Chinese Physics Letters, 2021, Vol. 38, No. 10, Article code 107101 Charge Density Wave and Electron-Phonon Interaction in Epitaxial Monolayer NbSe$_{2}$ Films Xuedong Xie (谢学栋)1, Dongjing Lin (林东景)1, Li Zhu (朱立)1, Qiyuan Li (李启远)1, Junyu Zong (宗君宇)1, Wang Chen (陈望)1, Qinghao Meng (孟庆豪)1, Qichao Tian (田启超)1, Shao-Chun Li (李绍春)1,2, Xiaoxiang Xi (奚啸翔)1,2, Can Wang (王灿)1,2*, and Yi Zhang (张翼)1,2* Affiliations 1National Laboratory of Solid State Microstructure, School of Physics, Nanjing University, Nanjing 210093, China 2Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China Received 25 June 2021; accepted 16 September 2021; published online 28 September 2021 Supported by the National Natural Science Foundation of China (Grant Nos. 11774154, 11790311, and 12004172), the National Key Research and Development Program of China (Grant No. 2018YFA0306800), the Fundamental Research Funds for the Central Universities (Grant No. 0204-14380186), the Jiangsu Planned Projects for Postdoctoral Research Funds (Grant No. 2020Z172), the Program for High-Level Entrepreneurial and Innovative Talents Introduction of Jiangsu Province, and the Program B for Outstanding Ph.D. Candidates of Nanjing University.
*Corresponding authors. Email: jerrywang@nju.edu.cn; zhangyi@nju.edu.cn
Citation Text: Xie X D, Lin D J, Zhu L, Li Q Y, and Zong J Y et al. 2021 Chin. Phys. Lett. 38 107101    Abstract Understanding the interplay between superconductivity and charge-density wave (CDW) in NbSe$_{2}$ is vital for both fundamental physics and future device applications. Here, combining scanning tunneling microscopy, angle-resolved photoemission spectroscopy and Raman spectroscopy, we study the CDW phase in the monolayer NbSe$_{2}$ films grown on various substrates of bilayer graphene (BLG), SrTiO$_{3}$(111), and Al$_{2}$O$_{3}$(0001). It is found that the two stable CDW states of monolayer NbSe$_{2}$ can coexist on NbSe$_{2}$/BLG surface at liquid-nitrogen temperature. For the NbSe$_{2}$/SrTiO$_{3}$(111) sample, the unidirectional CDW regions own the kinks at $\pm 41$ meV and a wider gap at 4.2 K. It is revealed that the charge transfer from the substrates to the grown films will influence the configurations of the Fermi surface, and induce a 130 meV lift-up of the Fermi level with a shrink of the Fermi pockets in NbSe$_{2}$/SrTiO$_{3}$(111) compared with the NbSe$_{2}$/BLG. Combining the temperature-dependent Raman experiments, we suggest that the electron-phonon coupling in monolayer NbSe$_{2}$ dominates its CDW phase transition. DOI:10.1088/0256-307X/38/10/107101 © 2021 Chinese Physics Society Article Text Two-dimensional (2D) layered transition-metal dichalcogenides (TMDs)[1] exhibit a variety of novel physics properties in electronics,[2,3] photonics,[4–6] and spintronics,[7,8] hence attracted more and more interest nowadays. Among them, NbSe$_{2}$ is a promising material for understanding the physical mechanism and interplay of its charge density wave (CDW) and superconductivity (SC) phases, which are the most famous electronic correlation phenomena in condensed matter physics.[9,10] For the monolayer 1H-NbSe$_{2}$ film grown on the graphene substrate, its SC transition temperature ($T_{\rm C}$) is suppressed to only $\sim$3.0 K compared with that of the bulk counterpart ($\sim$7.2 K).[11] On the contrary, the CDW transition temperature ($T_{\rm CDW}$) in monolayer NbSe$_{2}$ ($\sim$145 K) is significantly higher than that of the bulk counterpart ($\sim$33.5 K).