Density-induced BCS-Bose evolution in gated two-dimensional superconductors: The role of the interaction range in the Berezinskii-Kosterlitz-Thouless transition

We discuss the evolution from Bardeen-Cooper-Schrieffer (BCS) to Bose superconductivity vs. carrier density n in two-dimensional (2D) gated superconductors and address the fundamental role that the interaction range plays in the Berezinskii-Kosterlitz-Thouless transition. We investigate the density dependence of the critical temperature (T _c ), superfluid density, order parameter modulus, chemical potential and pair size. Our most important finding is that it is absolutely essential to include classical and quantum phase fluctuations, as well as finite-ranged interactions to explain the non-monotonic behavior of T _c vs. n and to guarantee that the upper bound on T _c is not exceeded in 2D superconductors, as experimentally observed in (Nakagawa Y. et al., Science, 372 (2021) 190), a lithium-intercalated layered nitride, and in magic-angle twisted trilayer graphene (Park J. M. et al., Nature, 590 (2021) 249). Furthermore, we show that we can extract, from measurements of T _c and the order parameter modulus, the effective mass of charge carriers and their interaction strength and range.