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Quasi-two-dimensional metallic hydrogen inside di-phosphide at high pressure

The method of mathematical modeling was used for the calculation of the structural, electronic, phonon, and other characteristics of various normal phases of phosphorus hydrides with stoichiometry PHk. It was shown that the di-phosphine may form 2D lattice of the metallic hydrogen, stabilized by phosphorus atoms under high hydrostatic compressive pressure. The resulting structure with the elements of H-P-H is a locally stable one in the phonon spectrum (or metastable). The properties of di-phosphine with the properties of similar structures such as thesulphur hydrides were compared.


Introduction
One of the areas of search for new superconducting materials with high critical temperatures is the study of compounds with high hydrogen content. In [1] it was discovered, that the transition to the superconducting state of the metallic phase of the hydrogen sulfide under pressure 170GPatakes place at the temperature T=203К. The idea is based on the theoretical works on the study of the metallic hydrogen properties, which predicted high critical temperature Tc ~ 200 ÷ 400K [2]. In the works [3,4] it was shown that such a phase of hydrogen may be metastable. After publication of the results [1] the interests in searching for compounds that can go into a superconducting state at higher temperatures have increased significantly. In particular, the preliminary experimental results on the compression of phosphide PH 3 and its superconductivity at 100K [5] should be mentioned. In [1] the fact is considered that at the high pressure the hydrogen forms a hydride SH n (n≤3) [6]through dissociation of the sulfur compounds. The properties of the SH 3 in the hydrogen sulfide can lead to the possible explanation ofthe hightemperature superconductivity existence. In [7][8][9] the SH 2 phase with the symmetry I4/MMM was found along with the compounds SH 3 , for which the electron and phonon spectra and the density of electron and phonon states in the pressure range 100÷225GPa were calculated.
In this paper we present the calculations of the electronic and phonon properties of the di-phosphine H2P-PH2 system compressed withup to 250 GPA hydrostatic pressures. Di-phosphine under normal conditions is a colorless liquid with the structure of molecules presented in Fig.1A [10].

Method.
The calculations of the structural, electronic and phonon characteristics of the molecules and the periodic crystal structure of PH k in the pressure range 0÷ 250GPa were performed using ab-initio method. The DFT approximation with the plane wave basis with the correlation functional GGA -PBE pseudopotential which preserves the norm was used. The unit cell of the structure used to calculate the electronic properties contains an element of H2P-PH2. All the calculations were performed in the spin-polarized approximation in order to compare the calculated energy values of different phases in an adequate manner.

Results.
At the 25GPa pressure the molecular di-phosphine P 2 H 4 phase becomes metallic because of the overlap of electron shells of the molecules. The compressionof the combination of such molecules in thepressure range 25 ÷ 250GPa leads to the formation of metallic crystalline phase. The main structural element of this phase H2P-PH2 acquires straight H-P-H bond directed at an angle of 180° ( Fig. 1.с). In the calculations of the first cycle, the pressure for the molecular phase was assumed to be the source of the initial cell symmetry with the P2H4 molecule havingthe symmetry P1. The resulting crystal structure at the pressure of 25÷125 GPA acquires the symmetry of the unit cell of I4/MMM. The structure formed in this range of pressures with a finalI4/MMM crystal symmetry ( Fig.1.e) as a result of the structural modification of the unit cell in the studied phase with the stoichiometry P 2 H 4 . At the next stage of the calculations the cell with the symmetry I4/MMM was used as a starting one (second cycle). Crystal structure with this unit cell symmetry was studied in the pressure range 25÷250GPa. The crystal forms a set of parallel planes of atoms with the full concentration of 25÷250GPa as a result of structural modification of the unit cell in the studied phase of P I4/MMM. The hydrogen atoms form a s result, the electronic properties of the theirown planes. Each phosphorus atom two hydrogen atoms above and below amounted to V=13.54A 3 , which about 1 elect./A 3 ). The effect of which is determined by the conditional considered as interesting one. Mulliken magnitude character. The hydrogen increases the negative charge that the pressure P "pushes away phosphorus atoms in the hydrogen atoms. Also the results of two approaching planes, in which concentrated, with increasing pressure P the pressure approaches to the value pressure P= 175GPa. Fig.2 shows that the Fermi level is that at the pressure P= 175GPa (Fig.2) at least one of the zones has effective masses of carriers near level crosses three subzones (Fig.2).
There are no imaginary frequencies in the pressure ra crystal P 2 H 4 -I4/MMM phase. That means that Maximum frequencies lie in the en corresponding to the displacement values of the wave vector q on segments connecting the symmetry points of the Brillouin zone ( Fig.1 becomes more rigid with increasing pressure Fig. 4 shows graphs of the enthalpy SH 3 sulfide, di-phosphide P 2 H 4 metastable in concern with the phase transition in phase XH for such a phase transition in experiments [1] was used. If this heating is eliminate I4/MMM can be formed in a metastable state. Indeed, its fre contain imaginary frequencies. In addition, the range of press phosphine PH 3 and the symmetry

