Underlying mechanism of charge transfer in Li-doped MgH₁₆ at high pressure

The realization of room-temperature superconductivity (SC) is one of the most challenging and very long standing issues in condensed matter physics Hydride-Rev2020-Eremets . For this issue, metallic hydrogen has been proposed Ashcroft as an ideal system exhibiting the conventional Bardeen-Cooper-Schrieffer (BCS) type SC BCS . The lightest atomic mass in metallic hydrogen gives rise to high vibrational frequencies, which lead to achieving high $T_{\rm c}$ with strong electron-phonon coupling. However, it is very challenging to synthesize metallic hydrogen under extremely high pressures over ${\sim}$400 GPa MetalicH-Rev.Mod.Phys2012 ; MetalicH-PRL2015 ; MetalicH-Science2017 ; hydrogen2020 using diamondanvil cells diamondanvil-Rev2009-Bassett ; diamondanvil-Rev2018-K.K.Mao . In order to accomplish the metallization of hydrogen at relatively lower pressures, metal hydrides have been employed to utilize the so-called chemical precompression of hydrogen through metal elements Ashcroft-MetalHydride . Motivated by the theoretical predictions of high-$T_{\rm c}$ SC in a number of hydrides LiHx-PANS2009 ; LiHx-acta cryst.2014 ; KHx-JPCC2012 ; CaH6-PANS2012 ; H3S-Sci.Rep2014 ; MgH6-RSC-Adv.2015 ; rare-earth-hydride-PRL2017 ; rare-earth-hydride-PANS2017 , experiments have been conducted to confirm that sulfur hydride H₃S exhibits a $T_{\rm c}$ of 203 K at pressures around 150 GPa ExpH3S-Nature2015 and more recently, lanthanum hydride LaH₁₀ exhibits higher $T_{\rm c}$ around 250$-$260 K at ${\sim}$170 GPa ExpLaH10-PRL2019 ; ExpLaH10-Nature2019 . Therefore, the combined theoretical and experimental breakthroughs in high-pressure compressed hydrides have triggered a new era of high-$T_{\rm c}$ superconductors Hydride-Rev2020-Eremets ; FeH5-Science2017 ; CeH9-Nat.Commun2019-T. Cui ; CeH-Nat.Commun2019-J.F. Lin ; Hydride-Rev2019-JCP .

To search for metal hydrides with higher $T_{\rm c}$, there have been many theoretical studies of binary compounds including alkali metals LiHx-PANS2009 ; LiHx-acta cryst.2014 ; KHx-JPCC2012 , alkaline earth metals CaH6-PANS2012 ; MgH6-RSC-Adv.2015 , and rare earth metals rare-earth-hydride-PRL2017 ; rare-earth-hydride-PANS2017 ; CeH9-Nat.Commun2019-T. Cui ; CeH-Nat.Commun2019-J.F. Lin . Recently, the realm of research has been extended to ternary compounds which may be more effective for achieving high-$T_{\rm c}$ SC because of an increase in the number of combinations of metal elements Li2MgH16-PRL2019 ; CaYH12-PRL2019 ; LiPH6-Npj2019 . Based on first-principles density-functional theory (DFT) calculations and the Migdal-Eliashberg formalism, Yanming Ma and his colleagues predicted that a ternary hydride Li₂MgH₁₆ exhibits a $T_{\rm c}$ of ${\sim}$473 K at 250 GPa Li2MgH16-PRL2019 . Such highest ever predicted $T_{\rm c}$ was enabled by Li doping in a binary hydride MgH₁₆ containing a large amount of H₂ molecules. Here, the supply of extra electrons via Li doping breaks the strong covalent bond of H₂ molecules to stabilize the clathrate H cages with weakly covalent H$-$H bonds. The resulting H network enhances the H-derived electronic density of states (DOS) at the Fermi level $E_{\rm F}$, giving rise to a high-$T_{\rm c}$ SC. It is natural that the charge transfer from Li dopants to H atoms in Li₂MgH₁₆ would be induced by a much lower electronegativity of Li atom compared to H atom Li2MgH16-PRL2019 .

