Disorder-Driven Enhancement of Coulomb Repulsion Governs the Superconducting Dome in Ionic-Liquid-Gated Quasi-2D Materials.

The superconducting dome in the T_{c} versus doping phase diagram, found in cuprates, nickelates, twisted bilayer graphene, and transition metal dichalcogenides, is often considered a signature of unconventional pairing. Identifying the underlying mechanisms of any of these phase diagrams and developing a reliable theoretical understanding of it remains a critical challenge. Here we demonstrate that, in ionic-liquid-gated quasi-2D materials, the disordered ionic potential from the frozen ionic liquid drives the system close to Anderson transition. In this regime, quenched charge fluctuations and reduced screening markedly enhance repulsive Coulomb interactions, suppressing T_{c} and naturally leading to the formation of a superconducting dome. By integrating a many-body approach including disorder with first-principles calculations, we obtain the phase diagrams and tunneling spectra of gated few-layer transition metal dichalcogenides in robust quantitative agreement with experiments. Our findings establish that disorder-driven enhancement of Coulomb repulsion is a fundamental feature of ionic-liquid-gated quasi-2D materials at high bias.