Tunable localization in an s-electron Kondo system at room temperature

TL;DR

This paper demonstrates that metal hydrides exhibit strong electron correlations at room temperature, potentially enabling high-temperature superconductivity through tunable localization similar to Kondo systems.

Contribution

It reveals room-temperature electron localization and Kondo-like behavior in metal hydrides, suggesting a new pathway for high-temperature superconductivity in hydrogen-rich compounds.

Findings

Strong electron correlations observed at room temperature in metal hydrides.

Divergence of carrier mass indicates proximity to Mott transition.

Signatures of a correlated metallic Kondo lattice at ambient conditions.

Abstract

To achieve room-temperature superconductivity, a mechanism is needed that provides heavy quasiparticles at room temperature. In heavy fermion systems such localization is prototypically present only at liquid helium temperatures. In these $f$-electron Kondo systems, conduction electrons magnetically couple to localized moments, enhancing their mass and scatting time. These quasiparticles may form Cooper pairs and cause unconventional superconductivity with a critical temperature $T_c$ of the order of the Fermi energy $\varepsilon_F$. In relative terms, this $T_c$ is much larger than in cuprate or BCS superconductors for which $T_c\ll \varepsilon_F$. This suggests that Kondo systems in general have the potential to be high-temperature superconductors. For this to occur, strong correlations that cause electron localization need to take place at much larger temperatures. Here we show that metal hydrides manifest strong electron correlations in a single $3d_{x^2-y^2}$ band at the Fermi level, similar to the cuprates but at room temperature. Hole doping of this band, by varying the hydrogen content, causes divergence of the carrier mass and suggests the approach of an ordered Mott transition with signatures of a correlated metallic Kondo lattice. These room-temperature phenomena are expected to be widespread across hydrogen-rich compounds, and offer a promising novel ground to encounter unconventional superconductivity in the class of the metallic hydrides.

Full text

Tunable localization in an s-electron Kondo system at room temperature

J.L.M. van Mechelen

dook.vanmechelen@ch.abb.com

ABB Corporate Research, Segelhofstrasse 1K, 5405 Baden-Dättwil, Switzerland

Department of Physics and Astronomy, VU University, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands

  

M.J. van Setten

present affiliation: IMEC, Kapeldreef 75, 3001 Heverlee, Belgium

Nanoscopic Physics, Institute of Condensed Matter and Nanosciences, Université catholique de Louvain, 1348 Louvain-la-Neuve, Belgium

††preprint: APS/123-QED

To achieve room-temperature superconductivity, a mechanism is needed that provides heavy quasiparticles at room temperature.Qazilbash2009 ; Basov2011a In heavy fermion systems such localization is prototypically present only at liquid helium temperatures. In these $f$-electron Kondo systems, conduction electrons magnetically couple to localized moments, enhancing their mass and scatting time. These quasiparticles may form Cooper pairs and cause unconventional superconductivity with a critical temperature $T_{c}$ of the order of the Fermi energy $\varepsilon_{F}$.Khomskii2014 In relative terms, this $T_{c}$ is much larger than in cuprate or BCS superconductors for which $T_{c}\ll\varepsilon_{F}$.Khomskii2014 This suggests that Kondo systems in general have the potential to be high-temperature superconductors.Pines2013 For this to occur, strong correlations that cause electron localization need to take place at much larger temperatures. Here we show that metal hydrides manifest strong electron correlations in a single $3d_{x^{2}-y^{2}}$ band at the Fermi level, similar to the cuprates but at room temperature. Hole doping of this band, by varying the hydrogen content, causes divergence of the carrier mass and suggests the approach of an ordered Mott transition with signatures of a correlated metallic Kondo lattice. These room-temperature phenomena are expected to be widespread across hydrogen-rich compounds, and offer a promising novel ground to encounter unconventional superconductivity in the class of the metallic hydrides.

