Superconductivity of Ca Exceeding 25 K at Megabar Pressures

Yabuuchi, Takahiro; Matsuoka, Toshifumi; Nakamoto, Yuki; Shimizu, Katsuya

doi:10.1143/jpsj.75.083703

Cited by 132 publications

(127 citation statements)

References 17 publications

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“…7 Very recently an increase of the superconducting transition temperature T c in the high-pressure phases has also been reported, i.e., 25 K at 161 GPa in Ca-V, which is the highest recorded for an element. 8 This result has attracted much interest in relation to pressure-induced electronic s-d transfer and the increase of the superconducting T c with pressure, which has been discussed also in Sr and Ba under pressure. [9][10][11] Information about the structures of Ca-IV and Ca-V is crucial for the clarification of the high T c in calcium.…”

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confidence: 95%

Theoretical study of the structure of calcium in phases IV and V viaab initiometadynamics simulation

et al. 2008

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We searched for the structure of calcium in phases IV and V by a metadynamics simulation based on ab initio calculations, and found two structures. One is a tetragonal lattice which consists of two helical chains along the c axis. The other is an orthorhombic lattice of four zigzag chains. We have calculated the x-ray diffraction patterns and enthalpies of the two structures discovered by our simulation. From comparisons of the patterns with the experimental x-ray patterns of the phases IV and V and from the pressure dependence of the enthalpies, we conclude that the structure with a helical pattern corresponds to phase IV and the structure with a zigzag pattern to phase V. Studies have revealed that many elements have complex structures with low symmetry at high pressures; McMahon and Nelmes have reviewed complex lattice structures of elements under high pressure. 1 Some elements have interesting structures beyond the simple cubic ͑sc͒ lattice at high pressure. Phosphorus has the sc structure ͑P-III͒ from 10 to 107 GPa, 2 which transforms, at 107 GPa, to a complex structure 3 ͑P-IV͒ whose structure has long been unidentified. But it has recently been theoretically predicted 4 and experimentally confirmed 5 to be an incommensurately modulated structure.Another example is calcium, which shows interesting successive structural phase transitions under pressure, where the transitions are from a closest-packed to a less close-packed structure. The fcc structure at ambient pressure transforms to the bcc at 20 GPa and then to the sc structure ͑Ca-III͒ at 32 GPa. 6 In 2005 Yabuuchi et al. pressurized calcium further and observed new structural phase transitions. 7 The sc transforms to phase IV ͑Ca-IV͒ at 113 GPa and then to phase V ͑Ca-V͒ at 139 GPa. 7 Very recently an increase of the superconducting transition temperature T c in the high-pressure phases has also been reported, i.e., 25 K at 161 GPa in Ca-V, which is the highest recorded for an element. 8 This result has attracted much interest in relation to pressure-induced electronic s-d transfer and the increase of the superconducting T c with pressure, which has been discussed also in Sr and Ba under pressure. [9][10][11] Information about the structures of Ca-IV and Ca-V is crucial for the clarification of the high T c in calcium.In this work, we have explored the crystal structures of Ca-IV and Ca-V using an ab initio metadynamics simulation 12 in which we employed density functional theory in the generalized gradient approximation ͑GGA͒. Metadynamics is a method used to find neighboring local minima by filling the potential wells with an artificial Gaussian potential ͑GP͒. To avoid rigid rotation of the system, we treated only the symmetric part of the cell matrix defined by h = ͑a ជ , b ជ , c ជ͒, where a ជ, b ជ , and c ជ are the lattice vectors. We update the simulation cell by the steepest-descent method with a stepping parameter ␦h: h ij t+1 = h ij t + ␦hF ij t / ͉F ij t ͉, where t is the number of updates of h and F is the driving force for the update. If we...

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Theoretical study of the structure of calcium in phases IV and V viaab initiometadynamics simulation

et al. 2008

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“…However, if we consider the pressure dependence of the electrical resistance in figure 4 of ref. 19, the pressures at which the electrical resistance changes drastically are shifted to lower values with respect to the phase boundaries. These changes may correspond to the onset of the structural phase transition.…”

Section: Resultsmentioning

confidence: 96%

Prediction of incommensurate crystal structure in Ca at high pressure

Arapan

Mao

Ahuja

2008

Proc. Natl. Acad. Sci. U.S.A.

