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Material with Kagome lattice provides an excellent platform for studying electronic correlation effects, topological states of matter, unconventional superconductivity, and geometric frustration. The recently discovered Kagome superconductors AV3Sb5 (A = K, Rb, Cs) have attracted widespread attention in the field of condensed matter physics, and many efforts have been made to elucidate their novel physical properties, such as charge density wave, unconventional superconductivity, and band topology. Meanwhile, many groups have effectively tuned these novel properties through chemical doping, offering a good opportunity for further understanding the materials of this system. In this paper, we comprehensively review the latest research progress of the doping effect of this rapidly developed AV3Sb5 system, with the objective of further promoting the in-depth research into Kagome superconductor. Specifically, we review the chemical doping in CsV3Sb5 with elements such as Nb, Ta, Ti, and Sn, and the surface doping with elements Cs or O as well, and describe their influences on the novel quantum properties, especially superconductivity, charge density wave, and electronic band structure of the material. Furthermore, the intricate physical mechanism of doping manipulation is discussed, in order to provide a basic knowledge for further understanding and studying the rich quantum effects of the system, such as charge density waves, time reversal symmetry breaking, and superconductivity.
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Keywords:
- Kagome lattice /
- chemical doping /
- superconductivity /
- charge density wave
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图 1 (a) Kagome晶格结构示意图; (b) AV3Sb5 (A = K, Rb, Cs)晶格结构示意图, V原子构成Kagome层
Figure 1. (a) Schematic diagram of the Kagome lattice structure; (b) Lattice structure of the AV3Sb5 (A = K, Rb, Cs), vanadium atoms constitute the Kagome lattice.
图 2 (a)低温不同磁场下CsV3Sb5电阻率的温度依赖关系[14]; (b)磁场平行于a轴时, CsV3Sb5奈特位移的温度依赖关系[15]; (c)低温下自旋晶格弛豫率的 Hebel-Slicheter共振峰[15]; (d)在CsV3Sb5的Cs表面(左图) 和Sb表面(右图)观察到的两种超导能隙谱[17]; (e) CsV3Sb5的STM原子形貌的傅里叶变换, 粉色圈中Q4/3a处的峰对应PDW相[19].
Figure 2. (a) Temperature-dependent resistivity at low temperature for CsV3Sb5 under various magnetic fields[14]; (b) temperature dependence of the Knight shift for CsV3Sb5[15]; (c) Hebel-Slicheter resonance peak of the spin lattice relaxation rate at low temperature[15]; (d) two kinds of superconducting gap spectra observed on the half-Cs surface (left image) and half-Sb surface (right image) for CsV3Sb5[17]; (e) Fourier transformation of atomically resolved STM topography for CsV3Sb5, the pink cycle at Q4/3a shows the PDW phase[19].
图 3 (a) DFT计算的CsV3Sb5能带结构[14]; (b) ARPES观察到的沿ΓKM方向的电子能带结构[26]; (c) Sb表面形貌图的傅里叶变换, 显示2×2电荷序(红色阴影区域)和1×4电荷序[33]; (d) 覆盖从局域跃迁机制到偏斜散射机制的σAHE与σxx关系图, 包含多种材料与CsV3Sb5和K1–xV3Sb5的对比 [37]; (e)手性磁通相的局域轨道磁矩分布及电荷分布[40]; (f) KV3Sb5的拉曼光谱, 低温条件下在25.4 meV和27.5 meV时观察到两种新的声子模式[45]; (g)外加0.4 T和5 T磁场时, 不同温度下c轴方向的电阻率随测量角度的依赖关系[43]
Figure 3. (a) Band structure of CsV3Sb5 calculated by DFT[14]; (b) ARPES intensity as a function of wave vector and binding energy measured along the ΓKM[26]; (c) Fourier transform of an Sb topographic image, showing 2×2 charge order vector peaks (red shaded area), and 1×4 vector peaks along Q1 direction [33]; (d) plot of σAHE versus σxx for a variety of materials compared with CsV3Sb5 and K1–xV3Sb5 spanning various regimes from the localized hopping regime to the skew scattering regime[37]; (e) local orbital magnetic moment distribution and charge distribution of chiral flux phase[40]; (f) Raman spectroscopy for KV3Sb5; two new phonon modes at 25.4 and 27.5 meV are observed below 30 K[45]; (g) angular dependent c-axis resistivity measured at different temperatures under magnetic fields of 0.4 and 5 T[43] .
