⇦Chinese Physics Letters, 2020, Vol. 37, No. 9, Article code 097402 Tunable Superconductivity in 2H-NbSe$_{2}$ via $\boldsymbol In~Situ$ Li Intercalation Kaiyao Zhou (周楷尧)1,2, Jun Deng (邓俊)1,2, Liwei Guo (郭丽伟)1,2,3, and Jiangang Guo (郭建刚)1,3* Affiliations 1Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China 2University of Chinese Academy of Sciences, Beijing 100049, China 3Songshan Lake Materials Laboratory, Dongguan 523808, China Received 28 June 2020; accepted 20 July 2020; published online 1 September 2020 Supported by the MoST-Strategic International Cooperation in Science, Technology and Innovation Key Program (Grant No. 2018YFE0202601), the National Key Research and Development Program of China (Grant Nos. 2017YFA0304700 and 2016YFA0300600), the National Natural Science Foundation of China (Grant Nos. 51922105 and 51772322), and the Chinese Academy of Sciences (Grant No. QYZDJ-SSW-SLH013).
*Corresponding author. Email: jgguo@iphy.ac.cn Citation Text: Zhou K Y, Deng J, Guo L W and Guo J G 2020 Chin. Phys. Lett. 37 097402    Abstract Using the newly-developed solid ionic gating technique, we measure the electrical transport property of a thin-flake NbSe$_{2}$ superconductor ($T_{\rm c} = 6.67$ K) under continuous Li intercalation and electron doping. It is found that the charge-density-wave transition is suppressed, while at the same time a carrier density, decreasing from $7\times 10^{14}$ cm$^{-2}$ to $2\times 10^{14}$ cm$^{-2}$ also occurs. This tunable capability in relation to carrier density is 70%, which is 5 times larger than that found using the liquid ionic gating method [Phys. Rev. Lett. 117 (2016) 106801]. Meanwhile, we find that the scattering type of conduction electrons transits to the $s$–$d$ process, which may be caused by the change of the occupied states of 4$d$-electrons in Nb under the condition of Li intercalation. Simultaneously, we observe a certain decrement of electron-phonon coupling (EPC), based on the electron-phonon scattering model, in the high temperature range. Based on data gathered from in situ measurements, we construct a full phase diagram of carrier density, EPC and $T_{\rm c}$ in the intercalated NbSe$_{2}$ sample, and qualitatively explain the variation of $T_{\rm c}$ within the BCS framework. It is our opinion that the in situ solid ionic gating method provides a direct route to describing the relationship between carrier density and superconductivity, which is helpful in promoting a clearer understanding of electronic phase competition in transition metal dichalcogenides. DOI:10.1088/0256-307X/37/9/097402 PACS:74.25.Dw, 74.20.Fg, 71.15.Mb © 2020 Chinese Physics Society Article Text Carrier density correlated to the electronic states at Fermi energy levels is an important factor affecting electronic phase transition.[1] Accurately calibrating the value of carrier density, the strengths of electron-electron interaction, and electron-phonon coupling (EPC) is crucial in terms of studying the origins of many emergent phenomena, such as magnetic phase transition,[2–5] the charge density wave (CDW),[6] and superconductivity (SC).[7–15] In Cu-based and Fe-based superconductors, complicated electronic phase diagrams have been constructed by tuning electron or hole density via introducing chemical substitution.[16–20] However, establishing an accurate relationship between carrier density, the strength of EPC, and the superconducting critical temperature ($T_{\rm c}$) is still necessary in order to correctly understand multiple phase interactions and the microscopic mechanism. Recently, a field effect technique, using a high-$\kappa$ dielectric of HfO$_{2}$ or BN as an insulating gate medium, has been developed to modulate the carrier density in thin-layer samples. This method can only induce carrier density variation in a maximum of about 10$^{13}$ cm$^{-2}$, which may not cover the full range observed in SC.