Competition of charge-density waves and superconductivity in sulfur

Crucial Role of S8-Rings in Structural, Relaxation, Vibrational and Electronic Properties of LiquidSulfur close to the λ Transition

Liquid sulfur has been studied by density-functional based molecular-dynamics simulations at different temperatures ranging from 400 K up to 700 K across the well-documented λ-transition. Structure models containing either a majority of Sn chains or S8 rings are considered and compared to experimental data from X-ray scattering. The comparison suggests a liquid structure of a majority of 2-fold sulfur at low temperature, dominated by S8 rings that open progressively upon temperature increase. Typical features associated with such rings are analyzed and indicate that they contribute to a specific third correlating distance in the pair correlation function and to a contribution at low wavevector k in reciprocal space. The vibrational properties of liquid sulfur are also considered and indicate a contribution at 60 meV that is associated with both chains and rings, albeit the latter lead to a more intense peak at this wavenumber. The underlying network structure also impacts the dynamic properties of the melts which display enhanced dynamic heterogeneities when S8 rings are present. The analysis of the electronic Kohn-Sham energies shows insulating character with a gap of about ≃2.0 eV, albeit the presence of localized mid-gap states is acknowledged that can be associated, in part, with the presence of S6rings.

Disproportionation of SO_{2} at High Pressure and Temperature

Materials once suffered at high-pressure and high-temperature (HPHT) conditions often exhibit exotic phenomena that defy conventional wisdom. The behaviors of sulfur dioxide (SO_{2}), one of the archetypal simple molecules, at HPHT conditions have attracted a great deal of attention due to its relevance to the S cycle between deep Earth and the atmosphere. Here we report the discovery of an unexpected disproportionation of SO_{2} via bond breaking into elemental S and sulfur trioxide (SO_{3}) at HPHT conditions through a jointly experimental and theoretical study. Measured x-ray diffraction and Raman spectroscopy data allow us to solve unambiguously the crystal structure (space group R3[over ¯]c) of the resultant SO_{3} phase that shows an extended framework structure formed by vertex-sharing octahedra SO_{6}. Our findings lead to a significant extension of the phase diagram of SO_{2} and suggest that SO_{2}, despite its abundance in Earth's atmosphere and ubiquity in other giant planets, is not a stable compound at HPHT conditions relevant to planetary interiors, providing important implications for elucidating the S chemistry in deep Earth and other giant planets.

Probing extreme states of matter using ultra-intense x-ray radiation

Extreme states of matter, that is, matter at extremes of density (pressure) and temperature, can be created in the laboratory either statically or dynamically. In the former, the pressure-temperature state can be maintained for relatively long periods of time, but the sample volume is necessarily extremely small. When the extreme states are generated dynamically, the sample volumes can be larger, but the pressure-temperature conditions are maintained for only short periods of time (ps toμs). In either case, structural information can be obtained from the extreme states by the use of x-ray scattering techniques, but the x-ray beam must be extremely intense in order to obtain sufficient signal from the extremely-small or short-lived sample. In this article I describe the use of x-ray diffraction at synchrotrons and XFELs to investigate how crystal structures evolve as a function of density and temperature. After a brief historical introduction, I describe the developments made at the Synchrotron Radiation Source in the 1990s which enabled the almost routine determination of crystal structure at high pressures, while also revealing that the structural behaviour of materials was much more complex than previously believed. I will then describe how these techniques are used at the current generation of synchrotron and XFEL sources, and then discuss how they might develop further in the future at the next generation of x-ray lightsources.

Pressure-induced structural transitions between successional superconducting phases in GeTe

Being a best-known prototype of phase-change materials, GeTe was reported to possess many high-pressure phases, whose structural evolution and superconductivity remain under debate for decades. Herein, we systematically investigated the pressure dependence of electrical transport and the structural evolution of the GeTe viain situangle-dispersive synchrotron x-ray diffraction and resistance measurements up to 55 GPa. At room temperature, the structural phase transitions from the initial rhombohedral phase to theFm3̄mphase, and then to an orthorhombicPnmaphase, were observed at pressures of about 4 and 13.4 GPa, respectively. Furthermore, the metallization occurred at around 11 GPa, where the superconductivity could also be observed. With increasing pressure, the superconducting transition temperature increases monotonically from 5.7 to 6.4 K and then is independent of pressure above 23 GPa in the purePnmaphase. These results provide insights into the pressure-dependent evolution of the structure and superconductivity in GeTe and have implications for the understanding of other IV-VI semiconductors at high pressure.

