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{Multiband Superconductivity in Lu$_3$Os$_4$Ge$_{13}$

Intermetallic R$_3$T$_4$X$_{13}$ series consists of cage like structure and have been in focus due to their unconventional electronic ground states. In this work, we report the normal and superconducting state properties of a high quality single crystal of Lu$_3$Os$_4$Ge$_{13}$. Lu$_3$Os$_4$Ge$_{13}$ belongs to the above mentioned series and crystallizes in a cubic crystal structure with the space group $\it{Pm\bar{3}n}$. Using electrical transport, magnetization and heat capacity measurements, we show that Lu$_3$Os$_4$Ge$_{13}$ is a type-II multi-band superconductor ($T{_c} =3.1$~K) with unusual superconducting properties. The analysis of the low temperature heat capacity data suggests that Lu$_3$Os$_4$Ge$_{13}$ is a moderately coupled multi-band BCS superconductor with two gaps ($2Δ/ {k{_B}T{_c}} = 3.68 \pm {0.04} ~\& ~0.34 \pm {0.02}$) in the superconducting state. The dc-magnetization ($M-H$) shows a large reversible region in the superconducting state similar to the vortex liquid phase observed in high-$T{_c}$ superconductors. The value of the Ginzburg number $G_{i}$ suggests that the thermal fluctuations, though small as compared to those in high-$T{_c}$ cuprates, may play an important role in the unpinning of the vortices in this compound. The electronic band structure calculations show that three bands cross the Fermi level and constitute a complex Fermi surface in Lu$_3$Os$_4$Ge$_{13}$