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Non-centrosymmetric superconductor Re$_6$Zr has attracted much interest, forits possible unconventional superconducting state with time reversal symmetrybroken. Here we report the $^{185/187}$Re nuclear quadrupole resonance (NQR)measurements on Re$_6$Zr ($T_c$ = 6.72 K) and the isostructural compoundsRe$_{27}$Zr$_{5}$ ($T_c$ = 6.53 K) and Re$_{24}$Zr$_{5}$ ($T_c$ = 5.00 K). Thenuclear spin-lattice relaxation rate $1/T_1$ shows a coherence peak below $T_c$and decreases exponentially at low temperatures in all three samples. Thesuperconducting gap $\Delta$ derived from the $1/T_1$ data is $2\Delta =3.58 $$k_BT_c$, 3.55 $k_BT_c$, and 3.51 $k_BT_c$ for Re$_6$Zr ,Re$_{27}$Zr$_{5}$, andRe$_{24}$Zr$_{5}$, respectively, which is close to the value of 3.53 $k_BT_c$expected for weak-coupling superconductivity. These data suggest conventional$s$-wave superconductivity with a fully-opened gap in this series of compounds.

Full-gap superconductivity in non-centrosymmetric Re$_6$Zr, Re$_{27}$Zr$_{5}$ and Re$_{24}$Zr$_{5}$