Gate Tuning of Electronic Phase Transitions in Two-Dimensional ${\mathrm{NbSe}}_2$

Recent experimental advances in atomically thin transition metal dichalcogenide (TMD) metals have unveiled a range of interesting phenomena including the coexistence of charge-density-wave (CDW) order and superconductivity down to the monolayer limit. The atomic thickness of two-dimensional (2D) TMD metals also opens up the possibility for control of these electronic phase transitions by electrostatic gating. Here, we demonstrate reversible tuning of superconductivity and CDW order in model 2D TMD metal ${\mathrm{NbSe}}_2$ by an ionic liquid gate. A variation up to $\sim 50\%$ in the superconducting transition temperature has been observed. Both superconductivity and CDW order can be strengthened (weakened) by increasing (reducing) the carrier density in 2D ${\mathrm{NbSe}}_2$. The doping dependence of these phase transitions can be understood as driven by a varying electron-phonon coupling strength induced by the gate-modulated carrier density and the electronic density of states near the Fermi surface.

Figure 1

(a) Top: Electronic band structure of undoped bilayer ${\mathrm{NbSe}}_2$ reproduced from ab initio calculations of Ref. [25]. The dashed line indicates the Fermi level at zero gate voltage and the shaded region represents the range of Fermi levels accessible by gating in our experiment. Bottom: Schematic of the first Brillouin zone and the Fermi surface around the, $\mathrm{\Gamma }$, $K$, and $K^{\prime }$ point. (b) Device schematic: Current was excited through electrode $S$ and $D$; longitudinal and transverse voltage drops were measured; gate voltage $V_G$ was supplied through an isolated electrode from the sample. (c) Optical image of a bilayer ${\mathrm{NbSe}}_2/\text{monolayer}$ ${\mathrm{MoS}}_2$ stack on a Si substrate with gold electrodes before drop casting the ionic liquid. Scale bar is $5\mu \mathrm{m}$.

Figure 2

(a)–(c) Temperature dependence of the longitudinal sheet resistance (a), (b) and the sheet Hall coefficient (c) at selected gate voltages. Longitudinal sheet resistance across the superconducting transition is shown in (b). Data from bulk ${\mathrm{NbS}}_2$ [38] are also shown as empty triangles in (c). (d) Gate voltage dependence of the sheet carrier density. The error bars are estimated from the uncertainties in the sheet Hall coefficient. The dashed line is a linear fit. All data are from device No. 120.

Figure 3

(a) $T_{C0}\text{−}{n}_{2\mathrm{D}}$ phase diagram of bilayer ${\mathrm{NbSe}}_2$. The horizontal error bars originate from the measurement uncertainty of the Hall coefficient. The filled area corresponding to the superconducting (SC) phase is a guide to the eye. (b) $H_{C2\perp }\text{−}{T}_C$ phase diagram of bilayer ${\mathrm{NbSe}}_2$ under a magnetic field perpendicular to the sample at different doping levels. The symbols are $T_C$ determined as the temperature corresponding to 50% of the normal state resistance. The lines are linear fits. The inset shows the carrier density dependence of the zero-temperature coherence length extracted from the linear fits.

Figure 4

(a) Dimensionless $e\text{−}\mathrm{ph}$ coupling constant as a function of sheet carrier density. The vertical and horizontal error bars are from fitting of the normal-state resistance to the $e\text{−}\mathrm{ph}$ scattering model and the measurement uncertainty of the Hall coefficient, respectively. (b) Superconducting transition temperature $T_{C0}$ as a function of $e\text{−}\mathrm{ph}$ coupling constant $\lambda$ for bilayer ${\mathrm{NbSe}}_2$. The solid line is the best fit to the strong-coupling formula [Eq. (1)] with ${\omega }_{\log }=50\mathrm{K}$ and ${\mu }^{*}=0.10$.