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The superconducting ground state of the newly discovered superconductorCs$_2$Cr$_3$As$_3$ with a quasi-one-dimensional crystal structure ($T_{\bfc}\sim$ 2.1(1) K) has been investigated using magnetization and muon-spinrelaxation or rotation ($\mu$SR), both zero-field (ZF) and transverse-field(TF), measurements. Our ZF $\mu$SR measurements reveal the presence of spinfluctuations below 4 K and the ZF relaxation rate ($\lambda$) shows enhancementbelow $T_{\bf c}\sim$ 2.1 K, which might indicate that the superconductingstate is unconventional. This observation suggests that the electrons arepaired via unconventional channels such as spin fluctuations, as proposed onthe basis of theoretical models. Our analysis of the TF $\mu$SR results showsthat the temperature dependence of the superfluid density is fitted better witha nodal gap structure than an isotropic s-wave model for the superconductinggap. The observation of a nodal gap in Cs$_2$Cr$_3$As$_3$ is consistent withthat observed in the isostructural K$_2$Cr$_3$As$_3$ compound through TF$\mu$SR measurements. Furthermore, from our TF $\mu$SR study we have estimatedthe magnetic penetration depth $\lambda_{\mathrm{L}}$$(0)$ = 954 nm,superconducting carrier density $n_s = 4.98 \times 10^{26}~ $m$^{-3}$, andcarrier's effective-mass enhancement $m^*$ = 1.61m$_{e}$.

Nodal superconducting gap structure in the quasi-one-dimensional Cs$_2$Cr$_3$As$_3$ investigated using $\mu$SR measurements