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Universal Critical Quantum Properties of Cuprate Superconductors

100%

Schneider T.

Acta Physica Polonica A

1997

vol. 91

issue 1

203-212

Using the scaling theory of quantum critical phenomena we explore the occurrence of universal critical behavior at the insulator-to-superconductor and superconductor-to-normal state transitions at zero temperature. Experimentally, these phase transitions are driven by doping and correspond to critical end points of the phase transition line in the temperature-hole concentration plane. Provided that the order parameter is a complex scalar in two dimensions, and that the London relation between superfluid number density and magnetic penetration depth holds, the scaling theory predicts universal behavior close to the insulator-to-superconductor transition. In particular, transition temperature and zero temperature penetration depth are universally related and the sheet resistance adopts a universal value. These predictions agree remarkably well with available experimental data and provide useful constraints for a microscopic theory.

Crossover from BCS to Bose-Einstein in Hubbard Model

51%

Pedersen M. H., Schneider T., Beck H.

We generalize the standard attractive Hubbard, having an on-site pair creation operator Q_{i} = a_{i↑}a_{i↓}, to one with n components Q_{iα} = a_{iα↑}a_{iα↓}, α=1,2,...,n. In the limit n → ∞ we obtain the Ginzburg-Landau functional. On this basis we explore the crossover from weak (BCS) to strong coupling (Bose-Einstein condensation) superconductivity. The associated self-consistent equations for the Ginzburg-Landau parameters are similar to those of the T-matrix approach. The evolution of the band structure with increasing interaction strength is studied and correlated with the behavior of the pair propagator and the transition temperature. We find that the pairing interaction creates a new band which moves downwards in energy as the interaction strength increases and separates into a lower Hubbard band when the interaction strength becomes comparable to the band width. In the strong coupling regime, a third band with small spectral weight is also found in between the lower and upper Hubbard bands.

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2 Acta Physica Polonica A

2 1997

2 Schneider T.

1 Beck H.

1 Pedersen M. H.

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Universal Critical Quantum Properties of Cuprate Superconductors

Crossover from BCS to Bose-Einstein in Hubbard Model