图 4 (a)从1.8 K到300 K, Cs(V1–xNbx)3Sb5的面内电阻率的温度依赖关系[46]; (b) Cs(V1–xNbx)3Sb5的相图, 表明了CDW和超导之间的竞争关系[46]; (c)温度为5 K时, 去除线性正常霍尔背底后提取的反常霍尔电阻率 [46]; (d)第一性原理计算得到的CsV3Sb5和Cs(V0.93Nb0.07)3Sb5的电子能带结构; (e)上图和中图分别为CsV3Sb5和Cs(V0.93Nb0.07)3Sb5沿ΓKM方向切割的ARPES强度图, 下图为拟合点的对比图[49]
Figure 4. (a) Temperature dependence of in-plane resistivity measured from 300 to 1.8 K for Cs(V1–xNbx)3Sb5[46]; (b) phase diagram of Cs(V1–xNbx)3Sb5, which illustrates the competition between CDW and superconductivity [46]; (c) extracted $ {\rho }_{yx}^{{\mathrm{A}}{\mathrm{H}}{\mathrm{E}}} $ taken by subtracting the local linear ordinary Hall background at 5 K[46]; (d) the electronic structure of CsV3Sb5 and Cs(V0.93Nb0.07)3Sb5 obtained through first principle calculation[46]; (e) the upper and middle figures show the ARPES intensity maps of CsV3Sb5 and Cs(V0.93Nb0.07) 3Sb5 along ΓKM, while the lower figure shows a comparison of the fitting points[49].
图 5 (a)在1.8—300 K范围内测得的Cs(V1–xTax)3Sb5面内电阻率的温度依赖关系, 插图显示了CDW转变温度; (b)超导转变温度附近Cs(V1–xTax)3Sb5的ρ(T)曲线放大图; (c) Cs(V1–xTax)3Sb5的相图; (d), (e)不同掺杂浓度Cs(V1–xTax)3Sb5 的X射线散射强度, 其中(d)为H-切割(左图沿[–2.5, 0.5, –13.5], 右图沿[–1, 0.5, –15.5]), (e)为L-切割(左图沿[–2.5, 0.5, L] , 右图沿[–1, 0.5, L])[51]
Figure 5. (a) Temperature dependence of in-plane resistivity measured from 1.8 K to 300 K for Cs(V1–xTax)3Sb5, where the inset shows dρ/dT as a function of temperature near the CDW transition. (b) Zoomed-in views of the ρ(T) curves near the superconductivity transition temperatures for Cs(V1–xTax)3Sb5. (c) Schematic phase diagrams of Cs(V1–xTax)3Sb5 [48]. (d), (e) X-ray scattering intensity of Cs(V1–xTax)3Sb5 with different doping concentrations: the (d) H-cut (left image along [–2.5, 0.5, –13.5], right image along [–1, 0.5, –15.5]) and (e) L-cut (left image along [–2.5, 0.5, L], right image along [–1, 0.5, L])[51].
图 6 (a), (b) Cs(V0.93Nb0.07)3Sb5和Cs(V0.86Ta0.14)3Sb5样品超导能隙的动量依赖关系示意图; (c) TCDW, Tc与晶格膨胀率的依赖关系的相图, 晶格膨胀率是由于化学替代引起的; (d) Tc以下和以上Cs(V0.86Ta0.14)3Sb5的零场µSR时间谱; (e)零场μ子自旋弛豫率在Tc附近的温度依赖关系; 表明在CDW被完全抑制时, Cs(V0.86Ta0.14)3Sb5的超导电性具有时间反演对称性破缺的特性[47]
Figure 6. (a), (b) Schematic momentum dependence of the SC gap magnitude of the Cs(V0.93Nb0.07)3Sb5 and Cs(V0.86Ta0.14)3Sb5 samples, respectively; (c) schematic phase diagram in which TCDW and Tc are plotted as function of the lattice expansion due to the chemical substitutions; (d) zero-Field (ZF) µSR time spectra for Cs(V0.86Ta0.14)3Sb5 below and above Tc; (e) temperature dependence of the zero-field muon spin relaxation rate in the temperature range across Tc, which indicates that time-reversal symmetry breaking in the superconducting state of the Cs(V0.86Ta0.14)3Sb5 sample with CDW fully suppressed[47].
