Closure of the Mott gap and formation of a superthermal metal in the Fr\"ohlich-type nonequilibrium polaron Bose-Einstein condensate in $\mathrm{U}{\mathrm{O}}_{2+x}$

Closure of the Mott gap and formation of a superthermal metal in the Fröhlich-type nonequilibrium polaron Bose-Einstein condensate in $U O_{2 + x}$

Steven D. Conradson et al.

Phys. Rev. B 96, 125114 – Published 8 September 2017

Abstract

Mixed valence O-doped $U O_{2 + x}$ and photoexcited $U O_{2}$ containing transitory $U^{3 +}$ and $U^{5 +}$ host a coherent polaronic quantum phase (CPQP) that exhibits the characteristics of a Fröhlich-type, nonequilibrium, phonon-coupled Bose-Einstein condensate whose stability and coherence are amplified by collective, anharmonic motions of atoms and charges. Complementary to the available, detailed, real space information from scattering and EXAFS, an outstanding question is the electronic structure. Mapping the Mott gap in $U O_{2}$ , $U_{4} O_{9}$ , and $U_{3} O_{7}$ with O XAS and NIXS and $U M_{5}$ RIXS shows that O doping raises the peak of the $U 5 f$ states of the valence band by ∼0.4 eV relative to a calculated value of 0.25 eV. However, it lowers the edge of the conduction band by 1.5 eV vs the calculated 0.6 eV, a difference much larger than the experimental error. This 1.9 eV reduction in the gap width constitutes most of the 2–2.2 eV gap measured by optical absorption. In addition, the XAS spectra show a tail that will intersect the occupied $U 5 f$ states and give a continuous density-of-states that increases rapidly above its constricted intersection. Femtosecond-resolved photoemission measurements of $U O_{2}$ , coincident with the excitation pulse with 4.7 eV excitation, show the unoccupied $U 5 f$ states of $U O_{2}$ and no hot electrons. 3.1 eV excitation, however, complements the O-doping results by giving a continuous population of electrons for several eV above the Fermi level. The CPQP in photoexcited $U O_{2}$ therefore fulfills the criteria for a nonequilibrium condensate. The electron distributions resulting from both excitations persist for 5–10 ps, indicating that they are the final state that therefore forms without passing through the initial continuous distribution of nonthermal electrons observed for other materials. Three exceptional findings are: (1) the direct formation of both of these long lived (>3–10 ps) excited states without the short lived nonthermal intermediate; (2) the superthermal metallic state is as or more stable than typical photoinduced metallic phases; and (3) the absence of hot electrons accompanying the insulating $U O_{2}$ excited state. This heterogeneous, nonequilibrium, Fröhlich BEC stabilized by a Fano-Feshbach resonance therefore continues to exhibit unique properties.

Received 4 January 2017
Revised 3 July 2017

DOI:https://doi.org/10.1103/PhysRevB.96.125114

Physics Subject Headings (PhySH)

Band gap Composition Defects Density of states Electrical conductivity Electronic structure Insulators Metals Multiband superconductivity Pairing mechanisms Phase separation Photoconductivity Polarons Quantum phase transitions

Condensed Matter, Materials & Applied Physics

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Vol. 96, Iss. 12 — 15 September 2017