Dense metallic hydrides form a material class with a tremendous societal potential for high-temperature superconductivity and energy storage.Ashcroft2004 ; Mohtadi2016 Their physics, however, is far from understood. Adding hydrogen to a metallic host strongly influences the electronic and structural properties. It may bind to impurities, manifests itself as an inert lattice gas and, at larger concentrations, can induce a metal-to-insulator transition.Huiberts1996 Dense hydrides, moreover, manifest high energy lattice vibrations and strong electron-phonon coupling and are therefore seen as an ideal testbed for conventional, electron-phonon mediated, superconductivity at high temperatures.Ashcroft1968 ; Ashcroft2004 Experimental confirmation was indeed obtained, first in elemental hydrides such as PdHx with $T_{c}\sim 10$ K and more recently in SH3 at $T_{c}\sim 203$ K although under gigantic pressures.PdHsupercond ; Drozdov2015

The path to even larger $T_{c}$ in metallic hydrides, without hydrostatic pressure, may be offered in a slightly different direction. In most high-temperature superconductors Cooper pair formation is caused by strong electron-electron correlations close to a Mott insulating state, rather than the electron-phonon interaction. Close to the Mott metal-to-insulator (MI) transition Kondo physics plays an important role,Georges1996 and is expected to strongly enhance $T_{c}$.Capone2002 In rare earth hydrides, the puzzling MI transition, which occurs at room temperature at a non-stoichiometric hydrogen concentration, cannot be explained with simple band theory.Huiberts1996 ; Eder1997 It has been proposed that additional hydrogen atoms added to the metallic $d^{1}$ dihydrides LaH2 and YH2 can be seen as Kondo impurities that antiferromagnetically couple to charge carriers, eventually leading to a Mott insulating state.Eder1997 ; Ng1999 ; Ng1997 This strongly correlated state may involve $s$-$d$ hybridization, which is much larger than the $p$-$d$ hybridization in oxide and pnictide superconductors. If such a Kondo lattice of H impurities exists, it is therefore expected to have a Kondo temperature $T_{K}>10^{3}$ K.Takada2015 This is an order of magnitude larger than $T_{K}$ of the iron pnictides superconductors, which are $d$-electron Kondo systems.Wu2016 Given that for most systems $T_{K}\propto T_{c}$, this implies that hydrogen-based Kondo systems are a prosperous candidate for high-temperature superconductivity.

Transition metal hydrides also exhibit MI transitions around hydrogen concentrations unlikely to cause a simple metal to band-insulator transition. Here we study the MI transition in the complex metal hydride Mg2NiHx at 298 K. Removal of H from the band insulator Mg2NiH4 breaks H–Ni bonding states and effectively hole dopes this $d^{10}$ system in the top of the Ni $3d_{x^{2}-y^{2}}$ band. We use optical spectroscopy to determine the charge dynamics within this band of single phase MgyNiHx thin films. The charge carrier density $\delta=32-8x$ is accurately tuned in the range $1.0\leqslant\delta\leqslant 3.5$ by a slight variation of the Mg/Ni ratio, $1.45\leqslant y\leqslant 1.52$, which has a strong effect on the hydrogenation kinetics and thus on $\delta$ (see Supplementary Information). This range of $x$ is far beyond the structural phase transition from hexagonal ($P6_{2}22$) to monoclinic ($C2/c$) occurring for $1<x<3$,Zolliker1986 ; Lohstroh2004 and away from the band insulator phase at $x=4$. For such a system, itinerant electron behavior would cause a Drude peak in the optical conductivity $\sigma_{1}(\omega)$ centered at zero photon frequency $\omega$. Carrier localization, however, would split the Drude peak in a renormalized coherent part at $\omega=0$ and an incoherent part at infrared frequencies (Fig. 1a).VanMechelen2008

The key result of our optical study is that metallic MgyNiH4-δ/8 manifests a coherent Drude peak with weight $W_{\text{coh}}=\hbar^{2}\omega_{p}^{2}$ that is substantially less than expected for unrenormalized itinerant electron behavior, which directly points to localization at room temperature (Fig. 1b,c). The lacking weight is recovered in a broad infrared band, shown by $\sigma_{1}(\omega)$, which forms the incoherent part of the Drude weight $W_{\text{incoh}}$ (Fig. 1b). The degree of localization is expressed by the effective electron mass $m^{*}/m_{e}=W_{\text{tot}}/W_{\text{coh}}$, where $m_{e}$ is the free electron mass. We obtain the total charge carrier weight $W_{\text{tot}}$ in two ways: by taking the sum of the coherent and incoherent Drude weights, and from Hall data through $W_{\text{tot}}=\delta\hbar^{2}e^{2}/\epsilon_{0}m_{e}V$, with $V$ the volume of the unit cell.Enache2004 The two approaches both evince a lack of $W_{\text{coh}}$ and thus a significant mass enhancement, which increases towards the insulating phase (Fig. 1d).

