Abstract
The electronic state and transport properties of hot dense iron are of the utmost importance for the understanding of Earth’s interior. Combining state-of-the-art density functional and dynamical mean field theories we study the impact of electron correlations on the electrical and thermal resistivity of hexagonal close-packed ϵ-Fe at Earth’s core conditions and show that the electron–electron scattering in ϵ-Fe exhibit a nearly perfect Fermi-liquid (FL) behavior. Accordingly, the quadratic dependence of the scattering rate, typical of FLs, leads to a modification of the Wiedemann–Franz law and suppresses the thermal conductivity with respect to the electrical one. The consequence is a significant increase of the electron–electron thermal resistivity, which is found to be of comparable magnitude to the electron–phonon one.
Highlights
Earth’s magnetic field plays a crucial role in the survival of the human race
It is well known that the analytical continuation methods needed to obtain the real-frequency data from imaginary-frequency self-energy are quite sensitive to the details of the procedure
Our DFT+DMFT calculations predict that electron scattering (EES) in ò- iron is FL-like at Earth’s core conditions
Summary
Earth’s magnetic field plays a crucial role in the survival of the human race. It keeps the ozone layer intact despite the solar wind and protects the Earth from destructive ultraviolet radiation [1]. The magnetic field is generated by self-sustained dynamo action in its iron-rich core [2] This geodynamo runs on heat from the growing solid inner core and on chemical convection provided by light elements issued from the liquid outer core on solidification [3]. The power supplied to drive the geodynamo is proportional to the rate of inner core growth, which in turn is controlled by heat flow at the core-mantle boundary [4]. This heat flow critically depends on the thermal conductivity of liquid iron under the extreme pressure and temperature conditions in the Earth’s core. For a long time there has been agreement that convection in the liquid outer core provides most of the energy for the geodynamo and has been doing so for at least 3.4 billion years [2, 5]
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