[12] The traditional viewpoint of the physical mechanism of the CDW in NbSe$_{2}$ varies from the Peierls instability triggered by the configuration of the Fermi surface (FS),[13–16] to the $q$-dependent electron-phonon coupling induced period lattice distortion,[17] and the FS nesting which seriously depends on the shape and the size of the FS, and it is still under discussion till now. However, for the mechanism of the superconducting, it is reported that the fine structure of the scanning tunneling spectroscopy (STS) induced by the spin fluctuations indicates an unconventional Cooper paring,[18] which is controversial with the consensus of conventional superconductor and opens a new way to understand the origin of the superconducting of NbSe$_{2}$. In this work, we successfully obtain atomically flat monolayer 1H-NbSe$_{2}$ films on various substrates of bilayer graphene (BLG), 0.7% Nb-doped SrTiO$_{2}$(111), and Al$_{2}$O$_{3}$(0001) using the molecular beam epitaxial (MBE) method. Combining the Raman spectroscopic, scanning-tunneling microscopic (STM), and angle-resolved photoemission spectroscopic (ARPES) measurements, we investigate the CDW transitions and the electron-phonon interactions in the epitaxial monolayer NbSe$_{2}$. It is found that different substrates will induce different strengths of the charge transfer to the grown NbSe$_{2}$ films, which will significantly influence the configurations of the FS and the strengths of the electron-phonon coupling in monolayer NbSe$_{2}$, thus giving rise to change of critical temperature of the CDW phase transitions. The growth of NbSe$_{2}$ films was performed in a combined MBE-STM-ARPES system with a base pressure of $1.5 \times 10^{-10}$ mbar. The BLG substrates were obtained by flash-annealing 4H-SiC(0001) wafers.[19] The SrTiO$_{3}$(111) and Al$_{2}$O$_{3}$(0001) substrates were well-prepared by thermo-degassing in an ultra-high vacuum (UHV) MBE chamber. The in situ APRES measurements were performed at low temperature $\sim$7 K, and the in situ STM measurements were performed at room temperature (RT). The low-temperature scanning tunneling microscopic (LT-STM) measurements were performed ex situ in an UNISIKO USM1600 system. The temperature-dependent Raman scattering measurements were conducted by the beam from a diode-pumped 532 nm laser which consists of a Montana Instruments Cryostation and a Princeton Instruments grating spectrometer with a base pressure of $10^{-4}$ Pa. More experimental details are provided in the Supplementary Material A.
Fig. 1. (a) Three-dimensional view, (b) top-view and (c) side-view sketches of monolayer NbSe$_{2}$ crystalline structure. (d)–(f) The RHEED patterns of NbSe$_{2}$ films grown on (d) BLG, (e) SrTiO$_{3}$(111) and (f) Al$_{2}$O$_{3}$ substrates. The upper insets in blue frames are the patterns of the substrates prepared for growth, the lower insets in red frames are the patterns of the grown NbSe$_{2}$ films. (g) and (h) The RT-STM images of the NbSe$_{2}$ films grown on (g) BLG with $\sim$70% coverage ($V_{\rm bias} = 400$ mV, $I_{\rm t} = 400$ pA) and on (h) SrTiO$_{3}$(111) ($V_{\rm bias} = 1$ V, $I_{\rm t} = 100$ pA, $T = 300$ K) substrates, respectively. (i) Height profiles along the blue lines shown in the STM images in (g) and (h). The upper are profiles of the bilayer NbSe$_{2}$ on BLG, the lower are the profiles of NbSe$_{2}$ on SrTiO$_{3}$(111), the average height of SrTiO$_{3}$(111) terraces is 0.21 nm, the values labeled by the red texts are the heights of monolayer NbSe$_{2}$ on monolayer NbSe$_{2}$ domain (0.6 nm), BLG (0.92 nm), and SrTiO$_{3}$ (0.54 nm), respectively.
