Junyu Zong(宗君宇) Yang Xie(謝陽(yáng)) Qinghao Meng(孟慶豪) Qichao Tian(田啟超) Wang Chen(陳望)Xuedong Xie(謝學(xué)棟) Shaoen Jin(靳少恩) Yongheng Zhang(張永衡) Li Wang(王利) Wei Ren(任偉)Jian Shen(沈健) Aixi Chen(陳愛(ài)喜) Pengdong Wang(王鵬棟) Fang-Sen Li(李坊森)Zhaoyang Dong(董召陽(yáng)) Can Wang(王燦) Jian-Xin Li(李建新) and Yi Zhang(張翼)

1National Laboratory of Solid State Microstructure,School of Physics,Nanjing University,Nanjing 210093,China

2Vacuum Interconnected Nanotech Workstation(Nano-X),Suzhou Institute of Nano-Tech and Nano-Bionics(SINANO),Chinese Academy of Sciences,Suzhou 215123,China

3Department of Applied Physics,Nanjing University of Science and Technology,Nanjing 210094,China

4Collaborative Innovation Center of Advanced Microstructures,Nanjing University,Nanjing 210093,China

Keywords: charge density waves,VSe2,band structures,STM,ARPES

1. Introduction

2. Methods

The MBE growth and experimental measurements of the 1T-VSe2films were performed in a combined MBE-STMARPES ultra-high vacuum (UHV) system with a base pressure of～2×10-10mbar (1 bar = 105Pa). The STM in the MBE-STM-ARPES system is a Pan-style one and performed at room-temperature.The BLG substrate was obtained by flash-annealing the 4H-SiC(0001)wafer to～1250°C for 60 cycles.[33]The V flux was produced from an electron-beam evaporator. The high purity Se (99.9995%) was evaporated from a standard Knudsen cell. The BLG substrate was kept at 280°C during the growth. The surface morphology was characterized by thein-situreflection high-energy electron diffraction RHEED and RT-STM.

Thein-situx-ray photoelectron spectroscopy (XPS) and VT-ARPES measurements were performed via a shared Scienta Omicron DA30L analyzer. The monochromatic x-ray(SIGMA) was generated from an Al electrode excitation source(Alα,1486.7 eV),and the ultraviolet(UV)light source was generated by a helium lamp (Fermi instruments) with a SPECS monochromator(He I,21.218 eV).The samples were cooled down to～7 K by a close-cycle cryogenerator during the measurements, and the sample temperature can be controlled by anin-situinner heater in the manipulator.

The ultra-low-temperature (ULT-) STM, VT-STM, and variable-temperature low-energy electron diffraction (VTLEED)were performedex-situat Nano-X,Suzhou Institute of Nano-Tech and Nano-Bionics (SINANO), China. The ULTSTM is the UNISOKU Co, USM 1300 with lowest temperature of～4 K. The VT-STM is the Scienta Omicron Co,VT-AFM XA50/500 with variable temperature operation from 30 K to 300 K. The VT-LEED is the Scienta Omicron Co,LEED 600 MCP with variable temperature operation from 80 K to 300 K.

The first-principles calculations were performed using the QUANTUM ESPRESSO package base on density functional theory(DFT).[34]The generalized gradient approximation with the Perdew–Burke–Ernzerhof functional was used to describe the electron exchange and correlation effects.[35]A plane-wave energy cutoff of 80 Ry (1 Ry=13.6055923 eV)and a 16×16×1kmesh was employed. Freestanding films were modeled with a 23-?A vacuum gap between adjacent layers in the supercell. The in-plane lattice parameterawas fixed to the experimentally reported value of 3.35 ?A.[36]Structures were fully optimized until ionic forces and energy difference are less than 10-3eV/?A and 10-5eV.

3. Results and discussion

3.1. The hidden incommensurate CDW phase in monolayer VSe2

The structure of the 1T-VSe2unit cell is represented as a ball and stick model shown in Fig.1(a). The triangle formed by the top layer of Se atoms is rotated by 180°relative to the bottom Se layer. The RHEED image of a monolayer 1T-VSe2film grown on BLG substrate is shown in the upper panel of Fig.1(b). The sharp RHEED patterns prove that the film was well-crystalized.In the lower panel of Fig.1(b),the XPS spectrum shows the characterized binding energies of Se 3d5/2(～56 eV), Se 3d3/2(～57 eV), V 2p3/2(～512 eV), and V 2p1/2(～520 eV) orbitals, indicating our film is indeed consisted of V and Se atoms.

Fig.1. (a)The structure of the 1T-VSe2 unit cell. (b)RHEED pattern(upper panel) and XPS spectrum (lower panel) of the monolayer 1T-VSe2 grown on BLG substrate. (c) STM image (300 nm×300 nm) scanned at roomtemperature. Scanning parameters: Vbias = 1 V, It = 100 pA. The white dashed line indicates the terrace step of the BLG/SiC(0001) substrate, and the black dashed lines depict the edges of the grown VSe2 domains. (d)The height profile line along the green dashed line in panel(c).

