Absence of superconductivity in iron polyhydrides at high pressures

Recently, C. M. Pépin et al. [Science 357, 382 (2017)] reported the formation of several new iron polyhydrides ${\mathrm{FeH}}_x$ at pressures in the megabar range and spotted ${\mathrm{FeH}}_5$, which forms above 130 GPa, as a potential high-$T_{\text{c}}$ superconductor because of an alleged layer of dense metallic hydrogen. Shortly after, two studies by A. Majumdar et al. [Phys. Rev. B 96, 201107 (2017)] and A. G. Kvashnin et al. [J. Phys. Chem. C 122, 4731 (2018)] based on ab initio Migdal-Eliashberg theory seemed to independently confirm such a conjecture. We conversely find, on the same theoretical-numerical basis, that neither ${\mathrm{FeH}}_5$ nor its precursor, ${\mathrm{FeH}}_3$, shows any conventional superconductivity and explain why this is the case. We also show that superconductivity may be attained by transition-metal polyhydrides in the ${\mathrm{FeH}}_3$ structure type by adding more electrons to partially fill one of the Fe-H hybrid bands (as, e.g., in ${\mathrm{NiH}}_3$). Critical temperatures, however, will remain low because the $d$-metal bonding, and not the metallic hydrogen, dominates the behavior of electrons and phonons involved in the superconducting pairing in these compounds.

Figure 1

${\mathrm{FeH}}_3$ (left) and ${\mathrm{FeH}}_5$ (right) from different perspectives. Fe atoms are shown in red, H atoms are in blue and cyan, and nearest-neighbor bonds are shown as bicolor sticks. The ${\mathrm{FeH}}_3$ cubic cell is chosen (a) with H in the middle and only its nearest-neighbor bonds shown, (b) with an fcc-like arrangement (Fe in the corners, H in the face centers) and all the nearest-neighbor bonds shown (Fe-Fe, H-H, and Fe-H), and (c) with Fe in the middle and the H-H nearest-neighbor bonds hidden, highlighting 12 H nearest neighbors within the cell and six Fe nearest neighbors in the six neighboring cells. For ${\mathrm{FeH}}_5$, we adopt a tetragonal unit cell, twice as large as the primitive cell, to help visual comparison to the “parent” structure ${\mathrm{FeH}}_3$: In cubic ${\mathrm{FeH}}_3$, the Fe cages are stacked along each of the three $xyz$ directions; in ${\mathrm{FeH}}_5$, instead of lining up along $z$, they are staggered to make room for the 13th (cyan) H atom, which saturates the vertical broken Fe-Fe bond of ${\mathrm{FeH}}_3$. The two visualizations of ${\mathrm{FeH}}_5$ correspond to (d) hiding the H-H bonds or (e) hiding the Fe-Fe bonds and horizontally shifting the origin along $x$ by half the horizontal lattice constant.

Figure 2

Electronic band structure and DOS of ${\mathrm{FeH}}_3$ (top) and ${\mathrm{FeH}}_5$ (bottom). The energy bands (black thin lines), decorated with dots whose size is proportional to their wave-function character, are shown for (a) and (d) Fe $e_g$, (b) and (e) Fe $t_{2g}$, and (c) and (f) H $1s$ states, along with the corresponding partial DOS. Total densities of states are shown in black, red indicates Fe atoms, blue shows the 12 nearest-neighbor H of Fe which are present in both ${\mathrm{FeH}}_3$ and ${\mathrm{FeH}}_5$, and cyan indicates the 13th nearest neighbor of Fe which exists only in ${\mathrm{FeH}}_5$ (see Fig. 1). The dashed green line indicates the energy needed to dope into bands with mixed $\mathrm{Fe}{e}_g\text{−}\mathrm{H}1s$ character. We use the notation for the special points of a simple tetragonal lattice for both ${\mathrm{FeH}}_3$ and ${\mathrm{FeH}}_5$ to facilitate comparison.

Figure 3

Phonon dispersion (left), phonon DOS (middle), and Eliashberg function ${\alpha }^{2}F\left(\omega \right)$ [right, Eq. (2)]. The top panels refer to ${\mathrm{FeH}}_3$ (blue curves), where Eq. (2) was also evaluated for two-electron-doped ${\mathrm{FeH}}_3$ (green) and for ${\mathrm{NiH}}_3$ (red). The dashed curves indicate the frequency-dependent coupling constant $\lambda \left(\omega \right)$. The bottom panels refer to ${\mathrm{FeH}}_5$ (blue curves), where Eq. (2) was also evaluated for one-electron-doped ${\mathrm{FeH}}_5$ (green) and unstable ${\mathrm{CoH}}_5$ (red; see text).

Figure 4

Low-energy band structure and LDOS [Eq. (3)] for (a) and (b) ${\mathrm{FeH}}_3$ and (c) and (d) ${\mathrm{FeH}}_5$ along a (100) plane, which cuts through Fe and H atoms in both compounds (see Fig. 1). In (a) and (d) the LDOS is displayed at the Fermi level of the corresponding compounds (red arrows); in (b) and (c) the LDOS is displayed at the energy of an empty Fe-H hybrid band above the respective Fermi levels (green arrows; see text), corresponding to an electron count of ${\mathrm{FeH}}_3+2e^{-}$ and ${\mathrm{FeH}}_5+0.5e^{-}$ in Fig. 5. The color scale used corresponds to $ln[\text{LDOS}/\text{max}(\text{LDOS}\left)\right]$ to improve visibility.

Figure 5

Critical temperature $T_{\text{c}}$ (top panel) and $e\text{−}\text{ph}$ coupling constant $\lambda$ (bottom panel) for a number of transition-metal polyhydrides. Blue dots indicate first-principles results for stable ${\mathrm{FeH}}_3$, ${\mathrm{CoH}}_3$, ${\mathrm{NiH}}_3$, and ${\mathrm{FeH}}_5$ and for unstable ${\mathrm{CoH}}_5^{*}$; red squares refer to rigid-band doping (see text).

Figure 6

$N\left(E_F\right)$ (first panel), $\lambda$ (second panel), ${\omega }_{\text{log}}$ (third panel), and $T_{\text{c}}$ (fourth panel) of ${\mathrm{FeH}}_5$ as a function of electronic smearing $\sigma$ and the pseudopotential [31, 36, 37].

Figure 7

Phonon dispersion, phonon DOS, ${\alpha }^{2}F$, and integrated $\lambda$ for ${\mathrm{NiH}}_3$.

Figure 8

Phonon dispersion, phonon DOS, ${\alpha }^{2}F$, and integrated $\lambda$ for ${\mathrm{CoH}}_5$.