Pressure-Sensitive Multiple Superconducting Phases and Their Structural Origin in Van der Waals ${\mathrm{HfS}}

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Pressure-Sensitive Multiple Superconducting Phases and Their Structural Origin in Van der Waals ${HfS}_{2}$ Up to 160GPa

Wei Zhong, He Zhang, Ertugrul Karaca, Jie Zhou, Saori Kawaguchi, Hirokazu Kadobayashi, Xiaohui Yu, Daniel Errandonea, Binbin Yue, and Fang Hong

Phys. Rev. Lett. 133, 066001 – Published 9 August 2024

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$Pressure-Sensitive Multiple Superconducting Phases and Their Structural Origin in Van der Waals ${\mathrm{HfS}}_{2}$ Up to 160 GPa (1)$

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$Pressure-Sensitive Multiple Superconducting Phases and Their Structural Origin in Van der Waals ${\mathrm{HfS}}_{2}$ Up to 160 GPa (2)$

Abstract

Superconductivity has been observed in many insulating transition metal dichalcogenides (TMDCs) under pressure. However, the origin of superconductivity remains elusive due to the lack of studies on their structures at low temperatures. Here, we report the observation of a high- $T_{c}$ superconducting state (SC-I phase) coexisting with other superconducting states in a compressed $1 T − {HfS}_{2}$ crystal up to approximately 160GPa. Insitu synchrotron x-ray diffraction results exclude the presence of decomposed sulfur and confirm two structural phase transitions at room temperature, as well as an additional transition at low temperature, which contribute to the emergence of multiple superconducting states. The SC-I phase exhibits an unsaturated $T_{c}$ of 16.4K at 158GPa, and demonstrates the highest upper critical field among the bulk TMDCs, $μ_{0} H_{c 2} (0) \approx 2 9.7 T$ for a $T_{c} \sim 1 5.2 K$ at 147GPa, exceeding the weak-coupling Pauli limit. These results reveal abundant SC properties together with sensitive structures in compressed ${HfS}_{2}$ , and thereby extend our understanding on TMDCs’ superconductivity.

$Pressure-Sensitive Multiple Superconducting Phases and Their Structural Origin in Van der Waals ${\mathrm{HfS}}_{2}$ Up to 160 GPa (3)$
$Pressure-Sensitive Multiple Superconducting Phases and Their Structural Origin in Van der Waals ${\mathrm{HfS}}_{2}$ Up to 160 GPa (4)$
$Pressure-Sensitive Multiple Superconducting Phases and Their Structural Origin in Van der Waals ${\mathrm{HfS}}_{2}$ Up to 160 GPa (5)$
$Pressure-Sensitive Multiple Superconducting Phases and Their Structural Origin in Van der Waals ${\mathrm{HfS}}_{2}$ Up to 160 GPa (6)$
$Pressure-Sensitive Multiple Superconducting Phases and Their Structural Origin in Van der Waals ${\mathrm{HfS}}_{2}$ Up to 160 GPa (7)$

Received 28 March 2024
Revised 25 June 2024
Accepted 3 July 2024

DOI:https://doi.org/10.1103/PhysRevLett.133.066001

Physics Subject Headings (PhySH)

Research Areas

High-pressure studiesPhase transitionsSuperconductivity

Physical Systems

Transition metal dichalcogenides

Techniques

X-ray powder diffraction

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Wei Zhong¹, He Zhang^2,3, Ertugrul Karaca^4,5, Jie Zhou^1,6, Saori Kawaguchi⁷, Hirokazu Kadobayashi⁷, Xiaohui Yu^2,3,8, Daniel Errandonea⁹, Binbin Yue^1,*, and Fang Hong^2,3,8,†

¹Center for High Pressure Science and Technology Advanced Research, 10 East Xibeiwang Road, Haidian, Beijing 100193, China
²Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
³School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
⁴Sakarya University, Biomedical, Magnetic, and Semiconductor Materials Research Center (BIMAS-RC), 54187 Sakarya, Turkey
⁵Center for Advanced Laser Techniques, Institute of Physics, 10000 Zagreb, Croatia
⁶Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, China
⁷SPring-8/JASRI, 1-1-1 Kouto, Sayo-gun, Sayo-cho, Hyogo 679-5198, Japan
⁸Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
⁹Departamento de Fisica Aplicada-ICMUV, MALTA Consolider Team, Universitat de Valencia, Avenue Doctor Moliner 50, 46100, Burjassot (Valencia), Spain