In strongly correlated systems, localization enhances both the electron mass and, because of the decreased Fermi velocity, also the scattering time, as mentioned before. That is, quasiparticle renormalization affects both $m^{*}$ and the scattering rate $1/\tau^{*}(\omega)$, such that the effect cancels at $\omega=0$.Millis1987 We determine $\tau^{*}(0)/\tau(0)$ from an extended Drude analysis (Fig. 1a, Supplementary Information). $\tau^{*}(0)/\tau(0)$ displays a strong electron renormalization that has a similar behavior as $m^{*}/m_{e}$, thereby pointing to an enhanced scattering time for heavier electrons (Fig. 1d).

In order to estimate the influence of band effects on the charge carrier renormalization, which are not taken into account in $m^{*}/m_{e}$, we performed Density Functional Theory (DFT) calculations within the generalized gradient approximation (GGA). The density of states (DOS) of Mg2NiH4 shows to be a band insulator with Ni $3d$ valence bands below $\varepsilon_{F}$ and empty Mg $3s$ and Ni $4s$ bands about 1.65 eV above these bands (Fig. 2a,c), consistent with earlier reports.Garcia1999 This indicates that the charge distribution in Mg2NiH4 is governed by the strong electronegativities of H and Ni. Ionic bonding occurs between Mg2+ and the complex NiH${}_{4}^{4-}$. Strong covalent bonding between Ni and H causes deep lying H bonding bands ($-10\ \text{eV}<\hbar\omega-\varepsilon_{F}<-4\ \text{eV}$), which indicates H to be in the anionic $1s^{2}$ state.Garcia1999 Therefore, Ni is in the particular $3d^{10}4s^{0}$ state and all its $3d$ bands are below $\varepsilon_{F}$. Calculations of MgyNiH4-δ/8 super cells with $\delta$ H vacancies (Fig. 2d) — no more than one per NiH4 cluster — show that each H vacancy dopes the system with one charge carrier. For $\delta\leqslant 1$, i.e., until one H vacancy per Mg16Ni8H32 unit cell, we find that a narrow half-filled band occurs around $\varepsilon_{F}$. These in-gap states have Ni $3d_{x^{2}-y^{2}}$ character hybridized with H $1s$ owing to the vacancy state. This is confirmed by the integrated DOS that shows a complete spectral weight transfer from the Ni-H bonding bands to the top of the in-gap states (see Fig. 2a,b). The removal of one H from a tetrahedral NiH4 cluster changes its structure to square-planar NiH3, thereby minimizing the electrostatic energy. Due to the increased Ni-H overlap this pushes the Ni $3d_{x^{2}-y^{2}}$ band above $\varepsilon_{F}$, similar as reported for the Mg2NiH4 model system with square planar NiH4 clusters.Garcia1999 Furthermore, removal of an additional H (on a different cluster) creates a similar, but due to the monoclinic structure distinct, in-gap state (cf. Fig. 2c for $\delta>1$). A slight variation of $y$, comparable to the sample compositions, qualitatively does not alter the DOS (see Supplementary Information).

The coherent Drude weight determined from the DFT calculations, $W_{\text{DFT}}=\hbar^{2}\omega_{p,\text{DFT}}^{2}$, is proportional to $\delta$ and becomes close to zero for $\delta_{c}\approx 0.25$ (Fig. 1c). At this concentration the H impurities are too distant to cause significant dispersion and sustain dc conductivity. Consequently, the band mass $m_{b}/m_{e}=W_{\text{tot}}/W_{\text{DFT}}$ diverges at this point. For $\delta>0.5$, $m_{b}/m_{e}\approx 3$ almost independent of the carrier concentration. The experimental optical mass $2<m^{*}/m_{b}<9$ is thus also strongly renormalized when taking band effects into account.

Both our experiments and DFT calculations combined unanimously show, by the properties of the electron mass and scattering rate, strong electron correlations in the single occupied $d_{x^{2}-y^{2}}$ in-gap states. These strong correlations in turn also renormalize the width of the in-gap states $\Gamma$. Furthermore, since the on-site Coulomb interaction on the Ni atom $U\sim 10$ eV is much larger than the unrenormalized in-gap band width, $\Gamma_{K}\sim 0.4$ eV for $\delta=1$, these states will spit in a lower and upper Hubbard band, and a Kondo resonance peak at $\varepsilon_{F}$ hosting the localized carriers (Fig. 2e). The presence of Kondo physics close to a Mott transition, although generally present,Georges1996 is here even more intuitive because of the impurity character of the hydrogen vacancies that antiferromagnetically couple to the Ni conduction electrons below $T_{K}$. $k_{B}T_{K}$ is equal to the width of the Kondo resonance $\gamma_{K}\lesssim\Gamma_{K}$, i.e., of the order $10^{3}$ K, and thus inside the predicted ballpark.Takada2015 This is further confirmed by the periodic Anderson model, for which $m^{*}/m_{b}=(\Delta_{\text{dir}}/T_{K})^{2}$, where $\Delta_{\text{dir}}\approx 0.4\,$eV is the direct hybridization gap energy (see Fig. 1b) with $m^{*}/m_{b}$ as in the inset of Fig. 1d. Below $T_{K}$ all magnetic moments are screened and the material becomes non-magnetic. Indeed, the magnetic susceptibility of Mg2NiHx has been reported to show a pronounced decrease upon $\delta\rightarrow 1.6^{+}$ at room temperature.Stucki1980 Mg2NiH4-δ/8 thus crosses a Mott metal-to-insulating transition well before $\delta=0$.

