On the theory of 2D superconductivity: The peculiarities of the Berezinskii–Kosterlitz–Thouless transition and crossover from local to Cooper pairs (Review Article)

We have analyzed superconducting properties of a strongly coupled two-dimensional (2D) superconductor with a boson-exchange attraction in the s- and d-wave pairing channels, with a focus on the properties near the Berezinskii–Kosterlitz–Thouless (BKT) transition, and with a more general goal to give a picture of the physics of cuprates at different dopings and temperatures. In the s-channel, we have found that superconductivity exists at all dopings and there is a crossover from the Bardeen–Cooper–Schrieffer (BCS) phase of large Cooper pairs to a state with local pairs, or Bose–Einstein condensation (BEC) phase, at all coupling strengths and bosonic frequencies. On the other hand, in the d-wave channel, we have found that superconductivity sets in at a finite doping and is suppressed at lower dopings due to a reduced, doping-dependent effective coupling. Moreover, the BCS–BEC crossover is absent in the d-wave channel. One rather unexpected result we found is an oscillatory dependence of the BKT critical temperature on doping in the d-pairing channel that is a result of an oscillatory dependence of the superconducting stiffness on the chemical potential. Obtained results may help to better understand superconducting properties of 2D materials, including cuprates, and might be used in modern technological applications.