Figures 1(a)–1(c) show the crystalline structure of monolayer 1H-NbSe$_{2}$. The NbSe$_{2}$ monolayer lattice has a layer of triangle-arranged Nb atoms in the central region, which is sandwiched by two layers of chalcogen Se atoms in a trigonal prismatic crystal structure. Figures 1(d)–1(f) show the RHEED patterns of the prepared BLG, SrTiO$_{3}$(111), Al$_{2}$O$_{3}$ substrates (upper insets in blue frames), and the grown NbSe$_{2}$ films on them (lower insets in red frames). The sharp ($1 \times 1$) diffraction stripes indicate the high-quality of the grown NbSe$_{2}$ films. We further confirmed the chemical constitution of the grown NbSe$_{2}$ films via x-ray photoemission spectroscopic (XPS) measurements, which clearly showed the core levels of Nb 3$d$ and Se 3$d$ orbitals of the grown NbSe$_{2}$ films on BLG and SrTiO$_{3}$(111) substrates (see Fig. S1 in Supplementary Material B). The surface morphology of NbSe$_{2}$ films grown on BLG and SrTiO$_{3}$(111) substrates was obtained in situ via STM measurements performed at room temperature (300 K). A $\sim 70$% (0.7 ML) coverage of NbSe$_{2}$ films with the average domain width of $\sim$100 nm grown on BLG and a nearly full coverage of monolayer NbSe$_{2}$ films grown on SrTiO$_{3}$(111) can be seen in Figs. 1(g) and 1(h). A few small bilayer NbSe$_{2}$ islands were formed on the monolayer NbSe$_{2}$ domains in the NbSe$_{2}$/BLG sample in Fig. 1(g), at the same time, we can also find that the NbSe$_{2}$ films follow the terrace-growth mode with much smaller but denser grain boundaries on SrTiO$_{3}$(111) in Fig. 1(h), without the formation of bilayer island. From the height profile shown in Fig. 1(i), we can see that the monolayer NbSe$_{2}$ domains on SiTiO$_{3}$(111) show lower height (0.54 nm) than that on the BLG substrate (0.92 nm) and the height of bilayer NbSe$_{2}$ island on monolayer NbSe$_{2}$ domain (0.6 nm), indicating that the interaction between NbSe$_{2}$ film and SrTiO$_{3}$(111) substrate is stronger than that between NbSe$_{2}$/BLG and NbSe$_{2}$ itself.[20,21] Therefore, it tends to form the nucleation along the boundary of the terrace and to enlarge the domain gradually by centering on the nucleation, hence the domains of the NbSe$_{2}$ film on SrTiO$_{3}$(111) are always smaller than those on BLG. The CDW state is a periodic modulation of the electronic density which reflects the distortion of the lattice structure, it is always accompanied by the dimerization or trimerization of the atoms on the original plane, which will induce a new periodic superstructure when lowering the temperature to an extent.[12,17] Researchers have reported the coexistence of two stable and topologically entangled competing structures of bulk NbSe$_{2}$ CDW states below 4.3 K.[22,23] Actually, the two CDW states hold the analogous atomic structures, that is, they are both comprised of small triangular Nb trimers and large triangular 6-atom Nb clusters in one $3 \times 3$ CDW unit cell. The difference lies in what the center of the Nb trimer and 6-atom Nb clusters covers, the structure centered on the hollow site is called the hollow-center CDW states (HC-CDW) [Fig. 2(c)], while the structure centered on the anion (Se) atoms is called the anion-center CDW states (AC-CDW) [Fig. 2(d)]. Here we found the coexistence of the two competing CDW states on NbSe$_{2}$/BLG at liquid-nitrogen temperature (76 K) in our atomic STM images. Figures 2(c) and 2(d) show the zoom-in LT-STM images of monolayer NbSe$_{2}$/BLG and the simulation of the HC- and AC-CDW structures shown in Fig. 2(a). The $3 \times 3$ CDW unit cell formed by the 4 Nb trimers and the triangular Nb sextet can be found in Fig. 2(c), the center locates at the hollow site of the Nb trimer, and it matches the simulation of HC-CDW states well. In the meantime, the brightest protrusion in Fig. 2(d) agrees well with the center Se atom of the triangular Nb sextet and the 4 Nb trimers also center on the Se anion, which matches the AC simulation well, thus demonstrating that the HC- and AC-CDW states can coexist at liquid-nitrogen temperature (76 K).