A Kondo lattice occurs when the observed Kondo phenomena occur periodically. A close inspection of the optical data indeed hints to a Kondo impurity lattice. For all compositions, $\sigma_{1}(\omega)$ shows typical characteristics of an ordered (poly)crystalline material opposite to that of an amorphous electron glass, such as a coherent Drude peak, well-defined phonon modes and a clearly distinct band gap. Particularly for $\delta\geq 2$ and $y\gtrsim 2$, we observe an absorption band around 0.3 eV as in the, periodic, DFT results for this composition (Fig. 3b,c). Moreover, the resemblance between the DFT results and the optical measurements can further be read off above 1.5 eV, where both have a very similar trend upon changing the Mg/Ni ratio (see Supplementary Information). For these reasons, we conjecture that in the vicinity of the Mott transition, Mg2NiHx has signatures of an ordered Kondo lattice consisting of vacancy states with $s$-character that localize Ni $d$ carriers.

Although strong electron correlations have never been experimentally observed in hydrides, Mott insulating phases and concomitant mass divergences have been reported for other systems such as Si:P, 3He and Sr doped LaTiO3.Rosenbaum1983 ; Tokura1993 ; Casey2003 Among those, Si:P may appear closest to the current hydride, but the disordered arrangement of P in the Si lattice rather causes a disorder induced Mott transition, opposite to the ordered Mott transition in Mg2NiHx. The main difference with all known systems that manifest a pure Mott phase, is that this state of matter in Mg2NiHx occurs at room temperature.

The strong correlations observed in hole-doped Mg2NiHx are likely to be omnipresent in related hydride systems. Previous work shows that systems similar to Mg2NiH4 and Mg2FeH6, with Ni or Fe substituted by Mn, Ni, Fe, Co and Cu have comparable electronic structures to Mg2NiH4-δ/8.Batalovic2014 ; VanSetten2007a Calculations on these systems evince an increased density of states similar to the in-gap states of Mg2NiH4-δ/8, which is not located mid-gap, but close to either the conduction or valence band. Besides, also the rare-earth hydrides YHx and LaHx are expected to possess strong electron correlations.Eder1997 ; Ng1997 It is further interesting noticing that DMFT calculations of H impurities in Ge8 and Ge64 supercells show a split H and Ge hybridized Hubbard band close to $\varepsilon_{F}$,Sims2013 which maybe implies that the class of strongly correlated hydrides is even larger than ones that show a MI transition.

On the question how encounter superconductivity in MgyNiHx, we conjecture that maintaining stoichiometry for $y$ is crucial as our work showed that only for $y\gtrsim 2$ an ordered Kondo lattice forms. The hydrogen concentration $x$ is most promising where strong renormalization effects take place, such as for $1\leqslant\delta\leqslant 2$, forming a correlated metal with $m_{b}/m^{*}\sim 0.2$ in the ballpark to allow superconductivity.Qazilbash2009 Above all, a comprehensive study is favored employing experimental techniques that directly evince a superconducting state.

**Acknowledgements We thank S. Biermann, W.E. Pickett, D. van der Marel and G.A. de Wijs for insightful discussions. We are grateful to R. Griessen and B. Dam for providing the experimental facilities, and to W. Lustenhouwer, S. Kars, H. Schreuders and J.H. Rector for technical support. Financial support by the Netherlands Organization for Scientific Research (NWO) is gratefully acknowledged.

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**Author Contributions  J.L.M.v.M. proposed and lead the study, conducted the optical and structural measurements, analyzed and interpreted the data. M.J.v.S. performed the DFT calculations and their interpretation in the context of the experimental data. Both authors wrote the manuscript.

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Data availability The datasets generated and analysed during the current study are available from the corresponding author on reasonable request.