Nodal and Nematic Superconducting Phases in ${\mathrm{NbSe}}_2$ Monolayers from Competing Superconducting Channels

Transition metal dichalcogenides like $2H\text{−}{\mathrm{NbSe}}_2$ in their two-dimensional (2D) form exhibit Ising superconductivity with the quasiparticle spins being firmly pinned in the direction perpendicular to the basal plane. This enables them to withstand exceptionally high magnetic fields beyond the Pauli limit for superconductivity. Using field-angle-resolved magnetoresistance experiments for fields rotated in the basal plane we investigate the field-angle dependence of the upper critical field ($H_{c2}$), which directly reflects the symmetry of the superconducting order parameter. We observe a sixfold nodal symmetry superposed on a twofold symmetry. This agrees with theoretical predictions of a nodal topological superconducting phase near $H_{c2}$, together with a nematic superconducting state. We demonstrate that in ${\mathrm{NbSe}}_2$ such unconventional superconducting states can arise from the presence of several competing superconducting channels.

Figure 1

(a) Optical image of sample 1 showing the monolayer region. The inset shows local Raman spectra at different positions used to identify the monolayer region. The spectra were shifted vertically. (b) Zero-field electrical resistance of our three monolayer devices. The left inset shows data up to 100 K. The right inset defines the in-plane field orientation in the honeycomb lattice with respect to the $x$ axis (angle $\varphi$).

Figure 2

(a) Resistance of sample 1 in a 12 T magnetic field of different in-plane orientations $\varphi =-10°$, $-5°$, 0°, 5°, 10°, 15°, 20°, 30°, 40°, 50°, 55°, 60°, 65°, 70°, 80°, 90°, 100°, 110°, 115°, 120°, 125°, 130°, 140°, 150°, 160°, 170°, 175°, and 180°. Offsets were added except for $\varphi =-10°$. The inset shows 0°, 90°, and 180° data without offsets. The stars mark temperatures at which 90%, and 50% of $R_N$ is reached. (b),(c) $\varphi$ dependence of the two characteristic temperatures marked in (a), which illustrate the symmetry of $T_c(12\mathrm{T})$. Blue lines are fitting functions for a sixfold nodal symmetry and a twofold nematic symmetry (see text for details). The red lines only consider a twofold nematic symmetry and fail to describe the kink structures. (d), (e) Similarly obtained $\varphi$ dependence of sample 2 for 90% and 50% of $R_N$ [see Supplemental Material, Fig. 2 [19] ]. The lines are fitting functions for a sixfold nodal symmetry (d), a sixfold sinusoidal symmetry (e), and twofold nematic symmetries (d), (e). (f) $\varphi$ dependence of $H_{c2}$ obtained from magnetoresistance data of sample 3 at 3.7 K [see Supplemental Material, Fig. 3(b) [19] ] at 90% of $R_N$. The line is a fitting function for a sixfold nodal symmetry and weak twofold nematic symmetry. (g) $\varphi$ dependence of the characteristics critical field $H_{c0}$ onset, above which zero resistance is lost, from sample 3 at 2.3 K [Supplemental Material, Fig. 3(a) [19] ]. The line is a fitting function for a weak sixfold sinusoidal variation and a twofold nematic symmetry. The insets in Figs. 2 illustrate the symmetry of the order parameter derived from the representation of the reciprocals of the fitting functions in a polar diagram.

Figure 3

(a) Magnetic field vs temperature phase diagram. The horizontal line marks the Pauli limit $H_P$. The stars mark the regions in which we observe a sixfold nodal or a twofold nematic order parameter symmetry. (b) Temperature dependence of the primary and secondary order parameter of the nematic superconducting state.