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Figure 1
O XAS and U M RIXS of $U O_{2 + x}$ and standards. (a) The energies for the $U O_{2}$ , $U_{4} O_{9}$ , and $U_{3} O_{7}$ XAS were obtained from the NIXS measurements and the others adjusted from literature values [32] to this $U O_{2}$ . The broadening of the overall $U 5 f − 6 d$ manifold of the mixed valence compounds occurs on the low energy edge of the upper Hubbard band. In addition to some variability in the relative amplitudes between different samples of the same compound (Fig. S1), the NIXS that is not distorted by self-absorbance shows that the 531.5 eV peak in the $U_{3} O_{7}$ spectrum is quite low relative to the others (Fig. S3). (b) The $U M_{5}$ valence-to-core $3 d 5 f$ RIXS, consists of the $U 5 f$ →O $2 p$ and intra-atomic $U 5 f$ → $5 f$ excitations at, respectively, energy transfers of $< - 3.5$ eV and −4 through 0 eV, and the elastic peak at 0 eV. The original spectra from around −4 to 2 eV that contains the elastic peak at 0 eV that overlaps with the $U 5 f$ peak on its low energy side are plotted on a larger scale to facilitate inspection of the RIXS that are lower in amplitude. The spectra over this range were then curve-fit with two Voigt functions and the one for the elastic peak was subtracted from the spectra that are plotted over the entire range on a smaller scale so that they are magnified relative to the elastic peak. The O $2 p$ states are therefore seen below −3.5 eV and the $U 5 f$ states at −4 through 0 eV. The dashed lines are the curve-fits for the $U 5 f$ peak.
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Figure 2
Tracking the Mott gap in O and photodoped $U O_{2 + x}$ . (a) LDA+U calculations of the total densities of states (DOS) for $U O_{2}$ , $U_{4} O_{9}$ , and $U_{3} O_{7}$ using the static, U(IV,V)-based structures derived from neutron scattering and energy minimization. (b) $U M_{5}$ RIXS of $U O_{2}$ and $U_{4} O_{9}$ showing the measured spectra that are the overlapping elastic and occupied $U 5 f$ peaks of the LHB scaled to a peak height of unity, the fits to two Voigt functions, the individual components of the fits, and the separated $U 5 f$ contributions to the data and their fits. (c) O XAS of $U O_{2}$ , $U_{4} O_{9}$ , and $U_{3} O_{7}$ showing the transitions to the unoccupied states of the UHB of predominantly $U 5 f$ character. The NIXS of $U O_{2}$ does not show the low energy tail displayed by the more surface sensitive XAS measurement. (d) 40 fs resolution pump-probe angle-integrated photoemission measurements coincident with the excitation pulse excited at the listed fluences with 3.1 and 4.7 eV pump energies. The solid lines at 0–5 eV are fits of the data to asymmetric Gaussian functions. The vertical green band is the 2.4 eV wide band gap, aligned with the calculation. The magenta bars show the shifts of the $U_{4} O_{9}$ / $U_{3} O_{7}$ band edges or centroid relative to $U O_{2}$ . The RIXS and tr-PES spectra with their different energy scales are aligned with respect to the center of the $U O_{2}$ $U 5 f$ states, with “0” energy equal to the elastic scattering for the RIXS and the Fermi level for the PES. The absorption edge of the $U O_{2}$ NIXS is aligned with the front portion of the DOS from the calculations and may exaggerate the actual width of the Mott gap. (e) Combined $U_{4} O_{9}$ RIXS after subtraction of the elastic peak, $U_{3} O_{7}$ XAS, and tr-PES at the highest fluence of both 3.1 and 4.7 eV excitation. Energy scales are the same as in the prior figures. The DOS from all of the measurements overlap around −1.0 eV with a nodal point a few percent of the maximum values, after adjusting the baselines to zero and scaling the maximum amplitudes of the RIXS and PES to 10 000 and the XAS to 30 000 to correspond to the calculation.
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Figure 3
O XAS of $U O_{2}$ and $U_{4} O_{9}$ at ambient and liquid $N_{2}$ temperature. The changes in the spectra on cooling that are much larger in the region dominated by the $U 5 f$ states are indicative of a redistribution of the mobile charges that, for $U O_{2}$ , should be more on the surface because bulk structure measurements show no temperature dependence, in contrast to EPR of powders.
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Figure 4
Fluence dependence on temperature at $t = 0$ . Linear fits to the logarithm of the intensity over the leading edge of the photoemission peak nearest the Fermi level are indicative of the temperature of the thermalized hot electrons after the photon impulse. Because $U O_{2}$ is an insulator the linear portion of the ln(DOS) provides qualitative information rather than a specific temperature. (a) 4.7 eV excitation does not have a thermalized component, suggesting that it is totally relaxed within the 40 fs time resolution. (b) The monotonic increase in the $x$ intercept with increasing fluence shows that the energy from 3.1 eV excitation relaxes sufficiently quickly within the same time interval to give this thermalized component whose temperature increases with increasing energy.
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Figure 5
Potentials/reaction coordinates for asymmetric double well potentials for fermion pairing. The pair potential is the curve across its entire range, the reaction coordinate is the range between the arrows. (a) Although energetically favored by ΔE, relaxation of the excited state is inhibited by an activation energy with a barrier height of $E_{a}$ , promoting the accumulation of particles to give an excess, nonequlibrium population in the closed channel that will become the condensate. The inhibition is maximized when the energy of the excited state is in proximity to the chemical potential that will be between the occupied ground state and lowest unoccupied state. (b) Coherent transfer between the open and closed channels is promoted by a Fano-Feshbach resonance that is maximized when the energy of the excited, $S = 0$ state is in proximity to the individual particle energy of the $S \neq 0$ state. The barrier height for the reverse reaction is therefore zero. ΔE for $U O_{2 + x} = - 2.2 eV$ , which is very close to the energy between the centers of the $U_{4} O_{9}$ $U 5 f$ highest occupied state and the lowest feature in the $U O_{2 + x}$ spectra [Figs. 2 and 2] that corresponds to the lowest energy excited state.
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Physical Review B

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Closure of the Mott gap and formation of a superthermal metal in the Fröhlich-type nonequilibrium polaron Bose-Einstein condensate in $U O_{2 + x}$

Steven D. Conradson et al.

Phys. Rev. B 96, 125114 – Published 8 September 2017

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Closure of the Mott gap and formation of a superthermal metal in the Fröhlich-type nonequilibrium polaron Bose-Einstein condensate in UO2+x

Steven D. Conradson et al.

Phys. Rev. B 96, 125114 – Published 8 September 2017

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Closure of the Mott gap and formation of a superthermal metal in the Fröhlich-type nonequilibrium polaron Bose-Einstein condensate in $U O_{2 + x}$