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Ca shows an interesting high-pressure phase transformation sequence, but, despite similar physical properties at high pressure and affinity in the electronic structure with its neighbors in the periodic table, no complex phase has been identified for Ca so far. We predict an incommensurate high-pressure phase of Ca from first principle calculations and describe a procedure of estimating incommensurate structure parameters by means of electronic structure calculations for periodic crystals. Thus, by using the ab initio technique for periodic structures, one can get not only reliable information about the electronic structure and structural parameters of an incommensurate phase, but also identify and predict such phases in new elements.ab initio calculations ͉ alkali metals T he continuous improvement of the high-pressure technique and the advances in the methods of characterization of materials under high pressure have opened new perspectives for materials physics community. The discovery of a series of phases for periodic table elements within the explored interval of pressures (1, 2) have stimulated an increased interest from both experimentalists and theoreticians to understand the unexpected behavior of simple elements under high pressure. Within the alkali and earth-alkaline metals, a series of complex structures at high pressure have been identified and, in particular, the complex phases of Ba-IV (3), Sr-V (4), Rb-IV (5), and K-III (6) have been determined as composite host-guest structures, which are incommensurate along the common axis of host and guest sub-lattices. The occurrence of such complex composite structures in a large number of elements and the robustness of these complex phases over a wide range of pressures and temperatures make the existence of composite incommensurate structures an intrinsic high-pressure phenomenon. Therefore, other elements may undergo similar high-pressure phase transitions. The nature of the transition to a composite structure is not completely understood yet, partly, because such an essential theoretical tool for describing the condensed matter as electronic structure calculations cannot be directly applied to study an incommensurate structure. However, one can perform first-principles calculations on commensurate analogues of an incommensurate phase and, indeed, such calculations can reproduce the phase transition sequence in close agreement with the experiment and provide reliable information about the electronic structure (7,8). Ab initio calculations of Ba-IV commensurate analogue (7) suggest that the transition from a closed, packed structure at low pressure to a more open, complex structure at high pressure might be because of the transfer of electrons from free-electron like s-bands to more directional d-bands. In the Ba-IV phase, the sd-hybridization occurs between the orbitals of two nonequivalent Ba atoms: guest atoms with a more d-like character and host atoms with a more s-like character. Therefore, from the electronic structure perspective, the composite s...

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“…The dramatic drop in the electrical resistance at around 109 GPa is also consistent with a transition from a locally disordered phase to a crystalline material. 9 In the pressure range of 110-140 GPa, the P4 3 2 1 2, Cmca, and Pnma structures become quasidegenerate again. Linear response calculations of the Pnma structure at 120 GPa and above, and of the Cmca structure at around 130 GPa indeed show strong coupling with λ > 1.0 in all the cases.…”

Section: Stability and Lattice Dynamicsmentioning

confidence: 95%

“…So far the higher pressure phases Ca-IV and Ca-V have attracted the most attention, and considerable progress has been made in identifying these phases through a combination of experimental 9,22,23 and theoretical 24,25,26 work. However, satisfactory agreement between experimental and theoretical work is still lacking.…”

Section: Comparison To Related Metalsmentioning

confidence: 99%

Competing phases, strong electron-phonon interaction, and superconductivity in elemental calcium under high pressure

Gygi

Pickett

2009

Phys. Rev. B

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The observed "simple cubic" (sc) phase of elemental Ca at room temperature in the 32-109 GPa range is, from linear response calculations, dynamically unstable. By comparing first principle calculations of the enthalpy for five sc-related (non-close-packed) structures, we find that all five structures compete energetically at room temperature in the 40-90 GPa range, and three do so in the 100-130 GPa range. Some competing structures below 90 GPa are dynamically stable, i.e., no imaginary frequency, suggesting that these sc-derived short-range-order local structures exist locally and can account for the observed (average) "sc" diffraction pattern. In the dynamically stable phases below 90 GPa, some low frequency phonon modes are present, contributing to strong electron-phonon (EP) coupling as well as arising from the strong coupling. Linear response calculations for two of the structures over 120 GPa lead to critical temperatures in the 20-25 K range as is observed, and do so without unusually soft modes.

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Superconductivity of Ca Exceeding 25 K at Megabar Pressures

Cited by 132 publications

References 17 publications

Theoretical study of the structure of calcium in phases IV and V viaab initiometadynamics simulation

Theoretical study of the structure of calcium in phases IV and V viaab initiometadynamics simulation

Prediction of incommensurate crystal structure in Ca at high pressure

Competing phases, strong electron-phonon interaction, and superconductivity in elemental calcium under high pressure

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