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The semimetallic or semiconducting nature of the transition metaldichalcogenide 1$T$-TiSe$_2$ remains under debate after many decades mainly dueto the fluctuating nature of its 2 $\times$ 2 $\times$ 2 charge-density-wave(CDW) phase at room-temperature. In this letter, using angle-resolvedphotoemission spectroscopy, we unambiguously demonstrate that the 1$T$-TiSe$_2$normal state is semimetallic with an electron-hole band overlap of $\sim$110meV by probing the low-energy electronic states of the perturbed CDW phasestrongly doped by alkali atoms. Our study not only closes a long-standingdebate but also supports the central role of the Fermi surface for driving theCDW and superconducting instabilities in 1$T$-TiSe$_2$.

Unveiling the Semimetallic Nature of 1$T$-TiSe$_2$ by Doping its Charge Density Wave