To further determine the surface morphology of the grown film,we took a 300 nm×300 nm STM image scanned at roomtemperature [Fig. 1(c)]. The grown 1T-VSe2film formed large-scale flat monolayer domains with a coverage of～80%.Few bilayer 1T-VSe2islands were formed on the monolayer 1T-VSe2surface,but they will not affect our VT-ARPES and VT-STM measurements due to their rather small sizes. From the height profile line shown in Fig.1(d), we can see that the height of second 1T-VSe2layer island to the monolayer domain is about～0.67 nm,which agree with the lattice constantcof the 1T-VSe2monolayer.[36]However, the height of the monolayer 1T-VSe2to the BLG substrate is obviously larger as～0.95 nm,which is due to the large interlayer spacing between the TMDCs film and BLG substrate.[29,37,38]

Fig. 2. (a)–(c) The atom-resolved STM images (6 nm×6 nm) obtained at(a) 4 K, (b) 165 K, and (c) 300 K, respectively. Scanning parameters: (a)Vbias = 1 V, It = 200 pA; (b) Vbias = 0.1 V, It = 3 nA; (c) Vbias = 0.3 V,It =1 nA. The green, blue, and cyan dots in the lattice model represent the V, top layer Se, and bottom layer Se atoms in 1T-VSe2, respectively. The red dashed lines in panel (a) indicate the () CDW reconstruction,and the blue dashed lines in panel (a) indicate the period of ～2a. (d)–(f)The corresponding FFT images of panels (a)–(c), respectively. (g)–(i) The analysis of the FFT patterns shown in panels(d)–(f).

When the temperature rises to room-temperature of 300 K, the RT-STM image in Fig. 2(c) shows that the stripelike incommensurate CDW phase in short range still exists but exhibits different formations. In the FFT image shown in Figs. 2(f) and 2(i), we can still observe the wave vectorq3≈(1/2)q0with a mis-angle around～10°, accompanied with other different incommensurate wave vectors (e.g.q5≈(1/3.2)q0,q6≈(1/2.7)q0). These newly emerged wave vectors may represent the short stripes depicted by the cyan dashed lines in Fig. 2(i), while the incommensurate (～2a)CDW order with wave vectorq3≈(1/2)q0can be found by the blue dashed lines but is not very obvious.

To confirm that the reconstructions shown in the STM images are indeed originated from the CDW phases rather than the lattice structure phase transition, we carried out the low-energy electron diffraction(LEED)taken at various temperatures. Figure 3 show the LEED images taken at 80 K,200 K, and 300 K. The (1×1) diffraction patterns from the BLG substrate can be clearly observed and are depicted by the white dashed hexagons. Besides,the spots depicted by the red dashed hexagons are originated from the(1×1)lattice of the grown 1T-VSe2. Fenget al.have reported that a weak diffraction pattern of the CDW order in monolayer 1T-VSe2can be observed in the LEED taken at 40 K,[30]but here we did not find any features on the CDW reconstructions. This may be due to the relative poorer resolution limit of our LEED system. However,for the TMDCs materials,the crystalline structure phase transitions usually can be easily distinguished by the electron diffraction method,e.g.,the 2H to 1T′phase transition in monolayer WSe2will produce an additional pattern in the electron diffraction images.[37,48]Here,except the(1×1)pattern from the 1T-VSe2, no other diffraction pattern was found in the VT-LEED measurements,indicating that no crystalline phase transition happens in 1T-VSe2. Thus,the stripelike CDW structures observed in STM are not from crystalline phase transition such as 1T to 1T′.

Fig.3. (a)–(c)LEED images of the grown monolayer 1T-VSe2 film on BLG substrates taken at (a) 80 K, (b), 200 K, and (c) 300 K, respectively. The white dashed hexagons indicate the(1×1)diffraction patterns from the BLG substrate, and the red dashed hexagons indicate the (1×1) diffraction patterns from the grown 1T-VSe2 film.

3.2. Two-step CDW gap structure transition

Fig.4. (a)BZ and constant-energy-mapping of the monolayer 1T-VSe2 at the binding energy of-0.1 eV taken at 7 K.(b)ARPES spectra along the Γ–M–K directions taken at 7 K. (c) and (d) Symmetrized EDCs at different temperatures at the momentum positions marked as the α and β points in panel (b),respectively. The different colored lines represent the different temperatures. (e)Temperature dependence of the CDW gap extracted from the symmetrized EDCs at the momentum position marked as the α point. The red line is the fitting result from Eq. (1) using a single Δ1. The blue and green dashed lines indicate the fitting results of Δ1 =30±6 meV and TC1 =151±6 K, respectively. (f) Temperature dependence of the CDW gap extracted from the symmetrized EDCs at the momentum position marked as the β point. The red line is the fitting result from Eq.(1)using a total Δ(T)=Δ1(T)+Δ2(T). The blue dashed lines indicate the fitting results of Δ1 =32±2 meV and Δ2 =30±1 meV,and the green and purple dashed lines indicate the fitting results of TC1=153±2 K and TC2=343±2 K,respectively. The errors of the fitting results are in 68%confidence interval. The error bars of the gaps data are set as?where kB is the Boltzmann constant,εs is the resolution limit(～5 meV)of the ARPES system.

