Almost 80 years ago it was predicted that hydrogen, under sufficient compression, would break its molecular bonds and form a new metallic solid state.
This new state is predicted to be a room temperature superconductor [Ashcroft 1968].
Its experimental realization is actually one of the main goals of solid state physics. The task has proven to be more challenging than expected, due to a very rich phase diagram that high-pressure hydrogen exhibits.
At this high pressure, it is impossible to obtain the crystal structure from diffraction data. Optical data, vibrational IR and Raman spectroscopy can be used to determine phase transitions but requires a theoretical analysis to determine the crystal structures. The goal of this project is the first-principles prediction of the (T, P) phase diagram of H and the simulation of the IR and Raman spectra of the stables phases. In both tasks, we will take into account the anharmonic thermal and quantum fluctuations of H atoms, thanks to a new numerical method introduced by our group members during this year.
These effects play a crucial role in phase stability and in superconductive proprieties, as recently proved by many calculations [Errea et.al. 2016, Borinaga et. al. 2016A, Borinaga et. al. 2016B].
The predicted IR-Raman phonon dispersion will be compared to the experimental signatures of H phase diagram to shed light on recent claims about the effective observation of the solid state of hydrogen.
[Ashcroft - Physical Review Letters - 1968]
[Borinaga, Errea, Calandra, Mauri, Bergara - Physical Review B - 2016A]
[Borinaga, Riego, Leonardo, Calandra, Mauri, Bergara, Errea - Journal of Physics: Condensed Matter - 2016B]
[Errea, Calandra, Pickard, Nelson, Needs, Li, Liu, Zhang, Ma, Mauri - Nature - 2016]
Anharmonicities and quantum effects on nuclei in metallic and pre-metallic hydrogen jeopardize the current interpretation of the phase diagram of high-pressure hydrogen.
Until now the most advanced anharmonic predictions of the Raman spectra of the different phases of high-pressure hydrogen have been calculated without considering quantum effects on nuclei [Magdau 2014], critical at room temperature since the Debye energy of hydrogen phonons is around 3500 K [Ashcroft 1968].
The proton quantum diffusion has been included in another phase diagram computation only recently [Drummond 2014] but neglecting the anharmonic coupling between modes, and therefore not considering the Raman/IR response, crucial to the correct structure/phase association, and for the experimental comparison.
The application of SSCHA to the whole hydrogen phase diagram would allow for the first time to fully consider both nuclei quantum effects, like zero-point motion, and anharmonicities, leading to a quantitative prediction of physical proprieties of all these phases and providing a correct interpretation for the measured Raman/IR spectral proprieties.
This is important to disentangle the puzzle of phase IV-V and VI, shedding light on the controversial observation of hydrogen metalization in static DAC experiments [Dias 2017, Loubeyre 2017, Goncharov 2017, Eremets 2017, Silvera 2017].
Previous attempts to apply SSCHA to pre-metallic hydrogen phases have failed.
Instabilities in the free energy's minimization procedure arise when both hard and soft phononic branches are affected by anharmonicities. This feature appears in every pre-metallic state of hydrogen since both intramolecular strong bonds and weak intermolecular interactions are present.
During my first year of PHD at "Università La Sapienza", Rome, I estimated analytically the Hessian matrix of the minimization algorithm, that unveils the intrinsic minimization instabilities of SSCHA algorithm.
A new procedure for the minimization can be defined, that corrects these instabilities through an appropriate preconditioning and changing the minimization variables.
The new algorithm has been implemented and tested: it strongly overcomes the standard SSCHA, requiring much less "ab-initio" forces evaluation, and it avoids the runaway solution artifacts that affected the old minimization. Currently, I'm writing a paper on this new methodological breakthrough.
Also, a recent work by Bianco et. al. [Bianco 2017] provided a new analytical correction to the phononic modes computed with SSCHA, allowing for a much more accurate Raman/IR spectrum prediction. This enables the precise determination of second order phase transition occurrence between high and low symmetric phases.
For the first time, it is possible to investigate the whole phase diagram of high-pressure hydrogen using full quantum anharmonic approach, considering also the mixed molecular phases. Since SSCHA is a free-energy based method, it is perfectly suited to study the energy difference between competing phases. Quantum diffusion and anharmonicities can substantially affect the relative free energies, stabilizing new unpredicted structures and reassemble the phase diagram, providing definitive constraints on the conditions required to finalize the hydrogen metalization quest.
[Ashcroft - Physical Review Letters - 1968]
[Bianco, Errea, Paulatto, Calandra, Mauri - Arxiv Preprint - 2017]
[Dias, Silvera - Science - 2017]
[Drummond, Monserrat, Lloyd-Williams, Rios, Pickard, Needs - Nature communications ¿ 2014]
[Eremets, Drozdov - Arxiv - 2017]
[Goncharov, Struzhkin - Arxiv - 2017]
[Loubeyre, Occelli, Dumas - Arxiv - 2017]
[Magdau, Ackland - Journal of Physics: Conference Series - 2014]