Electronic energy gap closure and metal-insulator transition in dense liquid hydrogen

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Electronic energy gap closure and metal-insulator transition in dense liquid hydrogen

Vitaly Gorelov, David M. Ceperley, Markus Holzmann, and Carlo Pierleoni

Phys. Rev. B 102, 195133 – Published 19 November 2020

Abstract

Using quantum Monte Carlo (QMC) calculations, we investigate the insulator-metal transition observed in liquid hydrogen at high pressure. Below the critical temperature of the transition from the molecular to the atomic liquid, the fundamental electronic gap closure occurs abruptly, with a small discontinuity reflecting the weak first-order transition in the thermodynamic equation of state. Above the critical temperature, molecular dissociation sets in while the gap is still open. When the gap closes, the decay of the off-diagonal reduced density matrix shows that the liquid enters a gapless, but localized, phase: there is a crossover between the insulating and the metallic liquids. Compared to different density functional theory (DFT) functionals, our QMC calculations provide larger values for the fundamental gap and the electronic density of states close to the band edges, indicating that optical properties from DFT potentially benefit from error cancellations.

Received 3 September 2020
Revised 27 October 2020
Accepted 29 October 2020

DOI:https://doi.org/10.1103/PhysRevB.102.195133

Physics Subject Headings (PhySH)

Band gap Density of states Dielectric properties Electrical conductivity First-principles calculations Liquid-liquid phase transition Localization Metal-insulator transition Temperature Transition temperature

Insulators Liquid metals Liquids

Band structure methods Density functional theory Path-integral Monte Carlo Quantum Monte Carlo

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Vitaly Gorelov ¹, David M. Ceperley ², Markus Holzmann^3,4, and Carlo Pierleoni ^1,5

¹Maison de la Simulation, CEA, CNRS, Université Paris-Sud, UVSQ, Université Paris-Saclay, F-91191 Gif-sur-Yvette, France
²Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
³Univ. Grenoble Alpes, CNRS, LPMMC, F-3800 Grenoble, France
⁴Institut Laue Langevin, Boîte Postale 156, F-38042 Grenoble Cedex 9, France
⁵Department of Physical and Chemical Sciences, University of L'Aquila, Via Vetoio 10, I-67010 L'Aquila, Italy

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Issue

Vol. 102, Iss. 19 — 15 November 2020

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Images

Figure 1
The fundamental energy gap of liquid hydrogen along the isotherms: $T = 900$ , 1500, and 3000 K as a function of pressure. Inset: the same gap as a function of $r_{s}$ , a measure of density. The lines connect the gap data only up to the molecular-atomic transition region. The colored rectangles show the coexistence region of the LLPT according to Ref. [49]. The dotted lines are the gaps reported by Cellier et al. [13]. The brown and green squares are the results of Nellis et al. for temperatures of 2000–3000 K [7] reanalyzed in Ref. [34]. The red circle is the gap reported by McWilliams et al. at 2400 K [18].
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Figure 2
Density of states of liquid hydrogen near the band edge at densities near the gap closure for three isotherms: (a) 900 K, (b) 1500 K, and (c) 3000 K. The insets show the equation of state as reported in [49]. The dashed and solid red lines indicate the atomic and molecular regions, respectively. The colors of the DOS match the colors of points in the insets.
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Figure 3
The absolute value of the off-diagonal part of the reduced single-particle density matrix, $n (r)$ [51], multiplied by $r^{3}$ as a function of distance $r$ for various densities around the gap closure. (a) At $T = 900$ , when the gap vanishes for $r_{s} ≲ 1.42$ , as the liquid crosses the LLPT, $n (r)$ changes, indicating more delocalized, Fermi-liquid-like behavior. (b) At $T = 3000$ , since $n (r)$ decays faster than $r^{- 3}$ at all densities, the electron liquid remains localized even when the gap vanishes ( $r_{s} ≲ 1.55$ ).
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Figure 4
Tauc analysis of the absorption profiles, computed with DFT-HSE for liquid hydrogen at $T = 1500 K$ and two densities: $r_{s} = 1.54$ and 1.47.
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Figure 5
(a) The fundamental gap calculated with different DFT exchange correlation functionals compared with the QMC gap at $T = 1500 K$ and $r_{s} = 1.54$ . The orange horizontal bar is the RQMC-GCTABC thermal gap with its statistical uncertainty given by its width. (b) Difference between the integrated density of states of QMC and DFT. A “scissor correction” on the horizontal axis from the gap value was applied to the DFT profiles before subtracting them from the QMC profile; $μ_{F}$ has been set by the maximum of the valence band.
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Figure 6
(a) The HSE and QMC band gaps along three isotherms. The dashed lines are the HSE values, and solid lines are the QMC results. Squares indicate pressures at which the reflectivity is 0.3 according to Ref. [38]. (b) Absorption at $ω = 2.3 eV$ along the $T = 1500 K$ isotherm. The dashed lines are the HSE values reported in Ref. [38], and the solid lines are computed using the QMC-corrected band gaps.
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