^*Contact author: yuebb@hpstar.ac.cn
^†Contact author: hongfang@iphy.ac.cn

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Vol. 133, Iss. 6 — 9 August 2024

$Pressure-Sensitive Multiple Superconducting Phases and Their Structural Origin in Van der Waals ${\mathrm{HfS}}_{2}$ Up to 160 GPa (8)$

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$Pressure-Sensitive Multiple Superconducting Phases and Their Structural Origin in Van der Waals ${\mathrm{HfS}}_{2}$ Up to 160 GPa (12)$
Figure 1
The electrical transport properties of ${HfS}_{2}$ under ultrahigh pressure. (a)The $R − T$ curves of superconductivity, from 78 to 158GPa. (b)The enlarged region of the SC transitions, and zero-resistance state can be seen clearly at 147 and 158GPa. The multistage drops of resistance indicate the possibility of multiple SC states, and different colored arrows show their $T_{c}$ .
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$Pressure-Sensitive Multiple Superconducting Phases and Their Structural Origin in Van der Waals ${\mathrm{HfS}}_{2}$ Up to 160 GPa (13)$
Figure 2
The magnetic field effect on the SC transition in ${HfS}_{2}$ at 147GPa. (a)The $R − T$ curves at various magnetic fields. (b)The relation between upper critical field and $T_{c}$ , fitting by the Ginzburg-Landau (G-L) formula and empirical formula $(EF) H_{c 2} (T) = H_{c 2} \times {(1 - T / T_{c})}^{1 + α}$ .
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$Pressure-Sensitive Multiple Superconducting Phases and Their Structural Origin in Van der Waals ${\mathrm{HfS}}_{2}$ Up to 160 GPa (14)$
Figure 3
High-pressure XRD results of ${HfS}_{2}$ at room temperature. (a)High-pressure powder XRD patterns obtained at 295K. Phase transition features are indicated by arrows. (b)The pressure dependent volume per formula ( $V / Z$ ) of three phases at 295K (trigonal $P \bar{3} m 1$ with a Z number of 1, orthorhombic $I m m m$ with a Z number of 4, tetragonal $I 4 / m m m$ with a Z number of 2). The curves were fitted by third-order Birch-Murnaghan equation of state.
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$Pressure-Sensitive Multiple Superconducting Phases and Their Structural Origin in Van der Waals ${\mathrm{HfS}}_{2}$ Up to 160 GPa (15)$
Figure 4
High-pressure XRD results of ${HfS}_{2}$ at low temperatures. (a)High-pressure powder XRD patterns obtained at 50K. (b)The XRD patterns obtained during the warming process at the highest pressure. The triangular and diamond symbols indicate peaks from platinum and rhenium, respectively. (c)The original diffraction patterns at 11K (154GPa) and 295K (165GPa), showing the phase transition features and the atomic structures of trigonal $R \bar{3} m$ and tetragonal $I 4 / m m m$ phases. To enhance the visual clarity, the diffraction peaks of $I 4 / m m m$ phase at 11K and 295K are aligned. The (103) peak in $I 4 / m m m$ phase is absent in $R \bar{3} m$ phase, and the (200) peak in $I 4 / m m m$ phase broadens toward lower diffraction angle at 11K.
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$Pressure-Sensitive Multiple Superconducting Phases and Their Structural Origin in Van der Waals ${\mathrm{HfS}}_{2}$ Up to 160 GPa (16)$
Figure 5
Proposed phase diagram of ${HfS}_{2}$ (a), and the summarized $T_{c}$ (b), and $μ_{0} H_{c 2} (0)$ (c) for different bulk TMDCs and sulfur. The $T_{c}$ of $S_{mag}$ and $S_{R T}$ are obtained from magnetic susceptibility and $R − T$ curves, respectively.
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