Fully-gapped superconductivity with rotational symmetry breaking in pressurized kagome metal CsV$_3$Sb$_5$

The discovery of the kagome metal CsV$_3$Sb$_5$ has generated significant interest in its complex physical properties, particularly its superconducting behavior under different pressures, though its nature remains debated. Here, we performed low-temperature, high-pressure $^{121/123}$Sb nuclear quadrupole resonance (NQR) measurements to explore the superconducting pairing symmetry in CsV$_3$Sb$_5$. At ambient pressure, we found that the spin-lattice relaxation rate 1/$T_1$ exhibits a kink at $T \sim$ 0.4 $T_\textrm{c}$ within the superconducting state and follows a $T^3$ variation as temperature further decreases. This suggests the presence of two superconducting gaps with line nodes in the smaller one. As pressure increases beyond $P_{\rm c} \sim 1.85$ GPa, where the charge-density wave phase is completely suppressed, 1/$T_1$ shows no Hebel-Slichter peak just below $T_\textrm{c}$, and decreases rapidly, even faster than $T^5$, indicating that the gap is fully opened for pressures above $P_{\rm c}$. In this high pressure region, the angular dependence of the in-plane upper critical magnetic field $H_{\rm c2}$ breaks the $C_6$ rotational symmetry. We propose the $s+id$ pairing at $P > P_{\rm c}$ which explains both the 1/$T_1$ and $H_{\rm c2}$ behaviors. Our findings indicate that CsV$_3$Sb$_5$ is an unconventional superconductor and its superconducting state is even more exotic at high pressures.