 k_BT_{HO}$. We discuss observable consequences spin resonance will have on neutron scattering and local density of states.

We consider the magnetic structure on the Fe(001) surface and theoretically study the scanning tunneling spectroscopy using a spin-polarized tip (SP-STM). We show that minority-spin surface states induce a strong bias dependence of the tunneling differential conductance which largely depends on the orientation of the magnetization in the SP-STM tip relative to the easy magnetization axis in the Fe(001) surface. We propose to use this effect in order to determine the spin character of the Fe(001) surface states. This technique can be applied also to other magnetic surfaces in which surface states are observed.