Mass enhancement in 3 d and s − p perovskites from symmetry breaking

In some $d$-electron oxides, the measured effective mass ${m}_{\mathrm{exptl}}^{*}$ has long been known to be significantly larger than the model effective mass ${m}_{\mathrm{model}}^{*}$ deduced from mean-field band theory, i.e., ${m}_{\mathrm{exptl}}^{*}=\ensuremath{\beta}{m}_{\mathrm{model}}^{*}$, where $\ensuremath{\beta}g1$ is the ``mass-enhancement'' or ``mass-renormalization'' factor. Previous applications of density functional theory (DFT), based on a symmetry-restricted structure with the smallest number of possible magnetic, orbital, and structural degrees of freedom, missed such mass enhancement. This fact has been taken as evidence of strong electronic correlation, often described via the symmetry-restricted dynamic mean-field approach of the many-body theory, being the exclusive enabling physics. This paper uses instead a static density functional approach that does not restrict positional or spin degrees of freedom (symmetry-broken structures). This approach analyzes the contributions of different symmetry-broken modalities to mass enhancement for a few nominally highly correlated $d$-electron perovskites as well as the nominally uncorrelated, closed-shell $s\text{\ensuremath{-}}p$ bonding perovskites. It shows that the energy-lowering symmetry-broken spin effects (e.g., nonzero local moment in the paramagnetic phase) and structural effects (e.g., atomic displacement) as described in mean-field DFT already manifest mass enhancement for both electrons and holes in a range of $d$-electron perovskites $\mathrm{SrV}{\mathrm{O}}_{3}, \mathrm{SrTi}{\mathrm{O}}_{3}, \mathrm{BaTi}{\mathrm{O}}_{3}$, and $\mathrm{LaMn}{\mathrm{O}}_{3}$, as well as $p$-electron perovskites $\mathrm{CsPb}{\mathrm{I}}_{3}$ and $\mathrm{SrBi}{\mathrm{O}}_{3}$, including both metals ($\mathrm{SrV}{\mathrm{O}}_{3}$) and insulators (the rest). This is revealed only when enlarged unit cells of the same parent global symmetry, which are large enough to allow for symmetry-breaking distortions and concomitant variations in spin order, are explored for their ability to lower the total energy. Positional symmetry breaking that leads to mass enhancement includes octahedral rotation in halide perovskites such as $\mathrm{CsPb}{\mathrm{I}}_{3}$, Jahn-Teller-like ${Q}_{2}^{+}$ distortion in $\mathrm{LaMn}{\mathrm{O}}_{3}$, and bond disproportionation in $\mathrm{SrBi}{\mathrm{O}}_{3}$, while magnetic symmetry breaking resulting in mass enhancement includes the formation of a distribution of local moments in $\mathrm{SrV}{\mathrm{O}}_{3}$ that averages to zero in the paramagnetic phase. Not all symmetry breaking leads to significant mass enhancement, e.g., the rather small octahedral rotations in the nearly perfectly cubic $\mathrm{SrTi}{\mathrm{O}}_{3}$ cause negligible mass enhancement, as do the paraelectric displacements in $\mathrm{BaTi}{\mathrm{O}}_{3}$. In principle, by ergodicity, the two descriptions, i.e., the symmetry-restricted dynamic approach with a single time-fluctuating magnetic moment and the symmetry-broken mean-field approach with a static distribution of spatially fluctuated local moments, are not mutually exclusive but are a choice of representation and consequently, a choice of computational efficiency. In approximate implementations, the symmetry-broken mean-field approach appears to remove much of what was strong correlation in dynamically correlated symmetry-restricted solutions, leaving smaller (``weak'') residual correlation with respect to the exact solution.