[21,22] More recently, with the aid of a solid ionic conductor, a new in situ gating technique has been shown to increase the carrier density of the sample by two orders of magnitude by means of the controllable intercalation of Li ions. Using this Li ion intercalation method, multiple superconducting phases in FeSe[23] and semiconductor-metal-superconductor transition in 1T-SnSe$_{2}$[24] have been found. In this work, by tracing the temperature-dependent transport property under gating, we clearly describe the relations between $T_{\rm c}$, EPC and carrier density, with the aim of investigating the SC of 2H-NbSe$_{2}$. It is well known that 2H-NbSe$_{2}$ is a type-II superconductor with a $T_{\rm c}$ of about 7.3 K, higher than observed in most transition metal dichalcogenides. Moreover, a CDW phase transition, occurs at $T_{\rm CDW} = 33$ K in bulk NbSe$_{2}$.[25] NbSe$_{2}$ possesses a hexagonal structure with a space group of $P6_{3}/mmc$, where a hexagonal plane of Nb atoms is sandwiched by two layers of Se atoms; each neutral NbSe$_{2}$ layer is connected by van der Waals force.[26] As the NbSe$_{2}$ is thinned to a monolayer, only one Nb-derived band crosses the $E_{\rm F}$, leaving one hole-pocket both at $\varGamma$ point and $K$ point.[27] The CDW order in bulk and thin layer NbSe$_{2}$ has been extensively studied. Strengthened electron-phonon coupling,[28,29] enhanced Fermi-surface nesting,[30,31] and saddle-point singularities[32] have also been reported recently. Here, we systemically tune the carrier density, EPC constant and SC in a thin layer NbSe$_{2}$ sample, using the solid-ionic-conductor gating technique, where intercalation of Li ions into NbSe$_{2}$ layers is controlled by an external electric field. Following a detailed analysis of the transport data, we find that the $T_{\rm c}$ continuously decreases below 1.5 K as the carrier density decreases and EPC is weakened. The decreased amount of carrier density is over 70%, which significantly exceeds the tunable capability of sole electrostatic doping in the ionic liquid technique. A superconducting phase diagram is constructed, based on our measurements, where the decrement of $T_{\rm c}$ is explained by decreased carrier density and weakened EPC within the BCS framework. Experimental Details. Bulk NbSe$_{2}$ single crystals were grown by a conventional chemical vapor deposition method, with iodine as a transport agent. The stoichiometric mixture of high-purity Nb powder (Alfa Aesar, 99.99%) and Se powder (Alfa Aesar, 99.999%) was sealed in an evacuated quartz tube (15 cm long), before being placed in a two-temperature zone tube furnace. The temperatures were set to 900 K and 800 K, respectively, and the growth process took place over two weeks. The typical single crystals were plate-like, with a size of $0.01{\,\rm mm} \times 0.5{\,\rm mm} \times 2$ cm. The crystal structure was verified using a Panalytical X'pert PRO diffractometer (Cu $K\alpha$ radiation) with a graphite monochromator in the 2$\theta$ range from 5$^{\circ}$ to 130$^{\circ}$.
cpl-37-9-097402-fig1.png
Fig. 1. Schematic fabrication process for a thin-flake NbSe$_{2}$ device, and its analysis via optical microscopy and AFM. (a) Schematic process for the device. (b) Optical image of the device. Scale bar 40 µm. (c) Sample thickness measured by AFM.
In a typical fabrication process, a 50 nm Au layer was first deposited on a SiO$_{2}$ (270 nm)/Si substrate by electronic beam evaporation. Next, Li$_{2}$Al$_{2}$SiP$_{2}$TiO$_{13}$ (LASPT) (KEJING Co. Ltd) was pasted onto the Au deposited substrate using silver conductive epoxy. A schematic of this process is shown in Fig. 1(a). A semi-transparent thin flake (size over $50 \times 30\,µ$m$^{2}$) of NbSe$_{2}$ was prepared by mechanical exfoliation from NbSe$_{2}$ single crystals, then transferred onto LASPT using polydimethylsiloxane (PDMS). A Hall bar with Ti(10 nm)/Au(100 nm) electrodes was then patterned onto the thin-flake, using e-beam lithography, as shown in Fig. 1(b). The sample surface was observed via optical spectroscopy (Olympus BX51). Its thickness of 20–80 nm was determined by atomic force microscopy (AFM) (Bruker AFM Multimode 8) [see Fig. 1(c)]. The sample's transport property was measured inside a closed-cycle cryostat (C-mag 9 T), equipped with a Keithley 2182 A and a 2400 source meter. Back-gated voltage $V_{\rm G} = 5.5$ V was applied to the LASPT, since the electrochemical window of LASPT is below 6 V. First principles calculations were performed using the Vienna ab initio simulation package (VASP).