Ionic liquid gating induced two superconductor-insulator phase transitions in spinel oxide Li$_{1 \pm x}$Ti$_2$O$_{4-\delta}$

The associations between emergent physical phenomena (e.g., superconductivity) and orbital, charge, and spin degrees of freedom of $3d$ electrons are intriguing in transition metal compounds. Here, we successfully manipulate the superconductivity of spinel oxide Li$_{1\pm x}$Ti$_2$O$_{4-\delta}$ (LTO) by ionic liquid gating. A dome-shaped superconducting phase diagram is established, where two insulating phases are disclosed both in heavily electron-doping and hole-doping regions. The superconductor-insulator transition (SIT) in the hole-doping region can be attributed to the loss of Ti valence electrons. In the electron-doping region, LTO exhibits an unexpected SIT instead of a metallic behavior despite an increase in carrier density. Furthermore, a thermal hysteresis is observed in the normal state resistance curve, suggesting a first-order phase transition. We speculate that the SIT and the thermal hysteresis stem from the enhanced $3d$ electron correlations and the formation of orbital ordering by comparing the transport and structural results of LTO with the other spinel oxide superconductor MgTi$_2$O$_4$, as well as analysing the electronic structure by first-principles calculations. Further comprehension of the detailed interplay between superconductivity and orbital ordering would contribute to the revealing of unconventional superconducting pairing mechanism.