Superconductivity in ${\mathrm{PtPb}}_{4}$ with possible nontrivial band topology

Superconductivity in ${PtPb}_{4}$ with possible nontrivial band topology

C. Q. Xu, B. Li, L. Zhang, J. Pollanen, X. L. Yi, X. Z. Xing, Y. Liu, J. H. Wang, Zengwei Zhu, Z. X. Shi, Xiaofeng Xu, and X. Ke

Phys. Rev. B 104, 125127 – Published 17 September 2021

Abstract

Superconductivity in topological quantum materials is much sought after, as it represents the key avenue to searching for topological superconductors, which host a full pairing gap in the bulk but Majorana bound states at the surface. To date, however, the simultaneous realization of nontrivial band topology and superconductivity in the same material under ambient conditions remains rare. In this paper, we study both superconducting and topological properties of the binary compound ${PtPb}_{4}$ $(T_{c} \sim 2.7 K)$ that was recently reported to exhibit large Rashba splitting, inherent to the heavy $5 d$ Pt and $6 p$ Pb. We show that in ${PtPb}_{4}$ , the specific heat jump at $T_{c}$ reaches $Δ C / γ T_{c} \sim 1.70 \pm 0.04$ , larger than the 1.43 expected for weak-coupling BCS superconductors. Moreover, the measurement of quantum oscillation suggests the possibility of a topological band structure, which is further studied by density functional theory calculations. Our study may stimulate future experimental and theoretical investigations in this intriguing material.

Received 4 March 2021
Accepted 13 September 2021

DOI:https://doi.org/10.1103/PhysRevB.104.125127

Physics Subject Headings (PhySH)

First-principles calculations Topological materials de Haas-van Alphen effect

Superconductors

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

C. Q. Xu^1,2, B. Li ³, L. Zhang², J. Pollanen ², X. L. Yi¹, X. Z. Xing¹, Y. Liu⁴, J. H. Wang ⁵, Zengwei Zhu⁵, Z. X. Shi^1,*, Xiaofeng Xu ^4,†, and X. Ke^2,‡

¹School of Physics and Key Laboratory of MEMS of the Ministry of Education, Southeast University, Nanjing 211189, China
²Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824-2320, USA
³Information Physics Research Center, Nanjing University of Posts and Telecommunications, Nanjing 210023, China
⁴Key Laboratory of Quantum Precision Measurement of Zhejiang Province, Department of Applied Physics, Zhejiang University of Technology, Hangzhou 310023, China
⁵Wuhan National High Magnetic Field Center, School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China

^*zxshi@seu.edu.cn
^†xuxiaofeng@zjut.edu.cn
^‡kexiangl@msu.edu

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Vol. 104, Iss. 12 — 15 September 2021

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Figure 1
(a) The optical view of a single crystal used in this study. (b) Energy-dispersive x-ray spectroscopy of a typical sample. (c) Schematic crystal structure of ${PtPb}_{4}$ . (d) X-ray diffraction pattern from the basal plane of a cleaved crystal, showing only (0 $l$ 0) reflections.
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Figure 2
(a) $T$ dependence of resistivity measured under zero magnetic field. Inset: Magnetic susceptibility as a function of temperature at a field of $H$ = 10 Oe in the zero-field-cooled (ZFC) and field-cooled (FC) modes, respectively. (b) The heat capacity $C_{p}$ divided by the temperature $T$ as a function of $T^{2}$ at low temperatures. The solid red line shows the fit to the data described in the text. Inset: $Δ C / T$ versus $T$ , where $Δ C = C - C_{n}$ , with $C_{n}$ being the heat capacity of the normal state. (c) Temperature dependence of the lower critical field $H_{c 1}$ extracted from the inset. The solid red line is the fit using the Ginzburg-Landau (GL) formula. (d) $T$ dependence of the upper critical field $H_{c 2}$ and its fit with the Werthamer-Helfand-Hohenberg (WHH) formula. Inset: The resistivity measured at various magnetic fields.
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Figure 3
Temperature dependence of resistivity at some selected fields. Inset: An enlarged view of the low-temperature region. (b) The MR at some fixed temperatures. Inset: The corresponding plot of Kohler's rule. (c) The Hall resistivity $ρ_{y x}$ at some selected temperatures. (d) The Hall conductivity ( $σ_{x y}$ ) at the same temperatures as indicated in (c). (e) The fits of electrical conductivity $σ_{x x}$ and Hall conductivity $σ_{x y}$ by the two-band model at 5 K. (f) The carrier density and the mobility vs $T$ extracted based on the two-band fitting.
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Figure 4
(a) Oscillatory signals $Δ M$ vs magnetic field $B$ at some selected temperatures after subtracting the background. (b) Fast Fourier transform (FFT) spectra of $Δ M$ oscillations. The asterisk marks the weak peak whose origin is not clear. (c) $T$ dependence of the FFT amplitude. The solid lines are fits to obtain the effective mass for each frequency. (d) The two-band Lifshitz-Kosevich (LK) fitting to the data measured at 1.9 K. (e) The $α$ -band and $β$ -band oscillations were extracted using the FFT filter and fitted with the single-band LK formula. (f) The Landau's fan diagram for $α$ and $β$ . Inset: Enlargement of the interception. (g) Angular dependence of the FFT frequency at 1.9 K. Inset: The rotation schematic diagram. (h) Angular dependence of the FFT frequency from both experiment and calculations. The colors of the $α$ , $β$ , $γ$ , and $δ$ bands are coded per their most likely bands.
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Figure 5
(a) Calculated band structure for orthorhombic ${PtPb}_{4}$ with SOC included. Bands crossing the Fermi level are marked by different colors and labeled by numbers. (b) The Brillouin zone with the high-symmetry points specified. (c–f) The 3D Fermi surfaces for each band. The extremal orbits are illustrated by lines for bands 1–3 when the magnetic field is applied along the $b$ axis.
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Physical Review B

covering condensed matter and materials physics

Superconductivity in ${PtPb}_{4}$ with possible nontrivial band topology

C. Q. Xu, B. Li, L. Zhang, J. Pollanen, X. L. Yi, X. Z. Xing, Y. Liu, J. H. Wang, Zengwei Zhu, Z. X. Shi, Xiaofeng Xu, and X. Ke

Phys. Rev. B 104, 125127 – Published 17 September 2021

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Physical Review B

covering condensed matter and materials physics

Superconductivity in PtPb4 with possible nontrivial band topology

C. Q. Xu, B. Li, L. Zhang, J. Pollanen, X. L. Yi, X. Z. Xing, Y. Liu, J. H. Wang, Zengwei Zhu, Z. X. Shi, Xiaofeng Xu, and X. Ke

Phys. Rev. B 104, 125127 – Published 17 September 2021

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Superconductivity in ${PtPb}_{4}$ with possible nontrivial band topology