[33,34] We adopted the generalized gradient approximation (GGA) in the form of the Perdew–Burke–Ernzerhof (PBE) functional[35] for the exchange-correlation potentials. The projector augmented-wave (PAW) pseudopotential[36] was employed, with a plane-wave energy cutoff of 500 eV. The Li$_{0.33}$NbSe$_{2}$ was simulated by a $3\times 3\times 1$ supercell of LiNbSe$_{2}$ with random Li vacancies. Monkhorst–Pack[37] $k$-meshes of $17\times 17\times 4$ and $6\times 6\times 4$ were used for sampling the first Brillouin zone in the self-consistent calculation, and $34\times 34\times 8$ and $11\times 11\times 8$ were used for the density of states for NbSe$_{2}$ and Li$_{0.33}$NbSe$_{2}$, respectively. Atomic positions and lattice parameters were relaxed until all the forces on the ions were less than 10$^{-2}$ eV/Å. Results and Discussion. Figure 2(a) shows an optical image of bulk single crystal NbSe$_{2}$ with a shiny surface. The lattice constant along the $c$-axis, 12.548 Å, was determined by the (002) peak position of the x-ray diffraction pattern depicted in Fig. 2(b). As shown in Fig. 2(c), the molar ratio of Nb and Se is $38.15\!:\!61.85$, which is close to nominal composition, regardless of the intrinsic errors associated with energy dispersive spectroscopy. Layered morphology and hexagonal symmetry can be observed in the image from the scanning electron microscope (SEM). The temperature dependence of electrical resistivity in bulk NbSe$_{2}$ was measured through the standard four-electrode method. Figure 2(d) shows a $T_{\rm c}^{\rm onset}$ of 7.27 K, and the residual resistance ratio (RRR) $R_{\rm s}$(300 K)/$R_{\rm s}$(8 K) is about 12.85. As is well known, mechanical exfoliation is a convenient method for obtaining high quality and thin-flake samples from a single crystal.[26] The PDMS dry-transfer method does not require any wet chemistry, thereby maintaining the purity of the sample.[38] We fabricated a hall bar on thin-flake NbSe$_{2}$ via a process of mechanical exfoliation and the PDMS dry-transfer method. In this work, the thickness of the thin-flake NbSe$_{2}$ is around 20–80 nm. The transport properties of the thin-flake sample were measured as shown in Fig. 2(e). It is observed that a sharp superconducting transition appears in the sheet electrical resistance ($R_{\rm s}$) curve, measured from 300 K to 1.5 K. The onset of superconducting critical temperature ($T_{\rm c}^{\rm onset}$) is 6.67 K and $T_{\rm c}^{\rm zero}$ is 6.65 K. The RRR of the thin-flake NbSe$_{2}$ is 16.95, even higher than that for bulk NbSe$_{2}$, demonstrating the high quality of the sample. To estimate the upper critical fields [$H_{\rm c2}(T)$] of the thin-flake NbSe$_{2}$, we systematically measured the temperature-dependent $R_{\rm s}(T)$ in applied magnetic fields. Figure 2(f) shows the corresponding results for $H$, perpendicular to the (001) plane. The $H_{\rm c2}(T)$ is determined by using a 10% drop in normal state resistance ($R_{\rm n}$). A satisfactory fitting of the curve of $H_{\rm c2}(T)$ by the Ginzburg–Landau model, $H_{\rm c2}(T) = (\varphi_{0} / {2\pi \xi }^{2})[1-(T/T_{\rm c})^{\rm b}]$, is obtained, where $\varphi_{0}$ is the flux quantum $2.067 \times 10^{-15}$ Wb and $\xi$ the superconducting coherence length. The ${\mu_{0}H}_{\rm c2}(0)$ is derived to be 2.39 T. According to the relationship, $\mu_{0}H_{\rm c2}(0)= \varphi_{0} / {2\pi \xi }^{2}$, the value of $\xi$ is derived to be 11.73 nm.
cpl-37-9-097402-fig2.png
Fig. 2. (a) Crystal structure of 2H-NbSe$_{2}$. (b) X-ray diffraction pattern of NbSe$_{2}$ single crystal. Inset: optical image of as-grown NbSe$_{2}$ on a 1 mm $\times$ 1 mm grid. (c) SEM image of NbSe$_{2}$. Scale bar is 50 µm. (d) Normalized temperature dependence of electrical resistivity of bulk NbSe$_{2}$. (e) Temperature dependence of $R_{\rm s}$ of the thin NbSe$_{2}$ sample. The enlarged section of $R_{\rm s}$ at low temperature is shown as an inset. (f) Upper critical field ($\mu_{0}H_{\rm c2}$) as a function of temperature. Inset: temperature dependence of $R_{\rm s}$ subject to an external magnetic field. (g) Temperature dependence of $I_{\rm G}$ with a gate voltage of 5.5 V.
