Penetration Depth Study of Superconducting Gap Structure of $2H\mathrm{\text{−}}{\mathrm{NbSe}}_2$

We report measurements of the temperature dependence of both in-plane and out-of-plane penetration depths (${\lambda }_a$ and ${\lambda }_c$, respectively) in $2H\mathrm{\text{−}}{\mathrm{NbSe}}_2$. Measurements were made with a radio-frequency tunnel diode oscillator circuit at temperatures down to 100 mK. Analysis of the anisotropic superfluid density shows that a reduced energy gap is located on one or more of the quasi-two-dimensional Nb Fermi surface sheets rather than on the Se sheet, in contrast with some previous reports. This result suggests that the gap structure is not simply related to the weak electron-phonon coupling on the Se sheet and is therefore important for microscopic models of anisotropic superconductivity in this compound.

Figure 1

Temperature dependence of the in-plane penetration depth, $\Delta {\lambda }_a$ in single crystals of ${\mathrm{NbSe}}_2$. Data for three different samples are shown, offset for clarity. The absolute scale of $\Delta {\lambda }_a$ is most accurate for sample 1 (see text). For sample 2 the data have been divided by 1.3. Inset: Frequency shifts at higher temperature showing the charge density wave transition.

Figure 2

Low temperature behavior of $\Delta {\lambda }_c$ determined by cutting the sample (see text). Data for two different samples are shown (samples 4 and 5). For sample 5 the data have been divided by 2 and offset for clarity. The results for $\Delta {\lambda }_a(T)$ (sample 1) are shown for comparison (dashed line). The solid line show a fit to Eq. (2) up to 2.4 K. The lower inset shows the geometry of the samples before (I) and after (II) cutting. Upper inset: Raw measured frequency shift for a thick sample with $H\perp c$ (same as sample 2 in Fig. 1).

Figure 3

Temperature dependence of the normalized in-plane superfluid density ${\tilde{\rho }}_a$ calculated using the ${\lambda }_a(0)$ values indicated. The solid lines are fits to the two-gap model described in the text. The dashed line is the weak coupling BCS prediction with ${\Delta }_0=1.76k_B{T}_c$.