Conclusions
The P 2 H 4 di-phosphine molecular phase of the overlap of the electron shells of molecules. pressures P = 50÷250GPa with structural modification of the unit cell in the studied formation of a square lattice of hydrogen atoms in this plane acquire quasi-two-dimensional metallic ch crystal di-phosphine P 2 H 4 -I4/MMM phase of atoms with the full concentration of all hydrogen atoms in these planes (Fig.1.e) in th as a result of structural modification of the unit cell in the studied phase of P he hydrogen atoms form a square lattice with a period depending on the pressure properties of the system acquire quasi-two-dimensional character. The phosphorus atoms form . Each phosphorus atom has four atoms Pin the first coordination sphere two hydrogen atoms above and below the plane. The calculated unit cell volume at gives the total electron density value of n=10 24 elect. he effect of the redistribution of the electron density between atoms with increasing pressure, which is determined by the conditional Mullikencharges of phosphorus Z M (P)and hydrogen(H) Mullikencharges of atoms of phosphorus Z M (P) are positive with the he hydrogen increases the negative charge Z M (H). It follows from the results of calculations away" the electron density from the areas of the loops of the electron density around the phosphorus atoms in the hydrogen atoms. Also the results of the calculations show the distance which hydrogen atoms forming quasi-two-dimensional square concentrated, with increasing pressure P. The total concentration of hydrogen atoms to the value P=150GPa. The Fig.2 shows the properties of the electron subsystem for the Fig.2 shows that the Fermi level is located at the electronic DOS Pa (Fig.2) at least one of the zones has dropped below the Fermi level. The e the Fermi level gives a value of about 0.1m e0 . At the pressure P=175GPA level crosses three subzones (Fig.2).
here are no imaginary frequencies in the pressure range 50÷250GPa (Fig.3) in the phonon spectrum of the I4/MMM phase. That means that the phase P 2 H 4 -I4/MMM is a stable one in this pressure range Maximum frequencies lie in the energy region of the order of 265meV. Note that the optical modes of oscillation corresponding to the displacement of hydrogen atoms (Fig.3)correspond not only to small q (point G), but also to wave vector q on segments connecting the symmetry points of the Brillouin zone ( Fig.1 with increasing pressure. e enthalpy ∆H with increasing pressure P for the most stable crystalline and phosphine PH 3 phases. Fig. 4 shows that compounds of the type XH phase transition in phase XH 3 , for which enthalpy has smaller val for such a phase transition in experiments [1] the heating of the contents of the diamond cells with eliminatedwhen compressing di-phosphine P 2 H 4 , then the phase with I4/MMM can be formed in a metastable state. Indeed, its frequency spectrum in the range contain imaginary frequencies. In addition, the range of pressures P, in which the structure with symmetry IMMM has no imaginary frequencies, is relatively small phosphine under normal conditions; b -isosurface of the electron density for molecules of di phosphine at the level of 0.6, indicating the covalent bonding in the molecule; c is a primitive cell with two elements of H ; d is the Brillouin zone corresponding to the primitive cell at the pressure P =150 hosphine at the pressure P=150GPa; The two-dimensional distribution of the concentration of hydrogen atoms is shown. phosphine molecular phase becomes metallic with pressure having values more than 25GPa electron shells of molecules. The crystal forms a set of parallel planes of atoms 250GPa with the full concentration of all hydrogen atoms in these planes as a result of tion of the unit cell in the studied P 2 H 4 phase with the final symmetry I4/MMM (Fig.1.e) with the formation of a square lattice of hydrogen atoms in this planes. As a result, the electronic dimensional metallic character. There are no imaginary frequencies I4/MMM phase in the pressure range 50÷ 250GPa.
