Superconducting condensate formation in quasi-2D systems with arbitrary carrier density

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-KosterlitzThouless (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-Tc superconducting compounds above their critical temperature. The transition to the pseudogap phase should also be regarded as a crossover. 74.20.Fg, 74.20.Mn, 64.60.Cn

Persistence of pseudogap formation in quasi-2D systems with arbitrary carrier density

“…For very low densities we find a large region between T c and T q BKT where the system is superconducting but one has two-dimensional and not three-dimensional order. It is difficult to say whether such behaviour can be observed experimentally because the densities are so low that the Fermi surface is absent [6,13].…”

“…Certainly at sufficiently large densities the BKT and PP region will disappear due to a direct transition to the state with long-range order particularly for low anisotropy. For example, in the case of an indirect interaction in 2D, it has already been shown [13] that the PP region only exists at low carrier density.…”

“…At very low densities (i.e. in the Bose limit of isolated pairs) and for physically reasonable values for the parameters, it has been shown for quasi-2D system [6,12,13] that long-range order is only established well below T BKT . However these densities are not realised physically.…”

Relativistic BCS Theory in Quasi-(2+1)-Dimensions: Effects of an Inter-layer Transfer in the Honeycomb Lattice Symmetry

“…( a similar model was discussed in Ref. [23] ). L K has both the usual Dirac kinetic term in (2+1)-dimensions and the inter-layer hopping terms.…”

The Coleman-Weinberg effective potential in superconductivity theory

“…This model is the quasi-(2+1) dimensional Nambu-Jona-Lasinio model which has a very similar and rather rich phase diagram [5]. However, it is not our purpose here to discuss the whole phase diagram of our model here as was done in [12,13] and we will restrict ourselves to the field theoretical aspects of the transition to the phase with broken symmetry. There is however an important difference between the model considered in [5] and the nonrelativistic model here.…”