Ab initio electronic conductivity of Fe-bearing post-perovskite

Abstract

The electrical conductivity of high-pressure silicates profoundly influences the interior dynamics of rocky planets. Employing the Kubo-Greenwood formalism, we perform ab initio calculations of electronic conductivity in Fe-bearing post-perovskite under super-Earth mantle conditions, up to 4000 K and 500 GPa. Electronic structures are obtained via many-body perturbation theory, incorporating dynamical screening and correlations among localized Fe-3d orbitals. In contrast to (Fe,Mg)O, for which metallization has been reported at comparable conditions, our results indicate that post-perovskite with Earth-like Fe contents is unlikely to metallize in super-Earth mantles via band-gap closure, yielding negligible low-frequency conductivity. Any substantial conductivity would require non-electronic mechanisms, such as thermally activated small-polaron hopping, which fall beyond the scope of band conduction.

Figures (11)

• Figure 1: Total electronic density of states of a molecular dynamics snapshot of (Mg$_{28}$Fe$_{4}$)Si$_{32}$O$_{96}$ pPv in high-spin state at 200 GPa and 4000 K obtained from different methods. The vertical black line represents the Fermi level ($E_F$). The upper and lower halves of the DOS plot correspond to the majority and minority spin states, respectively.
• Figure 2: Projected density of states (PDOS) for Fe-$3d$ states (a) and O-$2p$ states (b) in the same system as Fig. \ref{['fig:DOS']} obtained from different methods. Only the minority spin channel is shown. The vertical black lines represent the Fermi level ($E_F$).
• Figure 3: (a) Decomposition of the Kubo-Greenwood DC conductivity of the same system as Fig. \ref{['fig:DOS']} obtained from different methods. Each transition of electron is shown by a data point (at the average energy of the initial and final bands) that gives the contribution of that transition to the DC conductivity. The density of states in Fig. \ref{['fig:DOS']} is also shown for comparison. The upward and downward directions of the plot represent the majority and minority spin states, respectively. (b) Total Kubo-Greenwood DC conductivity obtained from different methods, calculated as the summation of data points in (a).
• Figure 4: Kubo-Greenwood DC conductivity of (Mg$_{28}$Fe$_{4}$)Si$_{32}$O$_{96}$ pPv (blue and orange) and (Mg$_{28}$Fe$_{4}$)(Si$_{31}$Al)O$_{96}$ pPv (green) in high-spin state under different pressure and temperature conditions. The experimental results of the bulk conductivity of (Mg$_{0.89}$Fe$_{0.11}$)SiO$_{3}$ pPv with Fe$^{3+}/\Sigma$Fe = 0.13 are shown for comparison ohta_electrical_2008.
• Figure S1: Self-consistent Hubbard $U$ value (a), enthalpy (b), and Gibbs energy (c) of (Mg$_{7}$Fe)Si$_{8}$O$_{24}$ pPv in high-spin (HS), intermediate-spin (IS), and low-spin (LS) states. Previous DFT+$U_{\rm sc}$ results yu_spin_2012 are shown for comparison. Both enthalpy and Gibbs energy values are normalized to those of HS states.