Intrinsic nature of chiral charge order in the kagome superconductor $\mathrm{Rb}{\mathrm{V}}_{3}{\mathrm{Sb}}_{5}$

Intrinsic nature of chiral charge order in the kagome superconductor $Rb V_{3} {Sb}_{5}$

Nana Shumiya, Md. Shafayat Hossain, Jia-Xin Yin, Yu-Xiao Jiang, Brenden R. Ortiz, Hongxiong Liu, Youguo Shi, Qiangwei Yin, Hechang Lei, Songtian S. Zhang, Guoqing Chang, Qi Zhang, Tyler A. Cochran, Daniel Multer, Maksim Litskevich, Zi-Jia Cheng, Xian P. Yang, Zurab Guguchia, Stephen D. Wilson, and M. Zahid Hasan

Phys. Rev. B 104, 035131 – Published 15 July 2021

Abstract

Superconductors with kagome lattices have been identified for over 40 years, with a superconducting transition temperature $T_{c}$ up to 7 K. Recently, certain kagome superconductors have been found to exhibit an exotic charge order, which intertwines with superconductivity and persists to a temperature being one order of magnitude higher than $T_{c}$ . In this work, we use scanning tunneling microscopy to study the charge order in kagome superconductor $Rb V_{3} {Sb}_{5}$ . We observe both a $2 \times 2$ chiral charge order and nematic surface superlattices (predominantly $1 \times 4$ ). We find that the $2 \times 2$ charge order exhibits intrinsic chirality with magnetic field tunability. Defects can scatter electrons to introduce standing waves, which couple with the charge order to cause extrinsic effects. While the chiral charge order resembles that discovered in $K V_{3} {Sb}_{5}$ , it further interacts with the nematic surface superlattices that are absent in $K V_{3} {Sb}_{5}$ but exist in $Cs V_{3} {Sb}_{5}$ .

Received 2 May 2021
Accepted 6 July 2021

DOI:https://doi.org/10.1103/PhysRevB.104.035131

Physics Subject Headings (PhySH)

Charge density waves Electronic structure Topological materials

Scanning tunneling microscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Nana Shumiya^1,*, Md. Shafayat Hossain ^1,*, Jia-Xin Yin ^1,*,†, Yu-Xiao Jiang^1,*, Brenden R. Ortiz², Hongxiong Liu^3,4, Youguo Shi^3,4, Qiangwei Yin⁵, Hechang Lei⁵, Songtian S. Zhang ¹, Guoqing Chang ⁶, Qi Zhang¹, Tyler A. Cochran¹, Daniel Multer¹, Maksim Litskevich ¹, Zi-Jia Cheng¹, Xian P. Yang¹, Zurab Guguchia⁷, Stephen D. Wilson², and M. Zahid Hasan^1,8,9,10,‡

¹Laboratory for Topological Quantum Matter and Advanced Spectroscopy (B7), Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
²Materials Department and California Nanosystems Institute, University of California Santa Barbara, Santa Barbara, California 93106, USA
³Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
⁴University of Chinese Academy of Sciences, Beijing 100049, China
⁵Department of Physics and Beijing Key Laboratory of Opto-electronic Functional Materials & Micro-nano Devices, Renmin University of China, Beijing 100872, China
⁶Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
⁷Laboratory for Muon Spin Spectroscopy, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland
⁸Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, New Jersey 08544, USA
⁹Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
¹⁰Quantum Science Center, Oak Ridge, Tennessee 37831, USA

^*These authors contributed equally to this work.
^†Corresponding author: jiaxiny@princeton.edu
^‡Corresponding author: mzhasan@princeton.edu

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Vol. 104, Iss. 3 — 15 July 2021

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Figure 1
(a)–(c) Crystal structure of kagome superconductor $Rb V_{3} {Sb}_{5}$ from three-dimensional view, top view, and side view, respectively. (d) Topographic image of a clean Sb surface ( $V = - 100 mV, I = 0.5 nA$ ). (e) Fourier transform of the topography showing Bragg peaks and charge ordering vector peaks. The $2 \times 2$ charge order vector peaks are highlighted by the shaded red ring, which includes pairs of $Q_{1}, Q_{2}$ , and $Q_{3}$ .
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Figure 2
(a)–(c) $d I / d V$ maps taken at the same clean Sb surface with $B = 0 T$ , −3 T, +3 T, respectively. The magnetic field is applied along the $c$ axis. The maps are all taken at $E = 30 meV$ with $V = - 100 mV$ and $I = 0.5 nA$ . (d)–(f) Spectroscopic $2 \times 2$ vector peaks taken at $B = 0 T$ , −3 T, +3 T, respectively. The images are Fourier transforms of spectroscopic maps. A circular region of the full Fourier-transformed image is shown for clarity, highlighting the six $2 \times 2$ vector peaks. The height of the three pairs of vector peaks is marked with arbitrary units for each data. The chirality can be defined as the counting direction (clockwise or anticlockwise) from the lowest to highest pair vector peaks as marked by the rotating arrows.
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Figure 3
(a),(b) Real space image of the $2 \times 2$ chiral charge order taken at $B = - 3 T$ and $B = + 3 T$ , respectively. The data are produced by the inverse Fourier transform of the $2 \times 2$ vector peaks in Fig. 2 and 2, respectively. (c),(d) Line-cut profile for along three directions marked in (a) and (b), respectively. The modulations along the three directions are different in both cases, defining a chirality. Magnetic field switch induces a switch of the strengths of two stronger modulations.
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Figure 4
Magnetic field tunability of the chiral charge order at a defect-free region. Comparison of intensities of three $2 \times 2$ vector peaks as a function of energy for the same defect-free region for $B = 0 T$ , −3 T, +3 T, respectively. The vector peaks have weak intensities at negative energies, and the magnetic field induced chirality switching effects are primarily observed at higher positive energies.
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Figure 5
Absence of chirality and magnetic tunability at standing-waves-rich region. (a) $d I / d V$ map data taken at a defect-rich Sb surface. The maps are all taken at $E = 0 meV$ with $V = - 100 m V$ and $I = 0.5 nA$ . This region hosts numerous defect-induced standing waves. The inset shows the Fourier transform of the map data, which exhibits additional ringlike signals within the $2 \times 2$ vector peaks. (b) Comparison of intensities of three $2 \times 2$ vector peaks for this defect-rich region as a function of energy for $B = 0 T$ , −3 T, +3 T, respectively. In this region, there is no apparent chirality of the charge order, and we do not observe a strong magnetic field response of the vector peaks.
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Physical Review B

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Intrinsic nature of chiral charge order in the kagome superconductor $Rb V_{3} {Sb}_{5}$

Phys. Rev. B 104, 035131 – Published 15 July 2021

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Physical Review B

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Intrinsic nature of chiral charge order in the kagome superconductor RbV3Sb5

Phys. Rev. B 104, 035131 – Published 15 July 2021

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Intrinsic nature of chiral charge order in the kagome superconductor $Rb V_{3} {Sb}_{5}$