Phase diagram
 
       
 
The cuprate high-Tc superconductors have the typical perovskite structure with the Cu-O two-dimensional plane. The mechanism of superconductivity is not still resolved although many theories have been proposed.

The origin of superconductivity certainly lies in the two-dimensional plane consisting of oxygen and copper atoms since the high-Tc oxides are quasi two-dimensional materials with large anisotropy. The superconducting gap has d-wave symmetry, and thus a superconductivity originating from the on-site Coulomb repulsion is a candidate for high-Tc superconductivity. We investigate the three-band model with copper and oxygen orbitals or the simplified single-band Hubbard model.
 
 
  As in the BCS scenario, two electron with opposite spins near the Fermi surface form a pairing state.
 

 
      
Superconductivity from the Coulomb repulsion

The size dependence of the SC condensation energy for the Hubbard model. The upper two lines are for the single-band Hubbard model, and the lower two lines are for the three-band Hubbard (d-p model). The diamond indicates the value for optimally doped YBCO. The blue solid line shows the results for the coexistent state of vertical stripes and SC. In this state the charge density has an oscillating component accompanying the spatial oscillation of the SC gap. In the underdoped region the SC competes and collaborates with antiferromagnetism at the same time. Because of the collaboration with AF, the SC can exists even in the low-doping region.
The obtained value for the SC condensation energy is about 0.2meV which agrees well with the value 0.26meV estimated from the specific heat measurements and 0.17meV from the thermodynamic critical magnetic field Hc.


Ref. K. Yamaji et al.: Physica C304 (1998) 225.
T. Yanagisawa et al.: Phys. Rev. B64, 184509 (2001).
T. Yanagisawa et al.: Phys. Rev. B67, 132408 (2003).




  The figure indicates the LTT crystal structure at low temperatures. In this phase the vertical striped-state with inhomogeneous spin and charge distributions is stabilized and coexists with SC.
  Condensed Matter Physics Group: Nanoelectronics Research Institute