Quantum spin liquid ground state with the evidence of roton-like excitations at elevated temperatures in the triangular-lattice delafossite YbCuSe${}_2$

We present a comprehensive experimental investigation of the temperature evolution of magnetic states in triangular-lattice delafossite YbCuSe${}_2$. Magnetization measurements on high-quality single crystals reveal easy-plane anisotropy. Specific heat, magnetization, and muon spin relaxation ($\mu$SR) establish the absence of magnetic order or spin freezing down to 0.03 K ($\le J_{\mathrm{a}\mathrm{v}\mathrm{g}}\mathrm{/}250$), demonstrating a dynamically fluctuating quantum spin liquid (QSL) ground state. Thermodynamic measurements uncover multiple characteristic energy scales at $T_H\approx 4.5$ K, $T_L\approx 1.8$ K, and $T^{\ast }\approx 0.7$ K. Below $T^{\ast }$, $\mu$SR detects a dynamical phase separation in which the majority of the spins are forming a QSL state whereas the remaining spins form a sporadic, disorder-induced state decoupled from the dominant QSL component. Remarkably, the unconventional temperature dependence of the $\mu$SR relaxation rate indicates roton-like excitations emerging between $T_H$ and $T_L$, a feature not previously observed in any QSL system, preceding the stabilization of the low-temperature QSL at 0.3 K. These findings identify YbCuSe${}_2$ as a unique QSL platform, providing valuable insights for further experimental and theoretical exploration.