Electron-hole balance and the anomalous pressure-dependent superconductivity in black phosphorus

Jing Guo, Honghong Wang, Fabian von Rohr, Wei Yi, Yazhou Zhou, Zhe Wang, Shu Cai, Shan Zhang, Xiaodong Li, Yanchun Li, Jing Liu, Ke Yang, Aiguo Li, Sheng Jiang, Qi Wu, Tao Xiang, Robert J. Cava, and Liling Sun

Phys. Rev. B 96, 224513 – Published 27 December 2017

Abstract

Here we report the in situ high-pressure (up to $\sim 50$ -GPa) Hall-effect measurements on single-crystal black phosphorus. We find a strong correlation between the sign of the Hall coefficient, an indicator of the dominant carrier type, and the superconducting transition temperature ( $T_{C}$ ). Importantly, we find a change from electron-dominant to hole-dominant carriers in the simple cubic phase of phosphorus at a pressure of $\sim 17.2$ GPa, providing an explanation for the puzzling valley it displays in its superconducting $T_{C}$ vs pressure phase diagram. Our results reveal that hole carriers play an important role in developing superconductivity in elemental phosphorus and the valley in $T_{C}$ at 18.8 GPa is associated with a Lifshitz transition.

Received 14 August 2017
Revised 23 October 2017

DOI:https://doi.org/10.1103/PhysRevB.96.224513

Physics Subject Headings (PhySH)

Superconductivity

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Jing Guo¹, Honghong Wang^1,5, Fabian von Rohr², Wei Yi¹, Yazhou Zhou^1,5, Zhe Wang^1,5, Shu Cai^1,5, Shan Zhang^1,5, Xiaodong Li³, Yanchun Li³, Jing Liu³, Ke Yang⁴, Aiguo Li⁴, Sheng Jiang⁴, Qi Wu¹, Tao Xiang^1,5,6, Robert J. Cava², and Liling Sun^1,5,6,*

¹Institute of Physics and Beijing National Laboratory for Condensed Matter Physics, Chinese Academy of Sciences, Beijing 100190, China
²Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
³Institute of High Energy Physics, Chinese Academy of Science, Beijing 100049, China
⁴Shanghai Synchrotron Radiation Facilities, Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201204, China
⁵University of Chinese Academy of Sciences, Beijing 100190, China
⁶Collaborative Innovation Center of Quantum Matter, Beijing 100190, China

^*Corresponding author: llsun@iphy.ac.cn

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Vol. 96, Iss. 22 — 1 December 2017

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Figure 1
Structural information for black phosphorus at ambient pressure and high pressure. (a) Experimental indexed x-ray diffraction patterns of black phosphorus at ambient pressure. The red crosses represent experimental data, and the green line and bars represent the calculated peak positions for the orthorhombic phase. The left inset is a scanning electron microscope (SEM) image of the as-grown black phosphorus single crystals. The right upper figure shows the crystal structure of orthorhombic black phosphorus. (b) Powder x-ray diffraction patterns of black phosphorus at different pressures (x-ray wavelength $= 0.6199 Å$ ), showing three structure phases up to 35 GPa. (c)–(e) Lattice parameters vs pressure in the $O$ , $R$ , and simple $C$ phases. (f) Pressure dependence of the atomic volume of black phosphorus.
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Figure 2
Electrical resistances at different pressures. (a)–(d) Electrical resistance as a function of temperature for single-crystal black phosphorus at different pressures. The insets display enlarged views of the resistance or normalized resistance in the lower temperature range around the superconducting transition.
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Figure 3
Diamagnetism of pressurized black phosphorous single crystals. (a) The real part of the alternating-current susceptibility (χ′) as a function of temperature at different pressures. The arrows denote the onset temperatures of the superconducting transitions. (b) Temperature dependence of electrical resistance of black phosphorous under different magnetic fields at 15.9 GPa.
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Figure 4
Structural, superconducting, and Hall coefficient ( $R_{H}$ ) phase diagram of black phosphorus at different pressures. (a) Pressure-temperature phase diagram combined with structural phase information. Here SM and ${SC}_{Rho − h}$ represent semimetal and superconducting phases with rhombohedral structures and dominant hole carriers, respectively. ${SC}_{cubic − e}$ and ${SC}_{cubic − h}$ stand for superconducting phase with cubic structure and dominance of electron carriers and hole carriers, respectively. $T_{C}^{onset} (R - 1)$ and $T_{C}^{onset} (R - 2)$ represent the onset temperature of superconducting transitions determined from resistance measurements for run 1 and run 2. $T_{C}$ (ac) represents the superconducting transition temperature determined by ac susceptibility measurements. (b) Pressure dependent $R_{H}$ measured at 15 K. The inset displays the detailed changes in $R_{H}$ at the structural phase-transition boundaries. The pink and blue solid points represent Hall coefficients obtained from two independent runs. $P_{c 1}$ and $P_{c 2}$ stand for the critical pressures of the Lifshitz transitions.
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Figure 5
Hall resistance ( $R_{x y}$ ) vs magnetic-field $(B)$ at 15 K and different pressures for black phosphorus single crystals. Plots of $R_{H} - B$ in the pressure range of (a) 0.4–2.3 GPa, (b) 2.3–9.6 GPa, (c) 9.6–15.5 GPa, and (d) 15.5–49.4 GPa. The inset of (b) displays the top view of the sample and the arrangements of electrode for our high-pressure Hall measurements in a diamond-anvil cell. The red square represents the black phosphorus single crystal, and the four white dashed triangles on the corners of the sample show the contact areas of the electrodes.
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