The concept of electronegativity describes the tendency of an atom to attract electron density towards itself. The electronegativity ${\chi}$ is usually assumed to be similar values in a variety of chemical environments. It is, however, noted that a recent quantum-mechanical model study electronegativity-under-pressure reported a significant variation of ${\chi}$ under pressure. Meanwhile, at high pressure, some materials behave as electrides, where some excess electrons are transferred from positively charged ions to interstitial regions hoffman ; hosono ; Li6P . Such loosely bound anionic electrons are here demonstrated to play an important role in the charge transfer process between Li dopants and H atoms in Li₂MgH₁₆.

In the present study, we propose the underlying mechanism behind the charge transfer from Li dopants to H atoms in Li₂MgH₁₆. Using first-principles DFT calculations, we reveal that the Li dopants locating in the pyroclore lattice sites exhibit an electride feature with the anionic electrons residing in interstitial regions. Such loosely bound anionic electrons are easily captured to stabilize the clathrate H cages composed of two H species, H₁ and H₂ [see Fig. 1(a)]. It is thus likely that anionic electrons play an essential role in the charge transfer from Li dopants to H atoms. Our findings demonstrate that the anionic electrons created by the pyroclore-structured Li dopants are of vital importance not only for stabilizing the clathrate H cages, but also for enhancing the H-derived DOS at $E_{\rm F}$. The presently proposed charge transfer mechanism via anionic electrons can be also applied for compressed LaH₁₀ ExpLaH10-PRL2019 ; ExpLaH10-Nature2019 , and hence, it is anticipated to be more generic to other compressed high-$T_{\rm c}$ superconducting hydrides with clathrate structures.

Our DFT calculations were performed using the Vienna ab initio simulation package with the projector-augmented wave method vasp1 ; vasp2 ; paw . Here, we included Li-1$s^{2}$2$s^{1}$, Mg-2$s^{2}$2$p^{6}$3$s^{2}$, and H-1$s^{1}$ electrons in the electronic-structure calculations. For the exchange-correlation energy, we employed the generalized-gradient approximation functional of Perdew-Burke-Ernzerhof (PBE) pbe . A plane-wave basis was taken with a kinetic energy cutoff of 850 eV. The ${\bf k}$-space integration was done with 16${\times}$16${\times}$16 $k$ points (in the Brillouin zone) for the structure optimization and 32${\times}$32${\times}$32 $k$ points for the DOS calculation. All atoms were allowed to relax along the calculated forces until all the residual force components were less than 0.001 eV/Å. Using the QUANTUM ESPRESSO package QE ; oncv , we calculated phonon frequencies with 4${\times}$4${\times}$4 $q$ points.

We first optimize the geometry of Li₂MgH₁₆ at a pressure of 300 GPa Li2MgH16-PRL2019 , which has a clathrate structure with the high crystalline symmetry of space group $Fd$$\overline{3}m$ [see Fig. 1(a)]. The optimized lattice parameters of the primitive unit cell are $a$ = $b$ = $c$ = 6.572 Å. It is noted that Mg atoms form a diamond lattice [see Fig. 1(b)], while Li dopants form a pyroclore or three-dimensional (3D) kagome lattice [see Fig. 1(c)]. As shown in Fig. 1(a), there are two kinds of H cages: i.e., one is the H₁₈ cage surrounding a Li atom and the other is the H₂₈ cage surrounding a Mg atom. The H₁₈ cage consisting of six pentagon rings is opened to connect to neighboring H₁₈ cages, but the H₂₈ cage consisting of twelve pentagon and four hexagon rings has a closed shape [see Fig. 1(a) and Fig. S1 in the Supplemental Information supple ]. The two cages are formed by two species of H atoms, H₁ (equivalent to H_96g in Ref. Li2MgH16-PRL2019 ) and H₂ (equivalent to H_32e). We find that the H${}_{1}-$H₁ bond length $d_{1}$ ($d_{1^{\prime}}$) is 1.195 (1.023) Å, while the H${}_{1}-$H₂ bond length $d_{2}$ is 1.084 Å. Note that the longer H${}_{1}-$H₁ bond arises from the pentagon ring, while the shorter one is shared by the pentagon and hexagon rings (see Fig. S1 in the Supplemental Information supple ). These values of $d_{1}$, $d_{1^{\prime}}$, and $d_{2}$ are in good agreement with those ($d_{1}$ = 1.20, $d_{1^{\prime}}$ = 1.02 Å, and $d_{2}$ = 1.08 Å) of a previous DFT calculation Li2MgH16-PRL2019 .

