Multiband Superconductivity of Heavy Electrons in a ${\mathrm{TlNi}}_2{\mathrm{Se}}_2$ Single Crystal

We have made the first observation of superconductivity in ${\mathrm{TlNi}}_2{\mathrm{Se}}_2$ at $T_C=3.7\mathrm{K}$, and it appears to involve heavy electrons with an effective mass $m^{*}=(14–20)m_b$, as inferred from the normal-state electronic specific heat and the upper critical field, $H_{C2}(T)$. We found that the zero-field electronic specific-heat data, $C_{\mathrm{es}}(T)$ ($0.5\mathrm{K}\le T<3.7\mathrm{K}$) in the superconducting state can be fitted with a two-gap BCS model, indicating that ${\mathrm{TlNi}}_2{\mathrm{Se}}_2$ seems to be a multiband superconductor, which is consistent with the band calculation for the isostructural ${\mathrm{KNi}}_2{\mathrm{S}}_2$. It is also found that the electronic specific-heat coefficient in the mixed state ${\gamma }_N(H)$ exhibits a $H^{1/2}$ behavior, which is considered as a common feature of the $d$-wave superconductors. ${\mathrm{TlNi}}_2{\mathrm{Se}}_2$, as a $d$-electron system with heavy electron superconductivity, may be a bridge between cuprate- or iron-based and conventional heavy-fermion superconductors.

Figure 1

(a) Crystal structure of stoichiometric ${\mathrm{TlNi}}_2{\mathrm{Se}}_2$ with the tetragonal ${\mathrm{ThCr}}_2{\mathrm{Si}}_2$ type. (b) Photos of ${\mathrm{TlNi}}_2{\mathrm{Se}}_2$ crystals (before being cleaved) and the ${\mathrm{TlNi}}_2{\mathrm{Se}}_2$ crystal. (c) Single-crystal XRD pattern of ${\mathrm{TlNi}}_2{\mathrm{Se}}_2$ and (d) XRD pattern of powder obtained by grinding ${\mathrm{TlNi}}_2{\mathrm{Se}}_2$ crystals. Its Rietveld refinement is shown by the solid lines.

Figure 2

(a) Temperature dependence of both in- and out-of-plane resistivity, ${\rho }_{ab}(T)$ and ${\rho }_c(T)$ for the ${\mathrm{TlNi}}_2{\mathrm{Se}}_2$ single crystal. (b) Temperature dependence of the normal-state magnetic susceptibility $\chi (T)$, measured at the 1 T field parallel to the $ab$ plane. (c) Specific heat divided by temperature, $C/T$ vs $T^2$, measured under 0, 1, and 6 T fields. Inset: (i) ${\rho }_{ab}(T)$ and ${\rho }_c(T)$ near the superconducting transition, (ii) $\chi (T)$ near the superconducting transition, measured at 5 Oe field parallel to the $ab$ plane (for minimizing the demagnetization factor) with both the zero-field cooling (ZFC) and field cooling (FC) processes, (iii) ${\rho }_{ab}(T)$ below 20 K measured under 0 and 1 T, the solid line indicates the fitting line using Fermi-liquid behavior.

Figure 3

(a) Reduced temperature $T/T_C$ dependence of electronic specific heat divided by temperature $C_{\mathrm{es}}/T$ in the superconducting state at zero field, where $C_{\mathrm{es}}=C-C_{\mathrm{latt}}$. Three solid lines show the individual and total contributions of the two gaps to $C_{\mathrm{es}}/T$, respectively. Inset: Reduced reciprocal temperature $T_C/T$ vs reduced electronic specific-heat $C_{\mathrm{es}}/{\gamma }_N{T}_C$. (b) Low-temperature specific heat divided by temperature $C/T$ vs $T^2$, measured at various fields near superconducting transition. Left inset: $C/T$ vs $T^2$ blow 1.7 K. Right inset: Magnetic field ${\mu }_{0}H$ dependence of electronic specific-heat coefficient ${\gamma }_N$ in the mixed state.

Figure 4

Upper critical field $H_{C2}$ vs $T$ of ${\mathrm{TlNi}}_2{\mathrm{Se}}_2$ crystals. The superconducting transition temperature was determined by both the middle temperature of transition in ${\rho }_{ab}(T)$ and the starting temperature of the jump in $C(T)$ measured at different magnetic fields, $H\parallel c$ axis. Inset: in-plane resistivity, ${\rho }_{ab}(T)$ in magnetic fields up to 1.0 T applied parallel to the $c$ axis.