Structural stability and equation of state of simple-hexagonal phosphorus to 280 GPa: Phase transition at 262 GPa

Akahama, Yuichi; Kawamura, Haruki; Carlson, Stefan; Bihan, T. Le; Häusermann, Daniel M.

doi:10.1103/physrevb.61.3139

Cited by 74 publications

(73 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recently, Akahama et. al 24 investigated the crystal structure of black phosphorus up to 280 GPa at room temperature using xray-diffraction experiment and found that sh phase goes to the bcc structure at 262 GPa. The sc phase exhibits superconductivity at 4.7 K 25,26 .…”

Section: Introductionmentioning

confidence: 99%

Raman anomalies as signatures of pressure induced electronic topological and structural transitions in black phosphorus: Experiments and theory

et al. 2017

View full text Add to dashboard Cite

We report high pressure Raman experiments of Black phosphorus (BP) up to 24 GPa. The line widths of first order Raman modes A 1 g , B2g and A 2 g of the orthorhombic phase show a minimum at 1.1 GPa. Our first-principles density functional analysis reveals that this is associated with the anomalies in electron-phonon coupling at the semiconductor to topological insulator transition through inversion of valence and conduction bands marking a change from trivial to nontrivial electronic topology. The frequencies of B2g and A 2 g modes become anomalous in the rhombohedral phase at 7.4 GPa, and new modes appearing in the rhombohedral phase show anomalous softening with pressure. This is shown to originate from unusual structural evolution of black phosphorous with pressure, based on first-principles theoretical analysis.

show abstract

Section: Introductionmentioning

confidence: 99%

Raman anomalies as signatures of pressure induced electronic topological and structural transitions in black phosphorus: Experiments and theory

et al. 2017

View full text Add to dashboard Cite

show abstract

“…Akahama et al [8] reported the appearance of a simple hexagonal (sh) phase, i.e., the P-V phase, which stabilizes above 137 GPa, and an intermediate phase, i.e., the P-IV phase, between sc and sh on the basis of x-ray diffraction data. At even higher pressures, the bcc structure (P-VI) has been theoretically predicted [9] and later identified in an experiment at 262 GPa [10]. The structure of phase IV, however, has not been identified experimentally.…”

mentioning

confidence: 99%

“…We checked the accuracy of our pseudopotential by comparing the calculated equation of states (EOS) with the experimental EOS for both the sc and the sh phase [8][9][10]. Calculated volume at 103 GPa for the sc phase is lower than the experimental value by 1.17%, and the volume at 151 GPa for the sh phase is lower by 2.33%.…”

mentioning

confidence: 99%

Determining the Structure of Phosphorus in Phase IV

et al. 2006

View full text Add to dashboard Cite

We explore the unknown structure of phosphorus in phase IV (P-IV phase) based on first-principles calculations using the metadynamics simulation method. Starting from the simple cubic structure, we find a new modulated structure of the monoclinic lattice. The modulation is crucial to the stability of the structure. Through refining the structure further by changing the modulation period, we find the structure whose x-ray powder diffraction pattern is in best agreement with the experimental pattern. We expect that the modulation period of the structure in the P-IV phase is very close to that found in this study and probably incommensurate. DOI: 10.1103/PhysRevLett.96.095502 PACS numbers: 61.50.Ah, 62.50.+p, 64.70.Kb Recent progress in high-pressure physics has enhanced our recognition of a wide variety of crystal structures. Development of high-pressure techniques has also enabled the identification of structures that are stabilized only in a narrow pressure range. Interesting structures were found unexpectedly through high-pressure experiments. For instance, modulated structures are often found in the highpressure phases of elements. Lattice modulations have been found in group Vb elements, including As, Sb, and Bi Scarcity of experimental ultrahigh-pressure data restricts high-pressure studies. Thus, researchers often encounter difficulties in the identification of a crystal structure on the basis of experimental data alone. A theoretical approach provides additional information on the same problem. First-principles theory for determining crystal structures is believed to be sufficiently accurate. However, the limitations of computational resources sometimes impede full structure searches.We will focus on the case of phase IV of the phosphorus (P-IV) phase. Observation of the P-IV phase was first reported by Akahama et al. [8] in 1999. In the sequence of pressure-induced transformations, the simple cubic (sc) phase (P-III) appears at 10 GPa at low temperature. Akahama et al. [8] reported the appearance of a simple hexagonal (sh) phase, i.e., the P-V phase, which stabilizes above 137 GPa, and an intermediate phase, i.e., the P-IV phase, between sc and sh on the basis of x-ray diffraction data. At even higher pressures, the bcc structure (P-VI) has been theoretically predicted [9] and later identified in an experiment at 262 GPa [10]. The structure of phase IV, however, has not been identified experimentally. Ordinary Rietveld analysis based on a knowledge of the monoclinic symmetry alone has not been successful, presumably owing to the complexity of the lattice. Thus, we must guess the crystal structure or a pseudocrystal.Several structures have been tested as candidate structures for P-IV. Ahuja considered a structure of space group Imma [11]. Ehlers and Christensen studied relative stability of the Ba-IV structure against sc and sh in the pressure range from 100 to 200 GPa [12]. The Ba-IV structure is a kind of modulated structure. Despite these extensive studies, the structure of P-IV remains unidentifi...