Figure 2(a) shows the valence charge-density isosurface of the isolated Li dopants [see Fig. 1(c)] whose structure is taken from the optimized structure of Li₂MgH₁₆. Since the Li-1$s$ core state is located at around $-$46.6 eV below $E_{\rm F}$ [see Fig. S2(a) in the Supplemental Information supple ], we exclude the 1$s^{2}$ core electrons to plot the valence charge density. It is noted that each Li atom in Fig. 2(b) has $\sim$0.08 electrons within the muffin-tin (MT) sphere having a radius of 0.713 Å [close to the size of the corresponding Bader basin in Li₂MgH₁₆: see Fig. 3(d)], indicating that Li loses about 0.92 electrons. Interestingly, we find that some electrons detached from Li atoms are well distributed in the interstitial regions surrounded by four adjacent Li atoms [see Fig. 2(a)]. The confinement of such anionic electrons around the A₁ and A₂ sites is confirmed by the electron localization function ELF (see Fig. S3 in the Supplemental Material supple ), which is effective for the characterization of interstitial electrons in electride materials ELF-elect1 ; ELF-elect2 ; ELF-elect3 . It is, however, noticeable that anionic electrons arising from Li dopants are extensively distributed over the regions within and outside the MT spheres around the A₁ and A₂ sites [see Fig. 2(b)]. Figure 2(c) shows the histogram of volume distribution for every charge density range of 0.01$e$/ų. This histogram reveals that, although anionic electrons have the highest densities at the A₁ and A₂ sites, they occupy more volume outside the MT spheres around the A1 and A2 sites compared to within the MT spheres. In order to examine how anionic electrons arising from Li dopants change as a function of pressure, we compare the valence charge densities of the isolated Li dopants at 250, 300, and 350 GPa, respectively (see Fig. S4 in the Supplemental Information supple ). We find that the charge density at the A₁ or A₂ site increases as 0.158, 0.164, and 0.170 $e$/ų at 250, 300, and 350 GPa, respectively, reflecting that anionic electrons around the A₁ and A₂ sites increase more dominantly with increasing pressure. It is thus likely that more anionic electrons can be captured to H cages with increasing pressure. Consequently, the H${}_{1}-$H₁ and H${}_{1}-$H₂ bond lengths are calculated to be shortened as ($d_{1}$, $d_{1^{\prime}}$, $d_{2}$) = (1.229, 1.043, 1.106), (1.195, 1.023, 1.084), and (1.168, 1.006, 1.065) Å at 250, 300, and 350 GPa, respectively. Based on these results, we can say that the Li dopants locating in the pyroclore lattice sites possess the electride characteristics with the A₁ and A₂ anions.

In Fig. 2(d), we present the band structure of the pyroclore-structured Li dopants. It is seen that one band is fully filled but three bands are partially filled, with four valence electrons coming from four Li atoms in the primitive unit cell. Specifically, one band exhibits a partially flat dispersion at ${\sim}$0.1 eV above $E_{\rm F}$. The charge character of this flat band at the ${\Gamma}$ point represents strongly localized electrons at the interstitial regions surrounded by adjacent four Li atoms [see Fig. 2(e)], much larger than the total valence charge density shown in Fig. 2(b). Such a flatband nature of localized electrons is likely attributed to the geometric character of 3D kagome lattice, which hosts the destructive interferences of Bloch wave functions Fe3Sn2-PRL . The destructive interfered electrons producing dispersionless flatbands have been theoretically proposed in 2D kagome lattices Kagome-JPA1992 , and their existence has been experimentally observed in real materials Fe3Sn2-PRL . We note that, despite the localized character of such interstitial electrons, the pyroclore-structured Li dopants show metallic behavior with multiple dispersive bands crossing $E_{\rm F}$ [see Fig. 2(c)].

