Effect of dimensionality on the charge-density wave in few-layer $2{H\text{-NbSe}}_2$

We investigate the charge-density wave (CDW) instability in single and double layers, as well as in the bulk $2{\text{H-NbSe}}_2$. We demonstrate that the density functional theory correctly describes the metallic CDW state in the bulk $2{\text{H-NbSe}}_2$. We predict that both monolayer and bilayer ${\text{NbSe}}_2$ undergo a CDW instability. However, while in the bulk the instability occurs at a momentum ${\mathbf{q}}_{\text{CDW}}\approx \frac{2}{3}\Gamma M$, in freestanding layers it occurs at ${\mathbf{q}}_{\text{CDW}}\approx \frac{1}{2}\Gamma M$. Furthermore, while in the bulk the CDW leads to a metallic state, in a monolayer the ground state becomes semimetallic, in agreement with recent experimental data. We elucidate the key role that an enhancement of the electron-phonon matrix element at $\mathbf{q}\approx {\mathbf{q}}_{\text{CDW}}$ plays in forming the CDW ground state.

Figure 1

Electronic structure of the undistorted bulk, bilayer, and monolayer $2{\text{H-NbSe}}_2$.

Figure 2

(Color online) Left: real part of the bare static electronic susceptibility (in arbitrary units) with constant matrix elements, same as the real part of the phonon self-energy ${\Pi }_{\sigma ,\mu }^{\prime }\left(\mathbf{q},\omega =0\right)$ [Eq. (1)], calculated using the LAPW band structure of a single layer ${\text{NbSe}}_2$. Center: the corresponding FS. Four Brillouin zones are shown; $\Gamma$ points are at the grid nodes. Right: the same for the resulting $4\times 1$ CDW.

Figure 3

Phonon dispersion of bulk (top) and monolayer (bottom) $2{\text{H-NbSe}}_2$. Each point corresponds to a linear-response calculations. The spline connecting the points is guide for the eyes.

Figure 4

(Color online) Pseudopotential electronic density of states for undistorted (black dashed) and distorted (red) bulk, bilayer, and monolayer $2{\text{H-NbSe}}_2$.

Figure 5

(Color online) LAPW plasma frequency and conductivity as a function of the gate-induced charge for a single-layer ${\text{NbSe}}_2$. The constant relaxation-time approximation is adopted. Experimental data (Ref. 10) are plotted assuming the charge neutrality at $\approx 30\times {10}^{12}{\text{cm}}^{-2}$. The gate voltage for the standard configuration of a 300 nm ${\text{SiO}}_2$ field-effect transistor can be obtained from the $x$ axis divided by $7.2\times {10}^{-2}{\text{cm}}^{-2}{\text{V}}^{-1}$. The charge is obtained from the integrated DOS.