图 7 (a), (b) Cs(V0.987Ti0.013)3Sb5和Cs(V0.95Ti0.05)3Sb5样品Sb表面电子态的傅里叶变换, 前者存在2×2的 CDW态, 后者CDW态消失[53]; (c)第一性原理计算得到的Cs(V1–xTix)3Sb5能带结构[53]; (d), (e)两课题组得到的Cs(V1–xTix)3Sb5的相图[52,53]; (f)在CsV3Sb5(黑色曲线)和CsV3–xTixSb5 (x = 0.03, 0.04, 0.15和0.27分别对应于蓝色、绿色和深绿色曲线)样品的Sb表面上获得的空间平均dI/dV谱, 随着Ti掺杂从V形变为U形[53]
Figure 7. (a), (b) Fourier transform was performed on the Sb surface electronic states of Cs(V0.987Ti0.013)3Sb5 and Cs(V0.95Ti0.05)3Sb5, the former shows the presence of 2×2 CDW states and the latter disappearing[53]; (c) the bands of Cs(V1–xTix)3Sb5 by first-principles calculations[53]; (d), (e) phase diagrams of Cs(V1–xTix)3Sb5 for two research groups[52,53]; (f) spatially-averaged dI/dV spectra obtained on the Sb surfaces of the CsV3Sb5 (black curve) and CsV3–xTixSb5 samples (x = 0.03, 0.04, 0.15 and 0.27, corresponding to blue, green, and dark green curves, respectively), showing a transition from V-shape to U-shape symmetry through Ti substitution[53]
图 8 (a) Cs(V1–xCrx)3Sb5的电子掺杂相图[54]; (b)通过减去5 K的线性霍尔背底提取Cs(V1–xCrx)3Sb5 (x = 0到x = 0.09)样品的反常霍尔电阻率[54]; (c) CsV3–xMoxSb5的相图[48]
Figure 8. (a) Electron doping phase diagram Cs(V1–xCrx)3Sb5[54]; (b) the extracted anomalous Hall resistivity by subtracting the local linear ordinary Hall background at 5 K for chromium doping content from x = 0 to x = 0.09[54]; (c) the electron doping phase diagram CsV3–xMoxSb5[48].
图 9 (a) CsV3Sb5–xSnx(x ≤ 0.06)的dM/dT随温度依赖曲线, CDW转变温度随着Sn掺杂降低, 高浓度Sn掺杂样品CDW转变消失[56]; (b) CsV3Sb4Sn的能带结构, 其中一个位于Kagome平面内的Sb原子被Sn取代[56]; (c) CsV3Sb4Sn的能带结构, 其中一个位于Kagome平面外的Sb原子被Sn取代[56]; (d)—(f)在T = 11 K时CsV3Sb5–xSnx样品的X射线散射强度图, 其中(d)和(e)分别是x = 0.025样品(H, K, 1.5)和(H, 1.5, L)平面的X射线散射强度图, (f) x = 0.15样品(H, K, –0.5)平面的X射线散射强度图[55]
Figure 9. (a) dM/dT -T for CsV3Sb5–xSnx (x ≤ 0.06), show a decrease in CDW transition temperature, and this transition disappears for higher Sn concentration[56]; (b) calculation of the band structure of CsV3Sb4Sn where one Sn has been substituted within the Kagome layer[56]; (c) calculation of the band structure of CsV3Sb4Sn where one Sn has been substituted at a Sb site outside of the Kagome layer[56]; (d)–(f) X-ray scattering intensities for CsV3Sb5–xSnx samples at 11 K, in which (d) and (e) are the X-ray scattering intensity in (H, K, 1.5)-plane and (H, 1.5, L)-plane, respectively, for the x = 0.025 sample, while (f) is the X-ray scattering intensities in the (H, K, –0.5)-plane for the x = 0.15 sample[55].
