Giant enhanced stability of the quantum electron solid from a weakened electron-electron interaction in double-layer ${\mathrm{MoS}}_2$

The melting temperature of the quantum electron solid in double-layer two-dimensional ${\mathrm{MoS}}_2$ stacked on opposite sides of a thin layer of BN is larger than previous single-layer results in Si-MOSFETs and bilayer estimates by four orders of magnitude. This giant enhancement of the stability of the solid comes from a shear modulus $\mu$ that is an order of magnitude larger than expected and comes from a weakened electron-electron interaction due to the screening by the polarization charges at the interfaces of the experimental structure. We found that the short-range part of the interelectron Coulomb potential actually provides for a negative contribution to $\mu$ and makes the lattice less stable. The weakening of this short-range contribution enhances $\mu$ by an order of magnitude. This large $\mu$, together with a larger energy scale $e^2/a_b$ for a smaller Bohr radius $a_b$ for the experimental structure, leads to a high melting temperature and makes possible using the structure as a practical logic device. Our understanding of this phenomenon guides us in optimizing its design. The large melting temperature and the small zero-temperature critical density agrees with experimental results extracted from the density and temperature dependence of the Coulomb drag resistance.