Anisotropic fully-gapped superconductivity in quasi-one-dimensional Li$_{0.9}$Mo$_6$O$_{17}$

Abstract

Superconductivity in quasi-one-dimensional Li$_{0.9}$Mo$_6$O$_{17}$ emerges from an exotic, non-metallic normal state that exhibits signatures of Tomonaga-Luttinger liquid behavior, emergent symmetry and excitonic order. The high upper critical field, $H_{c2}$, in Li$_{0.9}$Mo$_6$O$_{17}$ suggests that that the favored pairing state is spin-triplet in nature. Here, we report measurements of the magnetic penetration depth down to $0.08\,\mathrm{K}$ ($T/T_c \lesssim 0.04$) and the specific heat down to $0.4\,\mathrm{K}$ ($T/T_c \lesssim 0.2$), and show that they are consistent with a moderately-coupled, fully-gapped superconducting state with marked gap anisotropy and a minimum ($Δ_{\rm min} \simeq 0.4\,k_{\mathrm{B}}T_c$) occurring over a very narrow region in $k$-space. Combined with knowledge of $H_{c2}$, these measurements support the presence of a nodeless and possibly odd-parity spin-triplet superconducting order parameter in Li$_{0.9}$Mo$_6$O$_{17}$.

Figures (5)

• Figure 1: Main panel: The electronic specific heat of LMO (sample #4) in the vicinity of the SC transition. The black dashed line is a fit to a specific heat model consisting of two isotropic gaps as discussed in the main text. The anomaly at $T_c$, $\Delta C/\gamma T_c \simeq 1.64$, is greater than the BCS weak-coupling value of $\Delta C/\gamma T_c = 1.43$, indicating that superconductivity in LMO is moderately coupled. The grey dashed line is an exponential fit of the data up to $T_c/3$, with a residual $\gamma_{\rm res}$ = 0.53 mJ/mol.K$^2$. Inset: Low-$T$ specific heat plotted as $C/T$ versus $T^2$. The solid line is a fit to $C/T=\gamma+ \beta T^2$.
• Figure 2: (a) Normalized ac susceptibility curves for #1 and #2 (corrected for demagnetization effects). (b) $\Delta\lambda(T)$ for $T<$ 0.3 $T_c$. Solid black curves (dashed gray lines) are fits to power-law behavior up to 0.7$\,\mathrm{K}$ (activated exponential behavior up to 0.5$\,\mathrm{K}$). The activated exponential fits return gap values of $\Delta$ = 0.82 and 0.90 $k_{\mathrm{B}} T_c$ for samples #1 and #2, respectively. The curves have been offset for clarity.
• Figure 3: (a) Exponent $n$ derived from power-law fitting of the data as the upper limit of the fit, $T_{\mathrm{max}}$ is decreased. The result for a model line-nodal $d$-wave state in the clean and dirty limit ($\hbar\Gamma=0.005\,k_{\mathrm{B}}T_c$) is shown for reference. (b) Effect of decreasing $T_{\mathrm{max}}$ on $\Delta$ obtained from activated exponential fitting of the data.
• Figure 4: (a) Superfluid density of samples #1 and #2, determined using $\lambda_a(0)=15\,\mu\mathrm{m}$. The solid lines are fits to an anisotropic gap model as described in the main text. The dashed gray line is a fit to a two-isotropic-gap model. (b) Low-$T$ data.
• Figure 5: (a) Schematic of the anisotropic gap structure derived for $\beta=0.4$ and $\eta$ = 3.8 (#1), 3.3 (#2) and 1 (for comparison). Note that the locus of the gap minimum cannot be determined from this study. (b) Fermi surface of LMO as determined by the tight-binding parametrization from Ref. nuss2014.