Two Energy Gaps and Fermi-Surface “Arcs” in ${\mathrm{NbSe}}_2$

Using angle-resolved photoemission spectroscopy, we report on the direct observation of the energy gap in $2H\mathrm{\text{−}}{\mathrm{NbSe}}_2$ caused by the charge-density waves (CDW). The gap opens in the regions of the momentum space connected by the CDW vectors, which implies a nesting mechanism of CDW formation. In remarkable analogy with the pseudogap in cuprates, the detected energy gap also exists in the normal state ($T>T_0$) where it breaks the Fermi surface into “arcs,” it is nonmonotonic as a function of temperature with a local minimum at the CDW transition temperature ($T_0$), and it forestalls the superconducting gap by excluding the nested portions of the Fermi surface from participating in superconductivity.

Figure 1

Fermi-surface map of ${\mathrm{NbSe}}_2$ at 20 K ($h\nu =50\mathrm{eV}$). Momentum distribution of the photoemission intensity at the Fermi level (14 meV window). The map is normalized to the integrated intensity (356 meV window) to enhance the FS-related features. Contours are fits to the experimental data. The white arrows and color dashed lines are the primary CDW vectors. The $\Gamma$- centered barrels are far too large to be self-nested with the primary CDW vectors [4] and are smaller than would be expected for self-nesting with the secondary CDW vectors (e.g., ${\mathbf{q}}_{\mathbf{1}}-{\mathbf{q}}_{\mathbf{2}}$) [9]. The shape of the inner $K$ barrel is still far from being suitable for perfect self-nesting [6, 8, 32]. The ${\mathbf{k}}_F$ points on the $K$ barrel lying on the $\Gamma K$ symmetry lines cannot be connected by the noticeably shorter CDW vectors (green dashed lines), contrary to that suggested in Ref. 9.

Figure 2

Energy gaps. (a) Energy-momentum distribution of the intensity along the $K\mathrm{\text{−}}M\mathrm{\text{−}}K$ high symmetry direction ($T=19.5\mathrm{K}$, $h\nu =51\mathrm{eV}$). (b) Leading-edge midpoint (LEM) binding energy of all EDCs from (a). The energy position of the $k_F$-EDC’s leading edge was with an accuracy of better than 1 meV by taking a derivative of the fitting function. (c) Direct evidence for energy gap in CDW (19.5 K) and normal state (119 K). (d) Temperature dependence of the gap corresponding to positive and negative momentum values from (a).

Figure 3

Fermi-surface “arcs.” Gap is defined as a difference between the LEM’s binding energies of the ${\mathbf{k}}_F$ EDCs and plotted as a function of $\mathbf{k}$ in corresponding angular space. Dashed areas designate the regions where the LEMs cannot be correctly defined. Fermi-surface “arcs” are seen as disconnected segments of the inner $K$ barrel. The photon energy is 50 eV.

Figure 4

Superconductivity. (a) Energy-momentum distribution of the intensity along the cut through the ${\mathbf{k}}_F$ point 1 shown in (b) below and above the critical temperature ($T_c=7.2\mathrm{K}$). Photon energy is 21 eV. (c) ${\mathbf{k}}_F$-EDCs from the points 1, 2, and 3 located as shown in (b) below (blue or dark gray) and above (red or gray) the critical temperature $T_c$.