Inelastic Electron Tunneling in $2\mathrm{H}\text{\ensuremath{-}}{\mathrm{Ta}}_{x}{\mathrm{Nb}}_{1\ensuremath{-}x}{\mathrm{Se}}_{2}$ Evidenced by Scanning Tunneling Spectroscopy

Inelastic Electron Tunneling in $2 H − {Ta}_{x} {Nb}_{1 - x} {Se}_{2}$ Evidenced by Scanning Tunneling Spectroscopy

Xing-Yuan Hou, Fan Zhang, Xin-Hai Tu, Ya-Dong Gu, Meng-Di Zhang, Jing Gong, Yu-Bing Tu, Bao-Tian Wang, Wen-Gang Lv, Hong-Ming Weng, Zhi-An Ren, Gen-Fu Chen, Xiang-De Zhu, Ning Hao, and Lei Shan

Phys. Rev. Lett. 124, 106403 – Published 13 March 2020

Abstract

We report a detailed study of tunneling spectra measured on $2 H − {Ta}_{x} {Nb}_{1 - x} {Se}_{2}$ ( $x = 0 \sim 0.1$ ) single crystals using a low-temperature scanning tunneling microscope. The prominent gaplike feature, which has not been understood for a long time, was found to be accompanied by some “in-gap” fine structures. By investigating the second-derivative spectra and their temperature and magnetic field dependencies, we were able to prove that inelastic electron tunneling is the origin of these features and obtain the Eliashberg function of $2 H − {Ta}_{x} {Nb}_{1 - x} {Se}_{2}$ at an atomic scale, providing a potential way to study the local Eliashberg function and the phonon spectra of the related transition-metal dichalcogenides.

Received 30 October 2019
Revised 29 January 2020
Accepted 11 February 2020

DOI:https://doi.org/10.1103/PhysRevLett.124.106403

Physics Subject Headings (PhySH)

Electron-phonon coupling

Inelastic electron tunneling spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Xing-Yuan Hou^1,2, Fan Zhang^2,3, Xin-Hai Tu^5,4, Ya-Dong Gu^2,3, Meng-Di Zhang^2,3, Jing Gong^2,3, Yu-Bing Tu ¹, Bao-Tian Wang ⁵, Wen-Gang Lv², Hong-Ming Weng ^2,3, Zhi-An Ren^2,3, Gen-Fu Chen ^2,3, Xiang-De Zhu^4,*, Ning Hao^4,†, and Lei Shan ^1,2,3,‡

¹Key Laboratory of Structure and Functional Regulation of Hybrid Materials of Ministry of Education, Institutes of Physical Science and Information Technology, Anhui University, Hefei 230601, 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
⁴Anhui Province Key Laboratory of Condensed Matter Physics at Extreme Conditions, High Magnetic Field Laboratory, Chinese Academy of Sciences, Hefei 230031, China
⁵Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China

^*xdzhu@hmfl.ac.cn
^†haon@hmfl.ac.cn
^‡lshan@ahu.edu.cn

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Vol. 124, Iss. 10 — 13 March 2020

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Figure 1
(a) ( $31 \times 31$ )-nm topographic STM image of $2 H − {NbSe}_{2}$ single crystal cold-cleaved in situ. It was taken with a sample-tip voltage of 50 mV and tunneling current of 100 pA. Inset shows the Fourier transform of the atomically resolved image; atomic peaks and CDW wave vectors are indicated by red and blue arrows, respectively. (b) ( $15 \times 15$ )-nm topographic STM image of $2 H − {Ta}_{0.02} {Nb}_{0.98} {Se}_{2}$ single crystal. It was taken with a sample-tip voltage of 50 mV and tunneling current of 50 pA. (c) Large-energy-range tunneling spectrum of $2 H − {NbSe}_{2}$ measured at temperature below $T_{CDW}$ . The well-known 35-mV inflexion points are marked by arrows. (d) Tunneling spectrum of $2 H − {NbSe}_{2}$ measured below $T_{c}$ showing a clear superconducting gap.
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Figure 2
(a) Low-temperature tunneling spectra obtained on $2 H − {Ta}_{x} {Nb}_{1 - x} {Se}_{2}$ single crystals with different doping levels ( $x$ ). Spectra are normalized and shifted for clarity. All the features of shoulders or steps are marked by arrows. (b) Schematic of inelastic electron tunneling process taking place at a STM-based vacuum tunneling junction, in which $ℏ ω$ is phonon energy and $e V$ the energy difference between tip and sample. (c)–(e) Illustrative inelastic electron tunneling spectra of $I - V$ , $d I / d V - V$ , and $d^{2} I / d V^{2} - V$ , respectively, where two phonon modes are involved and indicated by arrows.
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Figure 3
(a) Spectra of $d^{2} I / d V^{2}$ derived from data in Fig. 2. The most prominent phonon modes are marked by vertical lines, almost irrelevant regarding the doping levels. Differences between the features of the positive- and negative-bias parts are most likely due to particle-hole asymmetry in the electron DOS. (b) Comparison of low-temperature spectra measured in the superconducting state and normal state with $H = 0$ and 8 T, respectively. Data were taken on sample with $x = 0.02$ . (c)–(e) Comparison between experimental data and calculated phonon DOS and Eliashberg function $α^{2} F (ω)$ . Positive- and negative-bias parts of measured spectra have been averaged and calculated curves have been smoothed to match energetic resolution of measurements.
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Figure 4
(a) Temperature evolution of $d^{2} I / d V^{2}$ spectra measured at $1.8 \sim 8 K$ (from bottom up). Top curve of 8 K (red) is overlapped with that taken at same temperature while under 8 T (black). (b) Temperature dependence of spectral weight integrated from 10 to 45 mV, as illustrated by the shadow in (a). (c) Temperature dependence of a peak intensity indicated by two-way arrow in (a). The two sets of data obtained at 0 and 8 T begin to diverge at $T_{c}$ with decreasing temperature. Dashed and solid lines are simulations considering a single Fermi-Dirac broadening and a double one, respectively. Inset illustrates the Fermi-Dirac broadening function.
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Figure 5
(a) Large-scale topographic image containing a step across the entire region. A trajectory of 21 nm is indicated by red arrow with its section profile plotted under the image, along which both superconducting spectra and $d^{2} I / d V^{2}$ spectra were taken sequentially at 64 evenly spaced points as given in (b) and (c), respectively. All data were obtained at 2.4 K. (d) Comparison of data taken at the step and far from it.
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Physical Review Letters

Inelastic Electron Tunneling in 2H−TaxNb1−xSe2 Evidenced by Scanning Tunneling Spectroscopy

Xing-Yuan Hou, Fan Zhang, Xin-Hai Tu, Ya-Dong Gu, Meng-Di Zhang, Jing Gong, Yu-Bing Tu, Bao-Tian Wang, Wen-Gang Lv, Hong-Ming Weng, Zhi-An Ren, Gen-Fu Chen, Xiang-De Zhu, Ning Hao, and Lei Shan

Phys. Rev. Lett. 124, 106403 – Published 13 March 2020

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Inelastic Electron Tunneling in $2 H − {Ta}_{x} {Nb}_{1 - x} {Se}_{2}$ Evidenced by Scanning Tunneling Spectroscopy