图 10 (a) CsV3Sb5–xSnx的空穴掺杂相图[56]; (b)高压下CsV3Sb5的相图[63]; (c) CsV3Sb5样品超导转变温度的压强依赖关系[63]; (d) T = 0 K时上临界场的压强依赖性[63]; (e)能带结构随空穴掺杂的演变和(f)两个范霍夫奇点相对于费米能级的位置[68]; (g) CsV3Sb5和CsV3(Sb0.977As0.023)5电阻率的温度依赖性; (h)超导转变温度附近的放大图; (i)在CDW转变温度附近的电阻率的导数[59]
Figure 10. (a) Hole-doping phase diagram for CsV3Sb5–xSnx [56]; (b) phase diagram of CsV3Sb5 under high pressure[63]; (c) pressure dependence of superconducting transition temperature for CsV3Sb5 samples[63]; (d) the pressure dependence of the upper critical field at T = 0 K[63]; (e) evolution of energy band structure with hole doping and (f) the position of two van Hove singularities relative to Fermi level[68]; (g) temperature dependence of resistivity for CsV3Sb5 and CsV3(Sb0.977As0.023)5; (h) amplification around the superconducting transition; (i) the derivative of resistivity around the CDW transition[59].
图 11 (a), (b) KxRbyCszV3Sb5 (x + y + z = 1)样品的 (a) CDW转变和(b)超导转变三元相图: 使用dM(T )/dT数据中的峰值提取到CDW转变温度TCDW; 使用电输运数据中零电阻率点提取超导转变温度Tc. (c), (d)将KxRbyCszV3Sb5(x+y+z =1)样品的 (c) TCDW和 (d) Tc与KV3Sb5, RbV3Sb5和CsV3Sb5三种母体的转变温度按照掺杂比例线性插值的数据进行比较[69]
Figure 11. (a) CDW transition and (b) superconducting transition ternary phase diagram of KxRbyCszV3Sb5 (x + y + z = 1). The CDW transition temperature TCDW data extracted using the peak in the d(MT )/dT data, the superconducting transition temperature Tc data extracted using zero resistivity points from electrical transport data. The (c) TCDW and (d) Tc of KxRbyCszV3Sb5 (x + y + z = 1) is compared with the linear interpolation of transition temperature of the parent KV3Sb5, RbV3Sb5, and CsV3Sb5[69].
图 12 (a) CsV3Sb5的能带结构, 不同颜色代表了不同轨道能带的特征; (b)母体和Cs处理后样品在Γ点附近的ARPES强度的比较[70]; (c)在T = 120 K沿ΓKM方向测得的ARPES强度与波矢、结合能的依赖关系; (d)与(c)相同, 但是Cs处理后的样品; (e) CsV3Sb5随空穴掺杂含量变化的相图[71]
Figure 12. (a) Band structure of CsV3Sb5, the orbital characters of different bands are represented by different colors; (b) comparison of the ARPES intensity around the Γ point between pristine and Cs-dosed samples[70]; (c) ARPES intensity as a function of wave vector and binding energy, measured at T = 120 K along the ΓKM for pristine sample; (d) the same as (c), but for Cs-dosed sample; (e) phase diagram of CsV3Sb5 with the variation of hole-doping content[71].
表 1 不同位置、不同元素掺杂CsV3Sb5 的掺杂效应
Table 1. Doping effect of CsV3Sb5 by different elements on different atomic sites.
掺杂位置 掺杂元素 电荷密度波 超导 反常霍尔效应 能带结构及费米面位置变化 掺杂类型 掺杂极限/% V Nb 抑制 增强 抑制 Γ点电子口袋扩张, 范霍夫奇点上移 等价掺杂 7 V Ta 抑制 增强 抑制 Γ点电子口袋扩张, 范霍夫奇点上移 等价掺杂 14 V Ti 抑制 待定 抑制 费米面降低, Γ点电子口袋减小, 范霍夫奇点上移 空穴 10 V Mo 增强 抑制 — — 电子 3.5 V Cr 抑制 抑制 抑制 — 电子 25 Sb Sn 抑制 双穹顶状 — 费米面降低, Γ点电子口袋减小, 范霍夫奇点上移 空穴 20 Sb As 抑制 增强 抑制 — 等价掺杂 2.3 Cs K 抑制 抑制 — — 等价掺杂 100 Cs Rb 抑制 增强 — — 等价掺杂 100 表面 Cs 抑制 — — 费米面上升, Γ点电子口袋扩张 电子 — 表面 O 抑制 穹顶状 — 范霍夫奇点上移, Γ点电子口袋减小 空穴 — 
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