In order to select a suitable gating temperature, we measure the temperature dependence of the leakage current $I_{\rm G}$ [see Fig. 2(g)]. We find that $I_{\rm G}$ is almost independent of the temperature at $T < 170$ K, and there is only a tiny negative noise current, given that the Li ions are still frozen in LASPT. In the temperature range from 170–250 K, $I_{\rm G}$ slowly increases, and for $T > 250$ K, the $I_{\rm G}$ steeply increases. Based on the temperature dependence of $I_{\rm G}$, we select a gating temperature between 170–300 K. Based on the dependence of $I_{\rm G}$ on temperature and gating voltage, we set the gating voltage to 5.5 V for the experiment below. Figure 3(a) illustrates the temperature dependence of $R_{\rm s}$, measured in a temperature range below 200 K, after 5.5 V gating for one hour at the selected gating temperature range. As the gating temperature increases, the Li ions in the LASPT are more active and migrating more readily into the space between the NbSe$_{2}$ layers. As a result, $T_{\rm c}$ gradually decreases below 1.5 K, which is beyond our measurement limit, and SC is suppressed. Moreover, the slope of the resistance curve levels off, suggesting the weakening of electron-phonon coupling strength. In addition, we do not observe a clear kink in the resistance curve at the proposed $T_{\rm CDW} = 33$ K, which is consistent with the electrical resistivity features of NbSe$_{2}$ reported in Refs. [39,40]. To examine the kink feature of resistivity in detail, we take the first-order derivative of the $R_{\rm s}(T)$ curves, as shown in Fig. 3(b); a kink can be faintly observed in pristine and slightly intercalated samples at around 25 K, and close to 33 K, the reported $T_{\rm CDW}$ for bulk NbSe$_{2}$, suggesting that this phenomenon is a signature of CDW transition. Having applied electric-field gating above 280 K, the kink in the first-order derivative ($dR_{\rm s}/dT$) disappears, implying the suppression of CDW transition. After each gating, we measured the magnetic field dependence of Hall resistance $R_{xy}$ so as to deduce the sheet's carriers density $n_{\rm 2D}$. The data are plotted in Fig. 3(c). A single-band model was used to fit the $R_{xy}$, from which we can calculate hall coefficient $R_{\rm H}$ by $R_{\rm H}=R_{xy} /B$. The $n_{\rm 2D}$ was derived from the equation $n_{\rm 2D} = 1/(eR_{\rm H})$, where $e$ denotes the electron charge. The $n_{\rm 2D}$ as a function of temperature is plotted in Fig. 3(d). For the pristine flake NbSe$_{2}$, the character of the major carrier changes from hole to electron below 30 K; this Lifshitz transition may be a signature of the CDW transition.[41] Comparing the difference in $n_{\rm 2D}$ at 50 K, we discover that the tunable ability of carrier density ($\Delta n_{\rm 2D}$) is about $2.59\times 10^{15}$ cm$^{-2}$, which is nearly 5 times the value $6\times 10^{14}$ cm$^{-2}$ obtained via ionic liquid gating.[42] Therefore, we have established that our gating technique can induce a much greater variation in carrier density, which also results in a wide variation in $T_{\rm c}$. Both of these factors provide further information relating to the study of SCs.
cpl-37-9-097402-fig3.png
Fig. 3. Transport properties of thin-flake NbSe$_{2}$ subsequent to gating in the selected gating temperature range from 170 K to 300 K. (a) Temperature-dependent $R_{\rm s}$. Inset: an expanded view of the low temperature range. (b) The first derivative of $R_{\rm s}$ on $T_{\rm c}^{\rm onset} < T < 200$ K. Lower right inset gives an enlarged view of CDW transitions at low temperature. (c) Field dependence of $R_{xy}$. (d) Temperature dependence of the $n_{\rm 2D}$.