Fig. 2. (a) and (e) The LT-STM images taken at 76 K of the CDW states in monolayer NbSe$_{2}$/BLG and NbSe$_{2}$/SrTiO$_{3}$(111), respectively. The $3 \times 3$ CDW states are illustrated by the green and blue dotted rhombuses in (a), the size of the images presented is $10 \times 10$ nm$^{2}$. (b) and (f) The FFT of (a) and (e). The white dotted circles indicate the ($1 \times 1$) Bragg spots and the green dotted circles indicate the spots of the ($3 \times 3$) CDW states. (c) and (d) Zoom-in LT-STM images around the HC- (green rhombus) and AC-CDW (blue rhombus) regions in (a). The sketches of the HC- and AC-CDW states are presented. The red and blue dots represent the Nb and Se atoms, respectively. The size of the images presented is $3 \times 3$ nm$^{2}$. (g) The IFFT images of (f), the 1$Q$ CDW regions are in a parallel arrangement, the $3 \times 3$ CDW states are in the short-range and distorted structure (green dotted rhombus), the size of the images presented is $8 \times 8$ nm$^{2}$. (h) The STS of the unidirectional (1Q) CDW regions on NbSe$_{2}$/SrTiO$_{3}$(111) taken at 4.2 K. The symmetric kinks locate at $\pm 41$ meV ($V_{\rm bias} = -50 \rightarrow 50$ mV, $I_{\rm t} = 200$ pA). The scanning parameters are as follows: (a) $V_{\rm bias}= -100$ mV, $I_{\rm t} = 100$ pA; (c) $V_{\rm bias} = -100$ mV, $I_{\rm t} = 100$ pA; (d) $V_{\rm bias} = -100$ mV, $I_{\rm t} = 100$ pA; (e) $V_{\rm bias} = 20$ mV, $I_{\rm t} = 220$ pA; (g) $V_{\rm bias}= 20$ mV, $I_{\rm t} = 220$ pA.
We also observed the CDW states in the monolayer NbSe$_{2}$ film grown on the SrTiO$_{3}$(111) substrate at liquid-nitrogen temperature (76 K) [Fig. 2(e)], which shows an inhomogeneous CDW structure compared with the regular $3 \times 3$ CDW state in NbSe$_{2}$/BLG. Figures 2(b) and 2(f) are the fast Fourier transform (FFT) of Figs. 2(a) and 2(e), respectively. They both exhibit explicit ($1 \times 1$) Bragg spots (${\boldsymbol q}_{1\times 1}$) corresponding to the original NbSe$_{2}$ lattice structure. The ($3 \times 3$) CDW spots of the monolayer NbSe$_{2}$ grown on BLG (${\boldsymbol q}_{1}$) are clearly observed in Fig. 2(b). However, for NbSe$_{2}$/SrTiO$_{3}$(111) [Fig. 2(e)], a set of blurry arcs (${\boldsymbol q}_{1}$) at 1/3 Bragg vector can be observed instead of the ($3 \times 3$) spots in Fig. 2(b). They are probably due to the smaller domains and different orientations between the terraces of the NbSe$_{2}$ films grown on SrTiO$_{3}$(111), which contribute to the inhomogeneity of the CDW state on NbSe$_{2}$/SrTiO$_{3}$(111). We then obtained the lattice constant of NbSe$_{2}$/SrTiO$_{3}$(111) and NbSe$_{2}$/BLG by inversing fast Fourier transformation (IFFT) of the ($1 \times 1$) Bragg spots (${\boldsymbol q}_{1\times 1}$). We should notice that the lattice constant of NbSe$_{2}$ on SrTiO$_{3}$(111) ($3.47 \pm 0.05$ nm) is shorter than that on BLG ($3.56 \pm 0.05$ nm), indicating $-2.5$% compressive strain modulated by the SrTiO$_{3}$ substrate applied to the grown NbSe$_{2}$ films, which was reported in the 1T$'$-WSe$_{2}$ film grown on SrTiO$_{3}$(100).