Superconducting gap and its Little-Parks like oscillations with high-order harmonics in lithium intercalated 1T-TiSe$_2$

The superconducting phase of doped 1T-TiSe$_2$ is a fruitful playground for exploring exotic quantum phenomena such as the anomalous metal state and spontaneously formed superconducting network. Here, we address these emergent states by studying the superconducting gap of lithium intercalated TiSe$_2$-a fundamental quantity that has remained unexplored so far. We fabricate a device that combines solid-state lateral lithium intercalation, resistance measurements and tunneling spectroscopy. We successfully probe the superconducting gap of TiSe$_2$ and reveal that the gap closing temperature well exceeds the transition temperature ($T_c$) expected from the Bardeen-Cooper-Schrieffer theory, indicating pronounced superconducting fluctuations even in a bulk-like system. Moreover, the symmetric gap persists even in the anomalous metal state, demonstrating the particle-hole symmetry of this exotic phase directly from the density of states. Finally, the superconducting gap shows magneto-oscillations with higher harmonics, attesting to a rather regular structure of the intrinsic superconducting network.