At low temperatures, the $R_{\rm s}$ can be fitted by the following power law function: $$ R_{\rm s}= R_{0} +AT^{\alpha }, $$ where $R_{0}$ denotes the residual square sheet resistance that is independent of temperature, $A$ is a constant, and $\alpha$ represents the exponent index, which is critically dependent on the type of interaction. The fitting was performed from the $T_{\rm c}$ to 30 K [see Fig. 4(a)]. For a conventional metal, described by the Fermi liquid theory, the $\alpha$ is 2. By increasing the amount of Li ions, the $\alpha$ increases to 3, indicating that the nature of the interaction turns from itinerant electron-electron interaction to the $s$–$d$ electron scattering variety. Similar interactions between $s$ and $d$ bands have been observed for NbC and TaC.[43] Here, the Li intercalation lowers the chemical valence of Nb$^{4+}$, and the increase of 4$d$ electrons may be responsible for inducing the observed change in the scattering process. Meanwhile, we find that the residual resistance $R_{0}$ has also increased monotonously, implying that many more scattering sites are created with increased Li-intercalation. The $T_{\rm c}$-dependent $\alpha$ is plotted on the upper panel of Fig. 4(b), where the $\alpha$ is shown to have rapidly increased as the $T_{\rm c}$ gradually decreases.
cpl-37-9-097402-fig4.png
Fig. 4. Transport properties of thin NbSe$_{2}$. (a) Temperature-dependent $R_{\rm s}$ and the fitted results based on the formula $R_{\rm s}= R_{0}+AT^{\alpha}$ (red curve), and the electron-phonon scattering model in the high-temperature limit (green curve). (b) Variation of $\alpha$ and $\lambda$ versus $T_{\rm c}$.
Furthermore, we fit the curve of high temperature range based on the electron-phonon scattering model in the high-temperature limit, so as to estimate the strength of EPC in intercalated thin-flake NbSe$_{2}$. In quasi-2D systems, the formula is given as follows:[39] $$ R_{\rm s}(T)\approx R_{0}+ \lambda \frac{2\pi k_{\rm B}m}{\hbar e^{2}n_{\rm 2D}}T=R_{0}+ \lambda \frac{{2\pi \hbar n}_{0}k_{\rm B}}{\varepsilon_{0}n_{\rm 2D}{(\hbar \omega_{\rm p0})}^{2}}T, $$ where $\lambda$, $\hbar $, and $k_{\rm B}$ correspond to an EPC constant, Planck's constant and the Boltzmann constant, respectively, and $n_{0}$ denotes bulk carrier density. The sheet carrier density is $n_{\rm 2D}=n_{0 }\times d$, with $d$ being the sample thickness. Here, $\omega _{\rm p}$ denotes the plasma frequency, $\omega_{\rm p0}= \sqrt {n_{0}e^{2}} / {\varepsilon_{0}m}$ with $\varepsilon_{0}$ is the vacuum permittivity, and $\hbar \omega_{\rm p0}=2.74$ eV for bulk NbSe$_{2}$.[44] The fitting data and obtained $\lambda$ are plotted in the right panel of Fig. 4(a) and the lower panel of Fig. 4(b), respectively. For pristine thin-flake NbSe$_{2}$, the $\lambda$ is 0.61, implying that NbSe$_{2}$ is an intermediately coupled superconductor. We find that $\lambda$ decreases as the injection amount of Li ions increases, and that the smallest $\lambda$ is 0.41.
cpl-37-9-097402-fig5.png
Fig. 5. Summarized $T_{\rm CD W}$, $\lambda$ and $T_{\rm c}$ in gated NbSe$_{2}$. Red solid circles correspond to the $T_{\rm CDW}$, defined as the sign change of $R_{\rm H}$. Black solid squares represent the $T_{\rm c}$. The blue solid triangle represents the scale of EPC constant. The color shade shows the transition of $\alpha$, implying the change of the electron interaction.
