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Magnetic fluctuations and superconducting pairing in $\varepsilon$-iron

A. S. Belozerov, A. A. Katanin, V. Yu. Irkhin, V. I. Anisimov

Abstract

We study Coulomb correlation effects and their role in superconductivity of $\varepsilon$-iron under pressure from 12 to 33 GPa by using a combination of density functional and dynamical mean-field theory. Our results indicate a persistence of the Fermi-liquid behavior below the temperature $\sim$1000 K. The Coulomb correlations are found to substantially renormalize the density of states, reducing the distance from the peak to the Fermi level to 0.4 eV compared to 0.75 eV obtained in DFT calculations. We find significant antiferromagnetic correlations, which are accompanied by the formation of short-lived local magnetic moments. We use the obtained results as a starting point for construction of the multi-band Bethe-Salpeter equation, which eigenvalues indicate that antiferromagnetic spin fluctuations may result in the superconducting pairing in $\varepsilon$-Fe. Moreover, the tendency to superconducting instability becomes weaker with the increase of pressure, which may explain the disappearance of superconductivity at $\sim$30 GPa.

Magnetic fluctuations and superconducting pairing in $\varepsilon$-iron

Abstract

We study Coulomb correlation effects and their role in superconductivity of -iron under pressure from 12 to 33 GPa by using a combination of density functional and dynamical mean-field theory. Our results indicate a persistence of the Fermi-liquid behavior below the temperature 1000 K. The Coulomb correlations are found to substantially renormalize the density of states, reducing the distance from the peak to the Fermi level to 0.4 eV compared to 0.75 eV obtained in DFT calculations. We find significant antiferromagnetic correlations, which are accompanied by the formation of short-lived local magnetic moments. We use the obtained results as a starting point for construction of the multi-band Bethe-Salpeter equation, which eigenvalues indicate that antiferromagnetic spin fluctuations may result in the superconducting pairing in -Fe. Moreover, the tendency to superconducting instability becomes weaker with the increase of pressure, which may explain the disappearance of superconductivity at 30 GPa.

Paper Structure

This paper contains 10 sections, 18 equations, 8 figures.

Table of Contents

  1. Introduction
  2. Computational details
  3. Results and discussion
  4. Electronic properties
  5. Magnetic properties
  6. Superconducting pairing
  7. Conclusions
  8. Superconducting pairing
  9. General formalism and the gap equation
  10. Bare and second-order vertex

Figures (8)

  • Figure 1: (a) Imaginary part of self-energy for degenerate $xy$ and ${x^2{-}y^2}$ states as a function of imaginary frequency $i\nu$ obtained by DFT+DMFT method at ${\beta=100}$ eV$^{-1}$. Inset: temperature dependence of the ratio of quasiparticle damping $\Gamma$ to temperature $T$. (b) Imaginary part of the above mentioned self-energy at the first Matsubara frequency as a function of temperature. Inset: the same for ${U=6}$ eV. The straight lines depict the fit to linear dependence.
  • Figure 2: Density of states of $\varepsilon$-Fe obtained within DFT and DFT+DMFT at ${T=290}$ K for different pressures. The Fermi level is at zero energy.
  • Figure 3: Local spin-spin correlation functions in the imaginary-time (a) and real energy (b) domains calculated by DFT+DMFT method at ${\beta=40}$ eV$^{-1}$. In the bottom panel, the obtained correlation functions are compared with that for $\alpha$-Fe footnote1. Inset: instantaneous average $\langle S_z^2 \rangle$ for $\varepsilon$-Fe as a function of pressure.
  • Figure 4: Temperature dependence of uniform magnetic susceptibility (a) and inverse local susceptibility (b) for $\varepsilon$-Fe obtained within DFT+DMFT method.
  • Figure 5: Momentum-dependence of the particle-hole bubble obtained within DFT and DFT+DMFT at ${\beta=100}$ eV$^{-1}$.
  • ...and 3 more figures