Charge density waves in low-dimensional material

Fan Jin-Ze; Fang Zhan-Bo; Luo Chao-Jie; Zhang Hui

doi:10.7498/aps.71.20220052

Abstract

Charge density waves (CDWs) have triggered off extensive research in low-dimensional systems. The discovery of CDW offers a new crucial clue to understanding the intrinsic mechanisms of low-dimensional electron-phonon coupling and electron correlation. In addition, the physical properties of low-dimensional material such as magnetism and superconductivity can be fine-tuned with accurately and effectively controlled CDW phase. At the beginning,we briefly introduce the basic properties of CDW in one-dimensional and quasi one-dimensional materials, revealing the physical proprieties of the CDW, for instance, the excited state and the manipulation technologies. Then, focusing on the CDW in a two-dimensional system, we mainly introduce the recent research progress and the generation mechanism of CDW of two-dimensional materials. The interaction between CDW and Mott insulator and between superconductivity and other orders such as spin density wave and pair density wave provide a new perspective to research the multi-electron collective excitation and electron interaction. The manipulation of multi-electron collective excitation and electron-phonon interaction in CDW through doping, high pressure and laser pulse is also introduced and shares similarity with the one-dimensional system. Finally, in this article we propose a potential research application of two dimensional CDW.

Keywords:

Authors and contacts

1.
Hefei National Laboratory for Physical Sciences at Microscale, University of Science and Technology of China, Hefei 230026, China
2.
Department of Physics, University of Science and Technology of China, Hefei 230026, China

Corresponding author: Zhang Hui, huiz@ustc.edu.cn

Funds: Project supported by the National Key Research and Development Program of China (Grant No. 2017YFA0205004) and the National Natural Science Foundation of China (Grant Nos. 11804324, 12074357).

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图 1 一维Peierls相变的基本原理　(a) 均匀排列的一维原子链示意图; (b) Peierls相变后的原子链示意图; (c) 发生Peierls相变前后的能带结构, 能带在k_F处打开带隙^[2]; (d) 一维、二维和三维自由电子气的Lindhard响应函数实部^[4]; (e) 2k_F处的声子软化过程^[4]

Figure 1. Fundamentals of Peierls transition: (a) Diagram of uniformly arranged one-dimensional (1D) atomic chain; (b) diagram of the 1D atomic chain after Peierls transition; (c) band structure of the 1D atomic chain before and after Peierls transition, with a gap opening at k_F^[2]; (d) real part of Lindhard function for 1D, two-dimensional (2D) and three-dimensional (3D) free electron gas models^[4]; (e) process of phonon softening at 2k_F^[4].

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图 2 (a) In-Si原子链在Peierls相变时的STM图, 插图是In-Si原子链相变前后的重构^[39]; (b) In-Si原子链中存在的手性拓扑孤子的STM图^[52]; (c) 缺陷调控的In-Si原子链金属相和绝缘相共存, 插图为缺陷密度对4×1相的面积分数的调控作用^[58]; (d) MTB结构的示意图^[62]; (e) 二维材料MoSe₂中MTB的STM图^[63]; (f) STS测量的二维材料MoSe₂中MTB和畴中心的dI/dV谱^[63]

Figure 2. (a) STM image of Peierls transition in In-Si atomic chain. Inset: 4×1 reconstruction before the Peierls transition and 8 × 2 reconstruction after the Peierls transition^[39]. (b) STM image of chiral topological solitons in In-Si atomic chain^[52]. (c) STM images of the coexistence of metallic phase and CDW phase in defect-rich In-Si atomic chain. Inset: manipulation of defect density on areal fraction of 4 × 1 phase^[58]. (d) Diagram of MTB structure^[62]. (e) STM image of MTB in 2D material MoSe₂^[63]. (f) dI/dV spectrum of MTB and domain center in 2D material MoSe₂ measured by STS^[63].

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图 3 常见二维材料的CDW性质, 数据来源于文献[68, 69].

Figure 3. CDW properties of 2D material, data from Ref. [68, 69].

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图 4 二维体系中CDW产生的几种机理图　(a) ARPES测量的单层VSe₂费米面结构^[71]; (b) 单层VSe₂中的完美费米面嵌套^[71]; (c) 通过非弹性X射线散射测量的不同温度下2H-NbSe₂中电声子耦合导致的声子软化^[84]; (d) ARPES测量的RbV₃Sb₅费米面结构, 在鞍点处有高态密度^[80]; (e) 1T-TiSe₂中Jahn-Teller畸变示意图^[92]; (f) 1T-TiSe₂中普通态和激子绝缘体的能带色散和光谱权重^[94]

Figure 4. Several mechanisms of CDW transitions: (a) Fermi surface map of monolayer VSe₂ measured by ARPES^[71]; (b) perfect Fermi surface nesting of monolayer VSe₂^[71]; (c) phonon softening in 2H-NbSe₂ at different temperature induced by Electron-phonon coupling, measured by inelastic X-ray scattering^[84]; (d) Fermi surface map of RbV₃Sb₅ measured by ARPES with high density of state around saddle point^[80]; (e) diagram of Jahn-Teller distortions in 1T-TiSe₂^[92]; (f) band dispersions and corresponding spectral weights of normal state and exciton insulator in 1T-TiSe₂^[94].