1.e) in the entire pressure range as a result of structural modification of the unit cell in the studied phase of P 2 H 4 with the symmetry on the pressure in these planes. As a dimensional character. The phosphorus atoms form in the first coordination sphere located in the plane, with . The calculated unit cell volume at the pressure P=125 GPA lect./cm 3 (14 electrons per cell, or electron density between atoms with increasing pressure, (P)and hydrogen(H), should be (P) are positive with the increasing in from the results of calculations the areas of the loops of the electron density around the the distance h change between square lattice with period a are within the planes occurs when Fig.2 shows the properties of the electron subsystem for the electronic DOS peak value. Fig.2 also shows dropped below the Fermi level. The estimation of the pressure P=175GPA the Fermi in the phonon spectrum of the s a stable one in this pressure range. meV. Note that the optical modes of oscillation toms (Fig.3)correspond not only to small q (point G), but also to all wave vector q on segments connecting the symmetry points of the Brillouin zone ( Fig.1.c). This range H with increasing pressure P for the most stable crystalline SH 2 and Fig. 4 shows that compounds of the type XH 2 are enthalpy has smaller values. Presumably, contents of the diamond cells with laser radiation , then the phase with the symmetry quency spectrum in the range 50÷250GPa does not ures P, in which the structure with stoichiometry of has no imaginary frequencies, is relatively small -100 ÷150GPa.
isosurface of the electron density for molecules of diin the molecule; c is a primitive cell with two elements of H-P-H at the pressure P =150GPa; e is the structure dimensional distribution of electron density in the with pressure having values more than 25GPa because crystal forms a set of parallel planes of atoms in the range of the full concentration of all hydrogen atoms in these planes as a result of the symmetry I4/MMM (Fig.1.e) with the . As a result, the electronic properties of the system here are no imaginary frequencies in the phonon spectrum of the P 2 H 4 phase with the I4/MMM maximum frequency lies in the pressure. The competing PH 3 phase crystal pressure range of its stability narrows the interval of Hydrostatic pressure not only forms a two "pushes away" the electron density to the Conventionally, this effect can be described as a "doping" of this plane. Basing on the calculations of properties of the normal phase of di range for the effect of supercondu compression the substance must show because it has the properties of two is stable (or metastable) in the pressure range 50÷250GPa. The he range becomes more rigid with increasing nthalpy at the given pressure P. The pressure values to the following one: P=100÷150GPa.
concentration of hydrogen, but also or phosphorus) in these planes.
phosphine we conclude that the optimal pressure . It seems to us that under hydrostatic a transition to the superconducting state at a higher temperature than PH 3 [5] n a wide range of pressures.
PDOS, the partial density of the number of phonon P 2 H 4 density of states, the sulfide SH 2 (symmetry I4/MMM); 2 -di-(symmetry IMMM); the empty symbols correspond e absence of imaginary frequencies; the intervals of the pressure P, in which the structures have only real frequencies.