Figure 5 summarizes the carrier density relationships, $T_{\rm c}$ and $\lambda$, in the Li-ion intercalated thin-flake NbSe$_{2}$. Note that $T_{\rm c}$ remains nearly unchanged until $n_{\rm 2D}$, less than $5\times 10^{14}$ cm$^{-2}$, then gradually decreases. For the sake of accuracy, we only plot the $T_{\rm CDW}$ determined from the sign change of $R_{\rm H}$, as shown in Fig. 3(b). The $T_{\rm CDW}$ seems to show a slight increase when $T_{\rm c}$ decreases. The color contrast bar at the top of Fig. 5 represents the $\alpha$ values calculated from the fitting of $R_{\rm s}= R_{0}+AT^{\alpha}$. As the $T_{\rm c}$ decreases, the $\alpha$ increases from 2 to 3, indicating that the $s$–$d$ electron scattering becomes dominant. It is understood that the intercalation of Li ions into FeSe[23] and SnSe$_{2}$,[24] driven by an electric field, favors SC in FeSe and SnSe$_{2}$, where the increased electron density plays a decisive role. The increase of electron density also induces a great change in the carrier density of NbSe$_{2}$, as analyzed via Hall measurement, such that the hole carrier value $n_{\rm 2D}$ reduces by $2.59\times 10^{15}$ cm$^{-2}$. However, in Li-intercalated NbSe$_{2}$, the $T_{\rm c}$ is only monotonously suppressed with an increase in the gating temperature, which is consistent with the trend in the Li$_{x}$NbSe$_{2}$ powder sample prepared by the solid-state reaction method.[45] As $x$ is about 0.3, the SC is suppressed by slightly increasing the lattice constants. However, this is different from the feature of Rb$_{x}$NbSe$_{2}$,[46] where intercalation of large size Rb$^{+}$ cations changes both crystal and electronic structures, and even suppresses the SC transition below 1% doping.
cpl-37-9-097402-fig6.png
Fig. 6. Energy band structures (left) and projected density of states (right) normalized as per formula for (a) NbSe$_{2}$ and (b) Li$_{0.33}$NbSe$_{2}$.
Our in situ Li-intercalation technique barely alters the structural symmetry and Nb–Se bond length. For a qualitative understanding of the evolution of the electronic structure, we calculate the energy band structures and projected density of state (PDOS) for NbSe$_{2}$ and hypothetical Li$_{0.33}$NbSe$_{2}$, as shown in Fig. 6. As we know, in a metal, the variation in carrier density due to Li intercalation should be determined by the specific location of Fermi energy $E_{\rm F}$. Assuming that the $E_{\rm F}$ lies at a valley (peak) of the density of states, the intercalation of Li$^{+}$ should push the $E_{\rm F}$ away from the valley (peak) thereby increasing (decreasing) the carrier density under the rigid model. In the NbSe$_{2}$ sample, theoretical calculations show that the $E_{\rm F}$ is almost at the peak of the density of states. Intercalating Li$^{+}$ drives the $E_{\rm F}$ away from the peak, lowering the value of 2.65 states/eV per formula to 1.50 states/eV per formula. Our experimental data also confirms that the carrier density is decreased from $7\times 10^{14}$ cm$^{-2}$ to $2\times 10^{14}$ cm$^{-2}$, which supports the trend indicated by the theoretical calculations. The states around $E_{\rm F}$ are primarily composed of the Nb-4$d$ and Se-4$p$ orbital states for both NbSe$_{2}$ and Li$_{0.33}$NbSe$_{2}$. In the Li$_{0.33}$NbSe$_{2}$, where there is still metallic conductivity, even the Fermi surface lifts a little bit. Further lifting the $E_{\rm F}$ to the gap between 1.2 eV and 2.0 eV would lead to semiconducting behavior. According to the BCS theory, the SC gap ${\varDelta} =2\hbar \omega_{\rm L} \exp[-1/N(E_{\rm F})\lambda ]$, occurs where $\hbar \omega_{\rm L}$ is the average phonon energy, and $N(E_{\rm F})$ is the density of state at the $E_{\rm F}$. In the present work, the intercalated Li directly reduces the values of $N(E_{\rm F})$ and $\lambda$; as a result, the $T_{\rm c}$ is decreased. In summary, we have observed that the $T_{\rm c}$ in NbSe$_{2}$ is gradually suppressed due to Li ionic intercalation and being subject to electric gating. According to the BCS theory, the suppression of $T_{\rm c}$ of the thin-flake NbSe$_{2}$ is explained by the mutual effect of reduced density of state at the $E_{\rm F}$, and the weakened interaction of electron-phonon coupling. This in situ solid gating method allows the carrier density to be tuned over a wide range, and may enable us to accurately identify multiple important physical parameters critically affecting the SC, providing conclusive evidence in terms of understanding the superconducting evolution of NbSe$_{2}$. 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