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

Abstract

The superconducting dome in the Tc 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 Tc 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-layers transition metal dichalchogenides 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.

Figures (11)

• Figure 1: Predicted superconducting critical temperature $T_{c}$ as a function of doping with disorder+interaction corrections for single-side gated MoS$_2$ (orange filled squares) and MoSe$_2$ (blue filled squares). The gray curve is the predicted critical temperatures for MoS$_2$ in the absence of disorder, while for MoSe$_2$ the correction is negligible. The empty circles represent experimental $T_{c}$ values from Refs.doi:10.1021/acs.nanolett.8b01390Costanzo2018doi:10.1126/science.1228006Saito2016doi:10.1126/science.aab2277AliElYumin2019.
• Figure 2: Theoretical versus experimental differential tunneling conductance for single-side gated MoS$_2$ at $n_e \approx 1.5 \times 10^{-14}/\mathrm{cm}^2$ as a function of voltage at 1.5 (orange) 5 (green) and 7 (blue) Kelvin. Experimental data have been extracted from Ref.Costanzo2018.
• Figure S3: Electronic band structure comparison between PythTB (orange) and Wannier90 (green) for bilayer MoS$_2$ at $n_e = 0.175~$/cell.
• Figure S4: Panel a):calculated two-dimensional conductivity $\sigma_{2D}(\omega)$ with a broadening $\eta=0.025$ eV for single side gated bilayer MoS$_2$ at $n_e = 0.125 ~e^-$/cell for various impurity concentration values $n_{imp}$. Panel b): two-dimensional conductivity $\sigma_{2D}$ as a function of the impurity concentration values $n_{imp}$ for selected systems (double gate conductivity is divided by two for graphical reasons).
• Figure S5: Charge potential induced by a positive charge placed in $(r,z_0)=(0,-3.0$) Å. The chalcogen nuclei in the 2D material are at $z=2$ Å.