Recently H$_3$LiIr$_2$O$_6$ has been reported as a spin-orbital entangled quantum spin liquid (QSL) [K. Kitagawa et al., Nature {bf 554}, 341 (2018)], albeit its connection to Kitaev QSL has not been yet identified. To unveil the related Kitaev physics, we perform the first Raman spectroscopy studies on single crystalline H$_3$LiIr$_2$O$_6$ samples. We implement a soft chemical replacement of Li$^+$ with H$^+$ from $alpha$-Li$_2$IrO$_3$ single crystals to synthesize the single crystal samples of the iridate second generation H$_3$LiIr$_2$O$_6$. The Raman spectroscopy can be used to diagnose the QSL state since the magnetic Raman continuum arises from a process involving pairs of fractionalized Majorana fermionic excitation in a pure Kitaev model. We observe a broad dome-shaped magnetic continuum in H$_3$LiIr$_2$O$_6$, in line with theoretical expectations for the two-spin process in the Kitaev QSL. Our results establish the close connection to the Kitaev QSL physics in H$_3$LiIr$_2$O$_6$.
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