Anisotropic Fully Gapped Superconductivity Possibly Mediated by Charge Fluctuations in a Nondimeric Organic Complex

We investigate low-temperature electronic properties of the nondimeric organic superconductor ${\beta }^{\prime \prime }\text{−}(\mathrm{ET}{)}_4[({\mathrm{H}}_3\mathrm{O})\mathrm{Ga}({\mathrm{C}}_2{\mathrm{O}}_4{)}_3]\mathrm{Ph}{\mathrm{NO}}_2$. By examining ultrasonic properties, charge disproportionation (CD) without magnetic field dependence is detected below $T_{\mathrm{CD}}\sim 8\mathrm{K}$ just above the superconducting critical temperature $T_c\sim 6\mathrm{K}$. From quantum oscillations in high fields, we find variation in the Fermi surface and mass enhancement induced by the CD. Heat capacity studies elucidate that the superconducting gap function is fully gapped in the Fermi surface, but anisotropic with fourfold symmetry. We point out that the pairing mechanism of the superconductivity is possibly dominated by charge fluctuations.

Figure 1

(a) Molecular arrangement of the ET molecules in the conducting plane of ${\beta }^{\prime \prime }\text{−}(\mathrm{ET}{)}_4[({\mathrm{H}}_3\mathrm{O})\mathrm{Ga}({\mathrm{C}}_2{\mathrm{O}}_4{)}_3]\mathrm{Ph}{\mathrm{NO}}_2$. (b) Temperature dependence of the relative change of the distance between the adjacent (0 8 2) lattice planes $\mathrm{\Delta }{d}_{082}/d_{082}$ and the FWHM of the (0 8 2) diffraction peak. (c),(d) Low-temperature ultrasonic properties, (c) the relative change of the ultrasonic attenuation $\mathrm{\Delta }\alpha$, and (d) the elastic constant $\mathrm{\Delta }{C}_L/C_L$, as a function of temperature. The arrows indicate the transition temperatures of the CD $T_{\mathrm{CD}}$ and superconductivity $T_c$. The red circles and blue boxes denote the data at 0 and 5 T, respectively. The inset in (d) is the enlarged graph around the superconducting transition temperature $T_c$.

Figure 2

(a) Magnetoresistance at various temperatures. (b) The oscillatory components above 25 T obtained by subtracting the nonoscillating background from (a). The dotted curves are fits by using the two-component Lifshitz-Kosevich formula. The dashed envelopes are guides for the eyes to clarify the amplitude of the oscillations. (c) Temperature dependences of the frequency of $F_2$. The gray curve is a guide for the eyes. (d) A mass plot of the SdH oscillations. The dotted curve is given by the LK formula with the effective mass $m^{*}/m_e=1.6$. The inset displays the ratio of $A$ of the obtained data and the calculation for $m^{*}/m_e=1.6$, $A/A(m^{*}/m_e=1.6)$.

Figure 3

(a) Temperature dependence of zero-field heat capacity plotted as $C_p/T$ vs $T^2$ for some samples. (b) Low-temperature heat capacity of sample No. 6 in various magnetic fields. The lines denote the contribution of the lattice $\beta T^2$ and electronic heat capacity ${\gamma }_N$, ${\gamma }^{*}$. (c) A logarithmic plot of temperature dependent electronic heat capacity at 0 and 2 T. The curves represent linear, squared, cubic relations $\sim T^n$ ($n=1–3$) and the $\alpha$-model calculations for the strong-coupling isotropic $s$-wave superconductivity and the anisotropic $s$-wave superconductivity. (d) Magnetic field dependence of the heat capacity at 0.7 K. The inset is the enlarged plot below 0.3 T. (e) Variation in $C_p/T$ for sample No. 7 in an in-plane field 0.5 T rotated from the $a$ axis to the $b$ axis. The solid curves are the fittings of the equation in the main text. (f) Temperature dependence of the fourfold component $C_4/T$. The negative values mean that the minima of the fourfold term are located at the directions of the crystal axes. The inset describes a schematic illustration of the angular dependence of the estimated gap function.