[24] Figure 2(g) is the IFFT of Fig. 2(e), the $3 \times 3$ CDW states shown are in short-range and distorted structure, causing the inhomogeneous $3 \times 3$ CDW states on SrTiO$_{3}$(111). Moreover, we found the unidirectional (1Q) CDW regions on NbSe$_{2}$/SrTiO$_{3}$(111), which are in parallel arrangement along the boundary, and the regions of different directions form a rotation of 120$^{\circ}$ with each other. Figure 2(h) shows the scanning tunneling spectrum (STS) of the 1Q CDW regions taken at 4.2 K, it owns a wide and symmetric U-shaped gap with kinks at $\epsilon_{_{\scriptstyle K}}=\pm 41$ meV. Different from the minimum $\epsilon_{{\min}}$ offset from $\epsilon_{_{\scriptstyle \rm F}}$ ($V_{\rm bias} = 0$) by 5 mV as reported,[25] our spectrum measured in the monolayer NbSe$_{2}$/SrTiO$_{3}$(111) shows a wider gap but with no offset from $\epsilon_{_{\scriptstyle \rm F}}$, which may be due to the monolayer nature of NbSe$_{2}$ rather than the asymmetric V-shaped gap in its bulk counterpart. For quasi-one-dimensional CDW materials, the CDW order is originated from the Peierls instability. That is to say, the distortion of the lattice structure will induce the periodic modulation of the electronic charge density, thus opening a gap at the Fermi level.[13,26] For two- and three-dimensional CDW materials, a nesting is believed to appear at the FS, and calculation and simulation have predicted the shape of the FS nesting,[27,28] but the typical FS nesting on NbSe$_{2}$ was not distinctly found.[29,30] To investigate the electronic band structures and the impact of the charge transfer between the NbSe$_{2}$/BLG and NbSe$_{2}$/SrTiO$_{3}$(111) samples, we carried out the in situ ARPES measurements at 7 K. Figures 3(a) and 3(d) show the ARPES spectra along the $M$–$\varGamma$–$K$ direction of Brillion zone on the NbSe$_{2}$/BLG and NbSe$_{2}$/SrTiO$_{3}$(111), respectively. Both of them display two broad and symmetrical bands which follow the trend of a hole-like conduction band structure and traverse the Fermi level, indicating the existence of a Fermi pocket around the $\varGamma$ point. We further obtained the FS mapping of monolayer NbSe$_{2}$ films on BLG [Fig. 3(b)] and SrTiO$_{3}$(111) [Fig. 3(e)]. For monolayer NbSe$_{2}$, the distinct hexagonal FS pocket dominated by Nb 4$d$ orbital centered at $\varGamma$ point can be clearly observed,[31] differing from the bulk NbSe$_{2}$, whose $\varGamma$ point is surrounded by a three-dimensional pancake-like FS composed of two double-walled Nb 4$d$ cylindrical bands and one Se 4$p$ derived band.