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图 5 (a) 1T-TaS₂中的David星、CCDW、NCCDW示意图^[97]; (b) 2H-NbS₂中的1T层示意图, 每个David星中心都有一个未配对的局域磁矩^[100]

Figure 5. (a) Diagrams of the Star of David pattern, CCDW, and NCCDW in 1T-TaS₂^[97]; (b) Diagram of the 1T layer in 2H-NbS₂, each Star of David contains an unpaired magnetic moment localized in the center^[100].

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图 6 二维体系中的CDW调控研究　(a) 1T-TaS₂中电脉冲诱导金属镶嵌相的STM图像, 插图为金属镶嵌相中CCDW的David星构型, 未发生过改变^[101]; (b) 光脉冲使1T-TaS₂在CCDW和隐藏态之间切换, 插图为实验装置的示意图^[104]; (c) 1T-TaS₂中部分吸附水分子层的STM图像, 插图为STM图像的傅里叶变换, 存在 $ \sqrt{\text{13}}\times \sqrt{\text{13}} $ 和3×3两种CDW周期^[109]; (d), (e) 单层的NbSe₂/双层石墨烯和NbSe₂/SrTiO₃的STM图像^[122]

Figure 6. CDW manipulation in 2D system: (a) STM image of metallic mosaic phase induced by voltage pulses in 1T-TaS₂. Inset: unchanged David-star formation in CCDW of metallic mosaic phase^[101]. (b) Switching between CCDW and hidden state induced by optical pulse in 1T-TaS₂. Inset: diagram of experimental setup^[104]. (c) STM image of partially water-adsorbed 1T-TaS₂. Inset: Fourier transform images of STM topography showing two types of CDW periodicity including $ \sqrt{\text{13}}\times\sqrt{\text{13}} $ and 3×3^[109]. (d), (e) STM images of monolayer NbSe₂/BLG and NbSe₂/SrTiO₃(111)^[122].

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图 7 CDW与Mott绝缘体的关系　(a) 1T-TaS₂中电阻和CDW相随温度的变化, 插图为CCDW、三斜CDW、NCCDW、ICCDW的示意图^[124]; (b), (c) STM测量的1T-TaS₂和4H_b-TaS₂中dI/dV谱的空间分布, 插图为1T-TaS₂和4H_b-TaS₂结构的示意图^[126]; (d) 单层1T-NbSe₂的STM图像, UHB的分布相对CDW有$\sqrt{\text{3}}\times\sqrt{\text{3}}$R30°的超结构^[132]; (e) 单层1T-NbSe₂中电荷转移绝缘体示意图^[99]; (f) STS测量的单层1T-NbSe₂的dI/dV谱^[99]

Figure 7. Relationship between CDW and Mott insulators: (a) The changes of resistivity and CDW phase with respect to temperature in 1T-TaS₂, where the insert is the diagram of CCDW, triclinic CDW, NCCDW and ICCDW^[124]. (b), (c) Spatial distribution of dI/dV spectrum of 1T-TaS₂ and 4H_b-TaS₂ measured by STS. Insets are diagrams of their structure^[126]. (d) STM image of monolayer 1T-NbSe₂. The distribution of UHB shows $\sqrt{\text{3}}\times\sqrt{\text{3}}$ R30° superstructure with respect to CDW^[132]. (e) Diagram of charge transfer insulator in monolayer 1T-NbSe₂^[99]. (f) dI/dV spectrum of 1T-NbSe₂ measured by STS^[99].

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图 8 超导与CDW的关系　(a) 1T-Fe_xTaS₂的相图^[167]; (b) ARPES测量的不同掺杂下1T- Fe_xTaS₂的能量分布曲线, 在Γ点有电子口袋^[167]; (c) Cu_0.08TiSe₂的STM图像, 插图为STM图的傅里叶变换^[173]; (d) STS测量的Cu_0.08TiSe₂中CDW区域和畴壁的dI/dV谱^[173]; (e) 电子辐照的2H-NbSe₂中温度-剩余电阻率相图^[162]

Figure 8. Relationship between CDW and superconductivity: (a) Phase diagram of 1T-Fe_xTaS₂^[167]; (b) ARPES-measured energy distribution curves of 1T-Fe_xTaS₂ at different doping level showing an electron pocket at Γ point^[167]; (c) STM topography of Cu_0.08TiSe₂, where the inset is the Fourier transform of STM image^[173]; (d) STS-measured dI/dV spectra of CDW regions and domain walls in Cu_0.08TiSe₂^[173]; (e) temperature-residual resistivity phase diagram of 2H-NbSe₂ upon electron irradiation^[162].

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图 9 (a) 2H-NbSe₂中拉曼谱的CDW模式和超导模式随温度变化, 进入超导态后谱权重从CDW模式向超导模式中转移, 插图为减去8 K测量数据后的拉曼谱^[213]; (b) 1T-TiSe₂中STM图像的傅里叶变换^[216]; (c) 图(b)中沿3个波矢方向的线截面^[216]; (d) STS测量的不同磁场下RbV₃Sb₅中dI/dV图的傅里叶变换^[223]

Figure 9. (a) Changes of CDW mode and SC mode of Raman spectra with respect to temperature in 2H-NbSe₂ with spectral weight transfer from CDW mode to SC mode when going into SC state, inset: Raman spectra subtracted from the data measured at 8 K^[213]; (b) Fourier transform of STS-measured dI/dV map in 1T-TiSe₂^[216]; (c) line profiles along three wave vectors of figure (b)^[216]; (d) Fourier transform of STS image in RbV₃Sb₅ at different magnetic field^[223].

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