Novel superconducting skutterudite-type phosphorus nitride at high pressure from first-principles calculations

State of the art variable composition structure prediction based on density functional theory demonstrates that two new stoichiometries of PN, PN3 and PN2, become viable at high pressure. PN3 has a skutterudite-like Immm structure and is metastable with positive phonon frequencies at pressures between 10 and 100 GPa. PN3 is metallic and is the first reported nitrogen-based skutterudite. Its metallicity arises from nitrogen p-states which delocalise across N4 rings characteristic of skutterudites, and it becomes a good electron-phonon superconductor at 10 GPa, with a Tc of around 18 K. The superconductivity arises from strongly enhanced electron-phonon coupling at lower pressures, originating primarily from soft collective P-N phonon modes. The PN2 phase is an insulator with P2/m symmetry and is stable at pressures in excess of 200 GPa.

The effect of lithium intercalation on the electronic structure of the ternary compound semiconductors ZrSe(2-x)S(x)

The electronic properties of the lithium intercalated layered transition metal dichalcogenide semiconductors ZrS(x)Se(2-x) for x = 0-2 have been calculated by density functional theory (DFT) using the WIEN2k code. The calculations have been carried out by the PBE functional and the TB-MBJ potential as proposed by Tran and Blaha. The calculations have been performed with and without spin-orbit coupling and reveal that the intercalation of lithium causes the conduction bands of LiZrS(x)Se(2-x) to shift by about 2 eV towards lower binding energy. From this, a Fermi level crossing and metallic behavior in the three intercalated compounds result. Moreover, a number of trends can be observed. Due to the contributions of the dichalcogenide p-states in the valence band the inclusion of SO coupling in the calculations lifts the degeneracy at the points Γ and A of the Brillouin zone in the same way as in the parent compounds. With regard to crystal field effects for each compound the splitting is larger at the A point than at the Γ point and the absolute value of the splitting increases with the atomic number of the chalcogenide. In particular, the simple Fermi surface consisting solely of barrels centered along the LML line makes LiZrS(x)Se(2-x) a promising Fermi liquid reference compound.

Pressure- and composition-induced structural quantum phase transition in the cubic superconductor (Sr, Ca)3Ir4Sn13

We show that the quasi-skutterudite superconductor Sr(3)Ir(4)Sn(13) undergoes a structural transition from a simple cubic parent structure, the I phase, to a superlattice variant, the I' phase, which has a lattice parameter twice that of the high temperature phase. We argue that the superlattice distortion is associated with a charge density wave transition of the conduction electron system and demonstrate that the superlattice transition temperature T(*) can be suppressed to zero by combining chemical and physical pressure. This enables the first comprehensive investigation of a superlattice quantum phase transition and its interplay with superconductivity in a cubic charge density wave system.

Understanding the complex phase diagram of uranium: the role of electron-phonon coupling

We report an experimental determination of the dispersion of the soft phonon mode along [100] in uranium as a function of pressure. The energies of these phonons increase rapidly, with conventional behavior found by 20 GPa, as predicted by recent theory. New calculations demonstrate the strong pressure (and momentum) dependence of the electron-phonon coupling, whereas the Fermi-surface nesting is surprisingly independent of pressure. This allows a full understanding of the complex phase diagram of uranium and the interplay between the charge-density wave and superconductivity.

High-pressure crystallography

The ability of pressure to change inter-atomic distances strongly leads to a wide range of pressure-induced phenomena at high pressures: for example metallisation, amorphisation, superconductivity and polymerisation. Key to understanding these phenomena is the determination of the crystal structure using x-ray or neutron diffraction. The tools necessary to compress matter above 1 million atmospheres (1 Megabar or 100 GPa) were established by the mid 1970s, but it is only since the early 1990s that we have been able to determine the detailed crystal structures of materials at such pressures. In this chapter I briefly review the history of high-pressure crystallography, and describe the techniques used to obtain and study materials at high pressure. Recent crystallographic studies of elements are then used to illustrate what is now possible using modern detectors and synchrotron sources. Finally, I speculate as to what crystallographic studies might become possible over the next decade.

Origin of the incommensurate modulation in Te-III and fermi-surface nesting in a simple metal

Inelastic x-ray scattering experiments have been performed on incommensurately modulated Te-III at high pressure and reveal a pronounced phonon anomaly. The anomaly is reproduced in first-principles lattice dynamics calculations of unmodulated, body-centered monoclinic (bcm) Te, which is shown to be dynamically unstable. The calculated Fermi surface of bcm Te exhibits surprisingly effective nesting for a simple, electronically three-dimensional metal. The combined experimental and theoretical results corroborate recent proposals that the modulated crystal structure of Te-III and other chalcogens is the manifestation of a pressure-induced charge-density wave state.

Structural transition in compressed amorphous sulfur

Properties of amorphous sulfur (a-S) were investigated by synchrotron x-ray diffraction up to 100 GPa between 40 and 175 K. Measurements of the structure factor yielded the radial distribution function and the densities of two amorphous forms. a-S undergoes a structural transition above 65 GPa, accompanied by density discontinuity of 7%. These results indicate the amorphous-amorphous transition, from a low-density to a high-density form, and open up the possibility for the direct measurements of density of liquid-amorphous materials at extreme conditions.