[27,32,33] In addition, we found the width ($Q_{\rm FS}$) of the FS pocket in NbSe$_{2}$/SrTiO$_{3}$(111) (0.91 Å$^{-1}$) is narrower than that in NbSe$_{2}$/BLG (1.04 Å$^{-1}$), indicating the lift-up of the Fermi level on NbSe$_{2}$/SrTiO$_{3}$(111) compared with that on NbSe$_{2}$/BLG. On the other hand, we also observed that six hole-like pockets centered at the six $K$ points are shrunk in the NbSe$_{2}$/SrTiO$_{3}$(111) sample compared with the NbSe$_{2}$/BLG. Moreover, the zoom-in spectra shown in Figs. 3(c) and 3(f) illustrate the distribution of photoemission intensity along the $K$–$M$–$K$ direction of BZ [corresponding to the white cut lines in Figs. 3(b) and 3(e)]. We found that the bottom of the band along $K$–$M$–$K$ direction of the NbSe$_{2}$/SrTiO$_{3}$(111) is 130 meV lower than that of NbSe$_{2}$/BLG in energy, indicating that the Fermi level on NbSe$_{2}$/SrTiO$_{3}$(111) is 130 meV higher than NbSe$_{2}$/BLG. The narrower the width of the FS pocket centered at the $\varGamma$ point, the more the shrinking of the six hole-like pockets at the $K$ point on NbSe$_{2}$/SrTiO$_{3}$(111) than NbSe$_{2}$/BLG, combining with the broadening of the distance along $K$–$M$–$K$ direction of BZ (see Fig. S2 in Supplementary Material C). All of them demonstrate the lift-up of the Fermi level. Furthermore, the charge transfer from the substrate to the grown NbSe$_{2}$ films will induce the heavier $n$-doping electronic structure in NbSe$_{2}$/SrTiO$_{3}$(111) than NbSe$_{2}$/BLG, thus will influence the electron-phonon coupling in monolayer NbSe$_{2}$, which will be discussed in the following Raman measurements.
Fig. 3. (a) and (d) ARPES spectra of NbSe$_{2}$ films grown on BLG and SrTiO$_{3}$(111) substrates measured along the $M$–$\varGamma$–$K$ direction taken at 7 K. (b) and (e) FS mapping of the NbSe$_{2}$/BLG and NbSe$_{2}$/SrTiO$_{3}$(111), respectively. All the yellow dotted pockets are composed of Nb 4$d$ orbital of the monolayer NbSe$_{2}$. (c) and (f) Zoom-in ARPES spectra along the white cut lines ($K$–$M$–$K$ direction) shown in (b) and (e), from which we can see that the Fermi level of the NbSe$_{2}$/SrTiO$_{3}$(111) is lift up by 130 meV compared to the NbSe$_{2}$/BLG.
It is reported that the weak feature at $\sim$190 cm$^{-1}$ appears when the temperature reaches the $T_{\rm CDW}$ from above and its strength increases with the decreasing temperature, which means that the weak feature at $\sim$190 cm$^{-1}$ can be treated as the signatures of the CDW phase.