Superconducting Condensate Formation in Quasi-2D Systems with Arbitrary Carrier Density

TL;DR

This paper derives a phase diagram for quasi-2D metals with variable carrier density, identifying normal, pseudogap, and superconducting phases, and explains their dependence on carrier density and implications for high-$T_c$ superconductors.

Contribution

It introduces a comprehensive phase diagram for quasi-2D systems with arbitrary carrier density, detailing the crossover between different phases and their experimental relevance.

Findings

Pseudogap and BKT regions vanish at high densities, aligning with BCS theory.

Large pseudogap phase exists at intermediate densities with negligible BKT region.

Both pseudogap and BKT regions are significant at very low densities.

Abstract

A phase diagram for a quasi-2D metal with variable carrier density has been derived. The phases present are the normal phase, where the order parameter is zero; the pseudogap phase where the absolute value of the order parameter is non-zero but its phase is random, and a superconducting phase with a crossover quasi-2D Berezinskii-Kosterlitz-Thouless (BKT) region. The crossover region is bounded by the quasi-2D BKT temperature and the temperature for the onset of conventional long-range order (CLRO). The practical observation of these regions however critically depends on the carrier density. At high densities both the pseudogap and BKT regions vanish asymptotically i.e. one obtains the standard BCS picture. At intermediate densities the pseudogap phase is large but the BKT region negligible. Finally at very low densities both the pseudogap and BKT regions are sizeable. An attempt is made to explain the behaviour observed in underdoped (intermediate densities) and optimally doped high-$T_{c}$ superconducting compounds above their critical temperature. The transition to the pseudogap phase should also be regarded as a crossover.