Projective quasiparticle interference of a single scatterer to analyze the electronic band structure of ZrSiS

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Projective quasiparticle interference of a single scatterer to analyze the electronic band structure of ZrSiS

Wenhao Zhang, Kunliang Bu, Fangzhou Ai, Zongxiu Wu, Ying Fei, Yuan Zheng, Jianhua Du, Minghu Fang, and Yi Yin

Phys. Rev. Research 2, 023419 – Published 30 June 2020

Abstract

Quasiparticle interference (QPI) of the electronic states has been widely applied in scanning tunneling microscopy to analyze the electronic band structure of materials. Single-defect-induced QPI reveals defect-dependent interaction between a single atomic defect and electronic states, which deserves special attention. Due to the weak signal of single-defect-induced QPI, the signal-to-noise ratio is relatively low in a standard two-dimensional QPI measurement. In this paper, we introduce a projective quasiparticle interference (PQPI) method in which a one-dimensional measurement is taken along high-symmetry directions centered on a specified defect. We apply the PQPI method to the topological nodal-line semimetal ZrSiS. We focus on two special types of atomic defects that scatter the surface and bulk electronic bands. With an enhanced signal-to-noise ratio in PQPI, the energy dispersions are clearly resolved along high-symmetry directions. We discuss the defect-dependent scattering of bulk bands with the nonsymmorphic symmetry-enforced selection rules. Furthermore, an energy shift of the surface floating band is observed, and a branch of energy dispersion ( $q_{6}$ ) is resolved. This PQPI method can be applied to other complex materials to explore defect-dependent interactions in the future.

Received 23 July 2019
Accepted 12 June 2020

DOI:https://doi.org/10.1103/PhysRevResearch.2.023419

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Topological phases of matter

Scanning tunneling spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Wenhao Zhang¹, Kunliang Bu¹, Fangzhou Ai¹, Zongxiu Wu¹, Ying Fei¹, Yuan Zheng¹, Jianhua Du¹, Minghu Fang^1,2, and Yi Yin ^1,2,*

¹Zhejiang Province Key Laboratory of Quantum Technology and Device, Department of Physics, Zhejiang University, Hangzhou 310027, China
²Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China

^*yiyin@zju.edu.cn

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Vol. 2, Iss. 2 — June - August 2020

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Images

Figure 1
(a) Crystal structure of ZrSiS, with a cleavage plane between S layers. The top view of the cleaved surface is shown on the right. The yellow, green, and blue dots represent S, Zr, and Si atoms, respectively. (b) The $25 \times 25 {nm}^{2}$ topography of ZrSiS taken under $I_{s} = 1$ nA and $V_{b} = 600$ mV. The two perpendicular white arrows represent lattice directions. (c) The average $d I / d V$ spectra at the top (red), bridge (orange), and hollow (black) sites in the supercell image (5.2 $\times$ 5.2 Å $^{2}$ ), which is shown in the inset. (d) Four different point defects in topography under the same bias voltage $V_{b} = 500$ mV.
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Figure 2
(a) The $16 \times 16 {nm}^{2}$ topography under $V_{b} = 300$ mV with defect 1 at the center. The orange and red line across the defect are along the lattice and diagonal directions, respectively. (b) The $d I / d V (V = 300 mV)$ map simultaneously taken with (a). (c) Fourier transform of the $d I / d V$ map in $q$ space. (d) A CCE model in $k$ space and (e) the calculated $q$ -space map following this CCE model. (f) and (g) QPI energy dispersions along the red and orange lines shown in (c).
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Figure 3
(a) Linecut measurement of $d I / d V$ spectrums along the red line in Fig. 2 for defect 1. (b) Fourier transform of the linecut measurement in (a). The maximum of the energy dispersion is guided by a red solid line and labeled $q_{3}$ . A red dashed line represents the absence of possible scattering of the $q_{4}$ branch. (c) Linecut measurement of $d I / d V$ spectra along the orange line in Fig. 2 for defect 1. (d) Fourier transform of the linecut measurement in (c). Maxima of two energy dispersions are guided with orange ( $q 1$ ) and black ( $q 6$ ) lines.
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Figure 4
(a) The $16 \times 16 {nm}^{2}$ topography under $V_{b} = 600$ mV with defect 2 at the center. (b) The $d I / d V (V = 300 mV)$ map simultaneously taken with (a). (c) Fourier transform of the $d I / d V$ map in $q$ space. (d) and (e) The energy dispersions along the $M − Γ − M$ direction. The result in (d) is extracted from a standard 2D $d I / d V$ map along the red line in (c). The result in (e) is extracted from a linecut measurement along the red line in (a). Two red guiding lines highlight the scattering of $q_{3}$ and $q_{4}$ branches. (f) and (g) The energy dispersions along the $X − Γ − X$ direction. The results are extracted from two different data sets similar to that described in (d) and (e). The orange dashed line represents the absence of possible scattering of the $q_{1}$ branch.
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Figure 5
(a)–(c) DFT calculation of the slab band structure along the $M − Γ − M, M − X − M$ , and $Γ − X − Γ$ directions in $k$ space. The blue, green, red, and orange dots represent $d_{x y}, d_{z^{2}}, d_{x z} / d_{y z}$ , and $d_{x^{2} - y^{2}}$ orbitals of Zr atoms, respectively. (d) and (e) Comparison of energy dispersions between the experimental result and the DFT calculation along the $M − Γ − M$ direction. (f) and (g) Comparison of two energy dispersions between the experimental result and the DFT calculation along $X − Γ − X$ direction for defect 1. The surface band has to be shifted 150 mV up to match the experimental result in (f).
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