Coexistence of a charge density wave and superconductivity in the cluster compound ${\mathrm{K}}_{2}\mathrm{M}{\mathrm{o}}_{15}\mathrm{S}{\mathrm{e}}_{19}$

Coexistence of a charge density wave and superconductivity in the cluster compound $K_{2} M o_{15} S e_{19}$

Christophe Candolfi, Martin Míšek, Patrick Gougeon, Rabih Al Rahal Al Orabi, Philippe Gall, Régis Gautier, Sylvie Migot, Jaafar Ghanbaja, Jiří Kaštil, Petr Levinský, Jiří Hejtmánek, Anne Dauscher, Bernard Malaman, and Bertrand Lenoir

Phys. Rev. B 101, 134521 – Published 29 April 2020

Abstract

The competition between charge density wave (CDW) and superconductivity is a central theme in condensed-matter physics with ramifications to correlated electron systems and high-temperature superconductivity. While the emergence of superconductivity is often observed upon suppressing the CDW transition by tuning the chemical composition or the external pressure, their coexistence has been reported in only a handful of materials, with the cuprates being the most prominent example. Here, we demonstrate that both cooperative electronic phenomena coexist in the cluster compound $K_{2} M o_{15} S e_{19}$ . The CDW transition sets in at $T_{CDW} = 114 K$ , accompanied by a commensurate periodic modulation of the crystal lattice along the $c$ axis evidenced by electron diffraction. Bulk type-II superconductivity develops upon further cooling below $T_{c} = 2.8 K$ . The presence of similar signatures of CDW ordering in other $A_{2} M o_{15} S e_{19}$ compounds shows that this electronic instability may be ubiquitous in these compounds, providing a novel family where the interplay between CDW and superconductivity may be systematically investigated.

Received 10 February 2020
Revised 23 March 2020
Accepted 25 March 2020

DOI:https://doi.org/10.1103/PhysRevB.101.134521

Physics Subject Headings (PhySH)

Charge density waves Superconductivity

Complex materials Low-temperature superconductors

Electron diffraction

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Christophe Candolfi ^1,*, Martin Míšek², Patrick Gougeon ^3,†, Rabih Al Rahal Al Orabi^4,5, Philippe Gall³, Régis Gautier ³, Sylvie Migot ¹, Jaafar Ghanbaja¹, Jiří Kaštil ², Petr Levinský², Jiří Hejtmánek ², Anne Dauscher ¹, Bernard Malaman¹, and Bertrand Lenoir ¹

¹Institut Jean Lamour, UMR 7198 CNRS–Université de Lorraine, Campus ARTEM, 2 allée André Guinier, Boîte Postale 50840, 54011 Nancy, France
²Institute of Physics, Czech Academy of Sciences, Cukrovarnická 10, 162 00 Praha 6, Czech Republic
³Université Rennes, INSA-ENSCR, CNRS, ISCR–UMR 6226, 35000 Rennes, France
⁴Solvay, Design and Development of Functional Materials Department, Axel’One, 87 avenue des Frères Perret, 69192 Saint Fons Cedex, France
⁵Department of Physics, Central Michigan University, Mt Pleasant, Michigan 48859, USA

^*christophe.candolfi@univ-lorraine.fr
^†patrick.gougeon@univ-rennes1.fr

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Vol. 101, Iss. 13 — 1 April 2020

