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The electronic thermal conductivity of iron at Earth's core conditions is anextremely important physical property in geophysics field. However, the exactvalue of electronic thermal conductivity of iron under extreme pressure andtemperature still remains poorly known both experimentally and theoretically. Afew recent experimental studies measured the value of the electronic thermalconductivity directly and some theoretical works have predicted the electronicthermal conductivity of iron at Earth's core conditions based on theKubo-Greenwood method. However, these results differ largely from each other. Avery recent research has confirmed that for iron at Earth's core conditions thestrength of electron-electron scattering could be comparable to that forelectron-phonon scattering, meaning that the electron-electron scatteringshould also be considered when evaluating the electronic thermal conductivityin the Earth's core situations. Here, by utilizing a newly developedmethodology based on direct non-equilibrium $ab~initio$ molecular dynamicssimulation coupled with the concept of electrostatic potential oscillation, wepredict the electronic thermal conductivity of iron in h.c.p phase. Ourmethodology inherently includes the electron-phonon and electron-electroninteractions under extreme conditions. Our results are comparable to theprevious theoretical and experimental studies. More importantly, ourmethodology provides a new physical picture to describe the heat transferprocess in $\epsilon-$iron at Earth's core conditions from the electrostaticpotential oscillation point of view and offers a new approach to study thermaltransport property of pure metals in planet's cores with different temperatureand pressures.

Insight of the thermal conductivity of $\epsilon-$iron at Earth's core conditions from the newly developed direct $ab~initio$ methodology