[12] Here, we obtained the temperature-dependent Raman spectrum of monolayer NbSe$_{2}$ grown on BLG [Fig. 4(a)], SrTiO$_{3}$ [Fig. 4(b)] and Al$_{2}$O$_{3}$ [Fig. 4(c)] from 3.4 K to 300 K. The peak of the phonon mode $A_{\rm 1g}$ (out-of-plane vibration, $\sim$230 cm$^{-1}$) and $E_{\rm 2g}$ (in-plane vibration, $\sim$250 cm$^{-1}$) can be seen clearly in our monolayer NbSe$_{2}$ films grown on these substrates. The weak feature at $\sim$190 cm$^{-1}$ diminishes linearly with the increasing temperature and vanishes at a temperature above 200 K in the NbSe$_{2}$/SrTiO$_{3}$(111) and NbSe$_{2}$/Al$_{2}$O$_{3}$ samples, but it cannot be found in the NbSe$_{2}$/BLG since a wide and strong mode lies at the frequency less than 100 cm$^{-1}$ (see Supplementary Material D) and an extremely sharp and strong $E_{2}$ mode around 200 cm$^{-1}$,[34] which cover the weak feature at 190 cm$^{-1}$. We calculated the areas of the above peaks depending on increasing temperature in order to obtain the $T_{\rm CDW}$ of these samples. For the NbSe$_{2}$/BLG, the $A_{\rm 1g}$ mode is stronger than $E_{\rm 2g}$ mode, contrary to the NbSe$_{2}$/SrTiO$_{3}$(111) and NbSe$_{2}$/Al$_{2}$O$_{3}$ samples, which may due to the weaker interface interaction in NbSe$_{2}$/BLG rather than that in NbSe$_{2}$/SrTiO$_{3}$(111) and NbSe$_{2}$/Al$_{2}$O$_{3}$ as discussed above. The area of the $E_{\rm 2g}$ mode decreases almost linearly with the increasing temperature and it vanishes when the temperature is above 200 K, but there is a sluggish kink at 100 K. The area of the $A_{\rm 1g}$ mode decreases drastically below 120 K and it remains almost unchanged from 150 K. The distinct inflection point at 135 K shown in Fig. 4(d) is coincident with $T_{\rm CDW}$ of monolayer NbSe$_{2}$/BLG. For the NbSe$_{2}$ grown on SrTiO$_{3}$(111) [Fig. 4(e)], the area of the $A_{\rm 1g}$ mode decreases slowly but still exists from 3.4 K up to 300 K, the area of the $E_{\rm 2g}$ mode decreases drastically until 150 K, then it dropped gently to 300 K, both of them have an inflection point around 140 K, indicating the critical point $T_{\rm CDW}$ on NbSe$_{2}$/SrTiO$_{3}$(111). For NbSe$_{2}$ on Al$_{2}$O$_{3}$ [Fig. 4(f)], the $A_{\rm 1g}$ and $E_{\rm 2g}$ mode displays a similar trend from 3.4 K to 300 K, the area of them both decreases until 200 K and more drastically from then on, the $A_{\rm 1g}$ mode finally vanishes at room temperature, indicating $T_{\rm CDW}$ above 200 K in the NbSe$_{2}$/Al$_{2}$O$_{3}$.
Fig. 4. The temperature dependence of the Raman spectra of NbSe$_{2}$ grown on (a) BLG, (b) SrTiO$_{3}$(111), and (c) Al$_{2}$O$_{3}$ substrates varied from 3.4 K to 300 K. The red dotted curves are the peak fittings of the soft mode at $\sim$190 cm$^{-1}$, $A_{\rm 1g}$ ($\sim$230 cm$^{-1}$) and $E_{\rm 2g}$ ($\sim$250 cm$^{-1}$) mode. (d)–(f) Temperature-dependent peak areas of the soft mode, $A_{\rm 1g}$ and $E_{\rm 2g}$ mode extracted from (a)–(c). The general trend of the modes is monotonically decreasing with the increasing temperature, and the reflection points/kinks (the green pentastar) indicate the transitions of the CDW phase in NbSe$_{2}$.