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Figure 1
Left panel: View of the hexagonal crystal structure of $K_{2} M o_{15} S e_{19}$ (space group $R \bar{3} c$ , No. 167, $Z = 6, a = 9.7093 Å$ , and $c = 58.1385 Å$ at 300 K) along the $a$ axis showing the spatial arrangement of the $M o_{9} S e_{11}$ clusters interconnected by smaller $M o_{6} S e_{8}$ clusters. The K atoms are shown in light blue. The structure refinement details and crystallographic parameters determined by single-crystal x-ray diffraction at 300 K are given in Tables S1 and S2, respectively, in the Supplemental Material [61]. Right panel: Crystal structure projected along the $c$ axis. In both panels, the hexagonal unit cell is represented by the black solid lines.
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Figure 2
Experimental signatures of the charge-density-wave order in $K_{2} M o_{15} S e_{19}$ observed in the temperature dependence of the (a) electrical resistivity $ρ$ , (b) magnetization $M$ , (c) specific heat $C_{p}$ , and (d) thermopower $α .$ The crossing solid black lines show how the transition temperature $T_{CDW}$ was determined. In panel (b), the small hump seen around 50 K is presumably due to a small concentration of oxygen trapped in the measurement system.
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Figure 3
(a) HRTEM image obtained on single-crystalline $K_{2} M o_{15} S e_{19}$ taken along the [ $10 \bar{1} 0]$ zone axis at 300 K. Inset: electron diffraction pattern of the HRTEM image. (b) HAADF-STEM image taken along the [ $10 \bar{1} 0]$ zone axis at 300 K. The sublattice of Mo atoms, shown in dark blue, is overlaid. The inset shows the inverse fast-Fourier transform (IFFT) of the HAADF-STEM image. Electron diffraction patterns taken along the [ $10 \bar{1} 0]$ zone axis (c) at 300 K and (d) below the transition temperature $T_{CDW} = 114 K$ . The additional Bragg reflections due to the structural modulation below $T_{CDW}$ are clearly observed along $c^{*}$ , as shown by the vertical black arrows.
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Figure 4
Experimental signatures of bulk superconductivity in $K_{2} M o_{15} S e_{19}$ observed in the temperature dependence of (a) the electrical resistivity $ρ$ , (b) the specific heat $C_{p}$ , and (c) the magnetic susceptibility $χ$ . The drop in $ρ$ and $χ$ combined with the lambda-type anomaly in $C_{p}$ demonstrates that bulk superconductivity develops below $T_{c} = 2.8 K$ . The superconducting transition temperature $T_{c}$ was determined as the end point of the resistivity transition, that is, when $ρ$ reaches zero. The specific-heat data were measured down to 0.35 K and under applied magnetic fields of 1, 2, and 3 T. The zero-field-cooled (ZFC) temperature-dependent volume magnetic susceptibility $χ$ was measured under an applied field of 10 Oe. The data were corrected for a demagnetization factor $N = 0.456$ determined from the shape and geometry of the sample measured and the formula derived for a cuboid-shaped sample in Ref. [62].
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Figure 5
(a) Magnification around the Fermi level $E_{F}$ of the electronic dispersion curves of $K_{2} M o_{15} S e_{19}$ , calculated along high-symmetry directions in the Brillouin zone. In these calculations, spin-orbit coupling was not taken into account. The four bands crossing $E_{F}$ are shown as solid blue and orange curves and dotted black and green curves. (b) Perspective views and projection along the $c^{*}$ axis of the Fermi surface sheets of $K_{2} M o_{15} S e_{19}$ , calculated without spin-orbit coupling, shown separately for the four bands crossed by the Fermi level. The Fermi surface comprises holelike cylinders centered at the zone center (two first top panels), small electronlike pockets (middle panel), and an electronlike “monster” (penultimate panel). The total Fermi surface is shown in the last bottom panel.
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Physical Review B

covering condensed matter and materials physics

Coexistence of a charge density wave and superconductivity in the cluster compound $K_{2} M o_{15} S e_{19}$

Christophe Candolfi, Martin Míšek, Patrick Gougeon, Rabih Al Rahal Al Orabi, Philippe Gall, Régis Gautier, Sylvie Migot, Jaafar Ghanbaja, Jiří Kaštil, Petr Levinský, Jiří Hejtmánek, Anne Dauscher, Bernard Malaman, and Bertrand Lenoir

Phys. Rev. B 101, 134521 – Published 29 April 2020

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Physical Review B

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Coexistence of a charge density wave and superconductivity in the cluster compound K2Mo15Se19

Christophe Candolfi, Martin Míšek, Patrick Gougeon, Rabih Al Rahal Al Orabi, Philippe Gall, Régis Gautier, Sylvie Migot, Jaafar Ghanbaja, Jiří Kaštil, Petr Levinský, Jiří Hejtmánek, Anne Dauscher, Bernard Malaman, and Bertrand Lenoir

Phys. Rev. B 101, 134521 – Published 29 April 2020

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Coexistence of a charge density wave and superconductivity in the cluster compound $K_{2} M o_{15} S e_{19}$