show abstract

“…In the range from 103 GPa to 137 GPa the structure Cmmm is stable [15]. Further, up to the pressure at 262 GPa, a simple hexagonal structure (sh) has been observed, whereas, for the pressure at p > 262 GPa, the stability of the body-centered cubic structure (bcc) has been noticed [15,16]. The superconducting state in phosphor was observed for the first time about fifty years ago [17,18].…”

Section: Superconducting Phase In Phosphor: the State Of Knowledgementioning

confidence: 99%

Characteristics of the Eliashberg Formalism on the Example of High-Pressure Superconducting State in Phosphor

et al. 2016

View full text Add to dashboard Cite

The work describes the properties of the high-pressure superconducting state in phosphor: p ∈ {20, 30, 40, 70} GPa. The calculations were performed in the framework of the Eliashberg formalism, which is the natural generalization of the BCS theory. The exceptional attention was paid to the accurate presentation of the used analysis scheme. With respect to the superconducting state in phosphor it was shown that the observed not-high values of the critical temperature ([TC] max p=30 GPa = 8.45 K) result not only from the low values of the electron-phonon coupling constant, but also from the very strong depairing Coulomb interactions. Additionally the inconsiderable strong-coupling and retardation effects force the dimensionless ratios R∆, RC, and RH -related to the critical temperature, the order parameter, the specific heat, and the thermodynamic critical field -to take the values close to the BCS predictions. Hamiltonian and fundamental equations of BCS model and Eliashberg formalismThe first microscopic theory of the superconducting state was formulated in 1957 by Bardeen, Cooper and Schrieffer (the so-called "BCS model") [1,2]. In the framework of the method of the second quantization the BCS Hamiltonian can be written with the following formula [3,4]:where the function ε k represents the electron band energy, V is the effective pairing potential, whose value is determined by the matrix elements of the electronphonon interaction, the electron band energy and the phonon energy. The symbols c † kσ and c kσ represent the creation and annihilation operator of the electron state in the momentum representation (k) for the spin σ ∈ {↑, ↓}. It should be noted that the sum denoted by the sign ought to be calculated only for those values of the momenta, for which the condition −Ω max < ε k < Ω max is fulfilled, where Ω max represents the Debye energy. In the considered case the effective pairing potential is positive, which allows the formation of the superconducting condensate. The fundamental equation of the BCS theory for the order parameter (∆ ≡ V k c −k↓ c k↑ ) is derived directly from Hamiltonian (1) using the mean field approximation to the interaction term. As a result the following can be obtained:) * corresponding author; e-mail: aduda@wip.pcz.pl where k B is the Boltzmann constant. Let us notice that Eq. (2) cannot be solved analytically. However, in the limit cases T → T C and T → 0 K the relatively simple calculations allow us to obtain the formulae for the critical temperature and the value of the order parameter k B T C = 1.13Ω max exp (−1/λ), ∆ (0) = 2Ω max exp (−1/λ). The electron-phonon coupling constant λ in the BCS model is given by λ ≡ ρ (0) V (the quantity ρ (0) represents the electron density of states on the Fermi surface). The BCS theory predicts the existence of the universal thermodynamic ratios, which are defined below:andThe symbols appearing in the formulae (4) and (5) denote respectively: C S -the specific heat of the superconducting state, C N -the specific heat of the normal state, and ...

show abstract

Structural stability and equation of state of simple-hexagonal phosphorus to 280 GPa: Phase transition at 262 GPa

Cited by 74 publications

References 20 publications

Raman anomalies as signatures of pressure induced electronic topological and structural transitions in black phosphorus: Experiments and theory

Raman anomalies as signatures of pressure induced electronic topological and structural transitions in black phosphorus: Experiments and theory

Determining the Structure of Phosphorus in Phase IV

Characteristics of the Eliashberg Formalism on the Example of High-Pressure Superconducting State in Phosphor

Contact Info

Product

Resources

About