Next, we explore the charge density of the parent MgH₁₆ system whose structure is taken from the optimized structure of Li₂MgH₁₆. Since the Mg-2$s$(2$p$) semicore states located at $-$77.8($-$44.6) eV below $E_{\rm F}$ are well separated from the valence states [see Fig. S2(b) in the Supplemental Information supple ], we exclude such semicore electrons to plot the valence charge density of MgH₁₆ in Fig. 3(a). It is seen that H atoms in the H₁₈ and H₂₈ cages are bonded to each other with covalent bonds. We note that each H$-$H bond has a saddle point of charge density at its midpoint, similar to the C$-$C covalent bond in diamond diamond . The charge densities at the midpoints of the H${}_{1}-$H₁ and H${}_{1}-$H₂ bonds are 0.60 and 0.80 $e$/ų, respectively [see the arrows in Fig. 3(a)]. It is, however, noticeable that the calculated phonon spectrum of MgH₁₆ exhibits imaginary frequencies in the whole Brillouin zone [see Fig. S5(a) in the Supplemental Material supple ], indicating that the MgH₁₆ structure without Li atoms is dynamically unstable. We further relax the structure of MgH₁₆ to find a saddle point. The calculated phonon spectrum of such a saddle point structre also shows imaginary-frequency phonon modes [see Fig. S5(b)], indicating that it is still dynamically unstable. Meanwhile, the Li₂MgH₁₆ structure is dynamically stable without any imaginary-frequency mode [see Fig. S5(c) in the Supplemental Information supple ]. It is thus likely that the stability of H cages in Li₂MgH₁₆ is enabled by capturing the anionic electrons in the pyroclore-structured Li dopants, as discussed below.

Figure 3(b) shows the calculated valence charge density ${\rho}_{\rm Li/MgH}$ of Li₂MgH₁₆, where the charge densities at the midpoints of the H${}_{1}-$H₁ and H${}_{1}-$H₂ bonds are 0.69 and 0.90 $e$/ų, respectively [see the arrows in Fig. 3(b)]. These values are larger than the corresponding ones (0.60 and 0.80 $e$/ų) in MgH₁₆, because the anionic electrons of the pyroclore-structured Li dopants are captured to the H₁₈ and H₂₈ cages. It is interestingly noticeable that the charge transfer from Li dopants to H atoms was interpreted in terms of a lower electronegativity of Li atom compared to H atom Li2MgH16-PRL2019 . By contrast, we here propose that the electride nature of Li dopants is an essential ingredient in the charge transfer between Li dopants and H atoms, thereby providing new insight into understanding the charge transfer mechanism in Li₂MgH₁₆. In order to examine the charge transfer from the Li dopants to H cages, we calculate the charge density difference, defined as ${\Delta}{\rho}$ = ${\rho}_{\rm Li/MgH}$ $-$ ${\rho}_{\rm Li}$ $-$ ${\rho}_{\rm MgH}$, where ${\rho}_{\rm Li}$ and ${\rho}_{\rm MgH}$ represent the separated charge densities of Li dopants [see Fig. 2(b)] and parent MgH₁₆ [see Fig. 3(a)], respectively. As shown in Fig. 3(c), ${\Delta}{\rho}$ illustrates that electronic charge is transferred from Li [including the anion sites A₁ and A₂ in Fig. 2(b)] and Mg to H atoms. We further estimate the number of transferred electrons between the Li/Mg and H atoms by calculating the Bader charges Bader of Li₂MgH₁₆. Figure 3(d) shows the Bader basins of the constituent atoms, obtained from the gradient of the total charge density of Li₂MgH₁₆ Bader . We find that the Bader charges inside Li, Mg, H₁, and H₂ basins are $-$2.22$e$, $-$8.34$e$, $-$1.18$e$, and $-$1.28$e$, respectively. Since this Bader charge of Li (Mg) includes 1$s^{2}$ (2$s^{2}$2$p^{6}$) core electrons, Li (Mg) atoms lose electrons of 0.78(1.66)$e$ per atom, while H₁ (H₂) atoms gain electrons of 0.18(0.28)$e$ per atom.

