Fully consistent density functional theory determination of the insulator-metal transition boundary in warm dense hydrogen

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Fully consistent density functional theory determination of the insulator-metal transition boundary in warm dense hydrogen

Joshua Hinz, Valentin V. Karasiev, S. X. Hu, Mohamed Zaghoo, Daniel Mejía-Rodríguez, S. B. Trickey, and L. Calderín

Phys. Rev. Research 2, 032065(R) – Published 10 September 2020

Abstract

Using conceptually and procedurally consistent density functional theory (DFT) calculations with an advanced meta-generalized gradient approximation (GGA) exchange-correlation functional in ab initio Born-Oppenheimer molecular dynamics (BOMD) simulations, we determine the insulator-metal transition (IMT) of warm dense fluid hydrogen from 50 to 300 GPa to be in better agreement with experiment than previous DFT predictions. The inclusion of nuclear quantum effects via path-integral molecular dynamics (PIMD) sharpens the transition and lowers its temperature relative to the BOMD results. A rapid decrease in the molecular character of the system, as observed via the ionic pair correlation function, coincides with an abrupt conductivity increase, confirming a metallic transition due to molecular hydrogen dissociation that is coincident with abrupt band-gap closure. Comparison of the PIMD and BOMD results clearly demonstrates an isotope effect on the IMT. Exploitation of differing methodologies for using the orbital-dependent and deorbitalized versions of the meta-GGA enables us to quantify exchange-correlation approximation effects. Distinct from stochastic simulations, these results do not depend upon any clever but uncontrolled combination of ground-state and finite-T methodologies and should provide a reliable benchmark for further studies.

Received 7 February 2020
Revised 11 May 2020
Accepted 20 August 2020

DOI:https://doi.org/10.1103/PhysRevResearch.2.032065

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Electrical conductivity First-principles calculations

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Joshua Hinz¹, Valentin V. Karasiev^1,*, S. X. Hu ¹, Mohamed Zaghoo¹, Daniel Mejía-Rodríguez ², S. B. Trickey ², and L. Calderín³

¹Laboratory for Laser Energetics, University of Rochester, Rochester, New York 14623, USA
²Quantum Theory Project, Department of Physics, University of Florida, Gainesville, Florida 32611, USA
³Department of Materials Science and Engineering, University of Arizona, Tucson, Arizona 85721, USA

^*vkarasev@lle.rochester.edu

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Issue

Vol. 2, Iss. 3 — September - November 2020

Subject Areas

Condensed Matter Physics

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Images

Figure 1
Emerging picture of the hydrogen and deuterium insulator-to-metal transition (IMT). Blue symbols show experimental results for hydrogen [7, 8, 10]. Upright blue triangles are the IMT from measured reflectivities [10]. All other blue symbols are from the laser heating curve plateau. Green symbols show reflectivity results for deuterium [12, 13, 14]. The black dashed and dotted curve is the melt line based on Ref. [61]. The solid light blue and solid light green curves are the predictions of PBE [29] and vdW-DF1 [13], respectively, for the case of quantum nuclei. Within this work all IMT temperature points are determined when the system reaches 2000 S/cm, which is indicated with solid circles or right pointed triangles. The corresponding solid lines between the solid circles are a guide to the eye. The red curve with circles is the SCAN-L+rVV10 prediction with classical nuclei and the orange triangles pointed to the right are three of the same classical nuclei predictions without the rVV10 correction. The corresponding blue and green curves with circles are the predictions with NQEs for hydrogen and deuterium, respectively. The red-shaded region indicates where classical or quantum H is metallic, whereas the blue-shaded region indicates where only quantum H is metallic. Inset: With NQE inclusion an apparent step in the IMT boundary appears. This feature apparently has not been seen previously in DFT studies but appears to be in agreement with CEIMC results which are indicated by the dashed blue (hydrogen) and dashed green (deuterium) curves [33]. Further analysis is required to ascertain the underlying cause of that feature.
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Figure 2
(a) Calculated dc conductivity of hydrogen along the 0.9 (squares) and $1.0 g / c m^{3}$ (circles) isochores for quantum (blue) and classical (red) ions. The black horizontal line indicates the primary IMT location criterion: metallic dc conductivity $> 2000 S / cm$ . Vertical lines are guides to the eye to mark the temperature at which 2000 S/cm is crossed. (b) Corresponding reflectivity at ∼1.96 eV relative to vacuum. (c) Height of the first peak of the ionic PCF, a measure of the molecular character of the system. (d) Indirect energy band gap [identified from the 0 K highest occupied molecular orbital (HOMO)–lowest unoccupied molecular orbital (LUMO) gap; see text]. The horizontal dotted black line indicates gap closure. Negative values indicate that the LUMO minimum lies below the HOMO maximum.
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