These distinct kinks of the temperature-dependence of Raman peaks imply the transitions of electron-phonon coupling strength, which coincide with the $T_{\rm CDW}$ and would play a key role in the CDW phenomena in monolayer NbSe$_{2}$. Considering that there is no charge transfer from Al$_{2}$O$_{3}$ to the grown NbSe$_{2}$ films, the $T_{\rm CDW}$ above 200 K is the intrinsic critical point of monolayer NbSe$_{2}$ itself in the NbSe$_{2}$/Al$_{2}$O$_{3}$ sample. The charge transfer effect in NbSe$_{2}$/SrTiO$_{3}$ reduces its $T_{\rm CDW}$ to $\sim$140 K compared with the intrinsic NbSe$_{2}$ grown on Al$_{2}$O$_{3}$, while the NbSe$_{2}$/BLG shows less charge transfer than NbSe$_{2}$/SrTiO$_{3}$ but shows slightly lower $T_{\rm CDW}$ of $\sim$135 K, implying that the strain effect would also affect the electron-phonon coupling. As mentioned above, we found that the NbSe$_{2}$/SrTiO$_{3}$(111) shows about $-2.5$% compressing strain compared with the NbSe$_{2}$/BLG. This compressing strain may play contrary effect on the $T_{\rm CDW}$ compared to the charge transfer effect. Therefore, the competing influence on the electron-phonon coupling between the strain effect and the charge transfer effect slightly increase the $T_{\rm CDW}$ in NbSe$_{2}$/SrTiO$_{3}$(111) by 5 K compared to the $T_{\rm CDW}$ in NbSe$_{2}$/BLG. Besides the distinct kinks of the temperature-dependence of the Raman peaks, we note that the $A_{\rm 1g}$ and $E_{\rm 2g}$ peaks also show different temperature-dependent slopes between the NbSe$_{2}$/BLG, NbSe$_{2}$/SrTiO$_{3}$(111), and NbSe$_{2}$/Al$_{2}$O$_{3}$, particularly the slopes show different changing trends after the CDW transition temperatures in these three samples. Therefore, we suggest that the temperature-dependent slopes of the Raman peaks depend not only on the electron-phonon interactions but also on the interface interactions in the 2D system. Considering that the interface interactions should not change before and after CDW transition, we can attribute the slope kinks to the transition of the electron-phonon interactions crossing $T_{\rm CDW}$. Moreover, the different changing trends of the slopes after the $T_{\rm CDW}$ imply that the electron-phonon interactions play different (positive or negative) effects to the temperature-dependent slopes of the Raman peaks in the NbSe$_{2}$/BLG, NbSe$_{2}$/SrTiO$_{3}$(111), and NbSe$_{2}$/Al$_{2}$O$_{3}$ samples. However, the specific mechanism of the electron-phonon interaction effect on the temperature-dependence of Raman peaks is not still very clear, and we expect more further theoretical and experimental works following up to resolve this issue. In summary, we have epitaxially grown monolayer NbSe$_{2}$ films on BLG, SrTiO$_{3}$(111), and Al$_{2}$O$_{3}$(0001) substrates by the MBE method. The STM measurements show a $-2.5$% compressing strain in the NbSe$_{2}$/SrTiO$_{3}$(111) compared with NbSe$_{2}$/BLG. We further found that the two stable NbSe$_{2}$ CDW states of HC- and AC-CDW can coexist in the NbSe$_{2}$/BLG at liquid-nitrogen temperature of 76 K, but the domain boundaries between them are blurred probably due to the thermal perturbation covering up the weakened quantum phase fluctuation and the small energy difference between HC- and AC-CDW states. The more charge transfer from the SrTiO$_{3}$(111) substrate to the grown NbSe$_{2}$ films is clearly observed by our ARPES measurements, inducing a 130 meV lift-up of the Fermi level in NbSe$_{2}$/SrTiO$_{3}$(111) compared with the NbSe$_{2}$/BLG, thus influencing the configurations of the Fermi surface. At the same time, the 1$Q$ CDW regions are observed on NbSe$_{2}$/SrTiO$_{3}$(111) at 4.2 K, they are in a parallel arrangement and form a 120$^\circ$ rotation with each other, the STS of the 1$Q$ regions shows a wide and symmetric U-shaped gap with the kinks at $\pm 41$ meV. Moreover, combining the temperature-dependent Raman experiments, we suggested both the charge transfer effect and the strain effect would affect the strength of the electron-phonon coupling in NbSe$_{2}$, which is suggested to play the dominant role in the CDW phase transition of NbSe$_{2}$ films, and also a key factor in generating the superconductivity in condensed matter.[35,36]
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