whereΔ(T) is the CDW gap,Γ1the single-particle scattering rate,Γ0the inverse particle–hole pair lifetime, andε(k) the single-particle dispersion. Using Eq. (2), we can calculate the single-particle spectral functionA(k,ω) via the Green’s function asA(k,ω) =-ImG(k,ω)/πwithG(k,ω) = [ω-ε(k)-Σ(k,ω)]-1. In our numerical calculations,ε(k) is obtained by the tight-binding fit to the first-principles calculations for 1T-VSe2(see Section 2), andΓ1=0.005 eV andΓ0=0.005 eV are chosen. Figures 5(a)–5(f) show the calculated spectral functions along theM–Γ–MandK–M–Kdirections at 343 K, 200 K, and 7 K, respectively. Figures 5(g)–5(l) are the experimental ARPES data at 340 K, 200 K, and 7 K, respectively. The calculated spectra show a good agreement to the experimental results. At 343 K, both theΔ1andΔ2equal zero according to Eq. (1), and the calculated spectra functions show no gap along bothΓ–MandM–Kdirections [see Figs. 5(a) and 5(b)], and ARPES spectra at 340 K show no gap along theΓ–Mdirection [see Fig. 5(g)], and a tiny gap that is smaller than the resolution limit and difficult to be directly distinguished along theM–Kdirection [see Fig. 5(h)]. When the temperature is reduced to be 200 K,Δ1keeps zero butΔ2becomes nonzero. SinceΔ2only exists along theM–Kdirection, the band along theM–Kdirection opens a small gap at the Fermi level[Figs.5(d)and 5(j)]but the band along theΓ–Mdirection still shows no gap[Figs.5(c)and 5(i)]. When the temperature is further reduced to be 7 K, bothΔ1andΔ2becomes nonzero. SinceΔ1exists in both theΓ–MandM–Kdirections whileΔ2not, thus the band along theM–Kdirection shows a larger gap[Figs.5(f)and 5(l)]than that along theΓ–Mdirection at the Fermi level[Figs.5(e)and 5(k)].

Fig.5. (a)–(f)Calculated spectral function at selected temperatures along the M–Γ–M and K–M–K directions. (g)–(l)ARPES spectra along the M–Γ–M and K–M–K directions scanned at the corresponding temperatures experimentally.

We note that some previous works on the CDW gap in monolayer 1T-VSe2also reported a similar two-step gap transition,[27,32]but they attributed one step of the gap transition to the metal–insulator transition[27]or the pseudogap.[32]Differently,with the unveiling of the hidden incommensurate CDW order, here we suggest the CDW gap consisted of two gap parts (Δ1+Δ2), which gives a well explanation and a comprehensive description on the two-step CDW transition.Interestingly, a similar two-stage CDW transition associated with the incommensurate CDW phase was also reported in the cuprates of La2-xBaxCuO4.[47]Besides,we note that by simply treating the scattering ratesΓ1andΓ0as constants in our calculations when using Eq. (2), we get a good agreement to the experimental data. It suggests that the single-particle scattering rateΓ1and the inverse pair lifetimeΓ0may show less or even no temperature dependence,and also affect less the CDW phase transitions and gap evolutions in monolayer 1T-VSe2.This is in contrast to the case in high-TCcuprates,[51]where bothΓ1andΓ0assumes a strong temperature dependence.

3.3. Discussion on the possible physical mechanism of the CDW phases in monolayer 1T-VSe2

Fig.6. (a)–(c)Secondary differential spectra along the M–Γ–M directions taken at 7 K,200 K,and 340 K respectively. (d)The temperature dependence of the γ band maximum EV1. (e)The temperature dependence of the momentum position of the pocket apex(kAP). The inset is the constant-energy-mapping at-0.1 eV and the position of kAP. (f)The temperature dependence of the width of the elliptic pocket around the M point(kW),the inset indicates the kW in the constant-energy-mapping at-0.1 eV.

4. Conclusion

Acknowledgments

Project supported by the National Natural Science Foundation of China (Grant Nos. 92165205, 11790311,12004172,11774152,11604366,and 11634007),the National Key Research and Development Program of China (Grant Nos.2018YFA0306800 and 2016YFA0300401),the Program of High-Level Entrepreneurial and Innovative Talents Introduction of Jiangsu Province,the Jiangsu Planned Projects for Postdoctoral Research Funds (Grant No. 2020Z172), and the Natural Science Foundation of Jiangsu Province,China(Grant No.BK 20160397).

Appendix A:Symmetrized EDCs around transition temperatures

The symmetrized EDCs around the transition temperatures are shown in the following figures.

Fig. A1. Symmetrized EDCs around the transition temperature TC1 (a) and TC2 (b). The black arrows and dashed lines indicate the close and closing trend of the gap around the transition temperatures.