The charge transfer from Li dopants to H cages is expected to shift the Fermi level upward into the conduction band of the parent MgH₁₆ system. To explore the rigid band shift due to such an electron doping, we compare the band structures of MgH₁₆ and Li₂MgH₁₆, which are displayed in Figs. 4(a) and 4(b), respectively. The band dispersions of the two systems are generally similar to each other. As expected, we find that the empty conduction-band states of the MgH₁₆ system are occupied by Li doping, thereby leading to a shift of $E_{\rm F}$ by ${\sim}$2.49 eV [see the arrow in Fig. 4(b)]. It is noteworthy that the Li-derived states show their highest local DOS (LDOS) peak at around 3.9 eV above $E_{\rm F}$ [see Fig. 4(b)], indicating that Li₂MgH₁₆ is an electron-doped magnesium hydride via Li doping. Especially, the LDOS values of Li, Mg, H₁, and H₂ atoms at $E_{\rm F}$ are 0.8${\times}$10^-3, 1.2${\times}$10^-3, 2.5${\times}$10^-3, and 6.6${\times}$10^-3 states/eV/ų, respectively [see Fig. 4(b)], indicating that the H-derived states are about 3$-$8 (2$-$5) times larger than Li (Mg)-derived states. Such large ratios of H-derived states in Li₂MgH₁₆ are different from the cases of other high-$T_{\rm c}$ hydrides such as H₃S H3S-Sci.Rep2014 and LaH₁₀ LaH10-liangliang where the LDOS of H-derived states at $E_{\rm F}$ is nearly the same as those of S- and La-derived states, respectively. Such large H-derived electronic states near $E_{\rm F}$ should increase electron-phonon coupling Li2MgH16-PRL2019 , which leads to the highest $T_{\rm c}$ ever reported.

Our first-principles DFT calculations have shown that the pyroclore-structured Li dopants exhibit an electride nature with anionic electrons ditributed in interstitial regions. Such loosely bound anionic electrons are easily captured to the H₁₈ and H₂₈ cages. We thus proposed that the electride nature of Li dopants importantly determines the charge transfer between Li dopants and H atoms. The present findings demonstrated that the anionic electrons created by Li dopants play important roles not only in stabilizing the clathrate H cages, but also in enhancing the H-derived DOS at $E_{\rm F}$. It is noted that the presently proposed charge transfer mechanism can be applicable to compressed LaH₁₀ LaH10-Seho which was recently synthesized ExpLaH10-PRL2019 ; ExpLaH10-Nature2019 to exhibit the highest $T_{\rm c}$ so far among experimentally available superconducting materials. Here, the charge transfer from La to H atoms is driven by the electride property of the La framework at high pressure (see Fig. S6 in the Supplemental Material supple ). Therefore, the underlying mechanism of charge transfer in Li₂MgH₁₆ would be more generic, and it will be useful for the discovery and design of new high-$T_{\rm c}$ hydrides in the future.

ACKNOWLEDGEMENTS

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean Government (Grants No. 2019R1A2C1002975, No. 2016K1A4A3914691, and No. 2015M3D1A1070609). The calculations were performed by the KISTI Supercomputing Center through the Strategic Support Program (Program No. KSC-2019-CRE-0183) for the supercomputing application research.