Condensed Matter Physics Group

Activities

（2）Mechanism of Superconductivity

Although the oxide high-Tc superconductors have been investigated intensively over the last decade, the mechanisms of superconductivity and anomalous metallic behaviors are not still clarified. We must resolve the following in the research of high-Tc superconductors:

• What is the mechanism of superconductivity?
• What is the anomalous metal? And its origin?
• What is the exact phase diagram in the underdoped region?
• What is the phase diagram for the electron-doped cuprates? And a symmetry between the hole-doped and electron-doped materials.

The on-site Coulomb interaction is the strongest candidate for the origin of attractive interaction between paired electrons. Although the Coulomb interaction is repulsive, the attractive interaction works for pairs of d-wave symmetry with the changes of sign across the nodes. It is, however, difficult to show that there is actually an attractive channel of d-wave symmetry for the Hubbard model or the three-band Hubbard model with d and p orbitals. In fact, it has not been established that the d-wave superconducting phase exists due to the Coulomb interaction for the Hubbard model in spite of intensive study over the last decade. One opinion concerning the theoretical study is "The superconductivity for the Hubbard model is not still established. So, we must consider the effective Hamiltonians to discuss the physical properties of high-Tc cuprates."

Then we investigate a possibility of superconductivity for the (three-band) Hubbard model in two ways. First, we consider the weak-coupling limit of the Coulomb repulsion U. In the limit of small U, the ground-state energy is calculated exactly by employing the perturbation theory in U. One must overcome, however, a numerical difficulty in order to obtain a solution for the gap equation for small U because the numerical errors are comparable to or greater than the critical temperature or the superconducting order parameter. Although for the intermediate value of U, the solution of the gap equation is derived correctly, the existence of solutions do not confirm the possibility of superconductivity since the perturbation theory is not justified for the intermediate value of U. Recently Prof. Kondo developed the method to make it possible to calculate the magnitude of superconducting gap even for a small U. He has shown that the d-wave superconducting state is stable in ground state of the Hubbard model in the limit of small U. If we suppose that the continuity principle holds for small U, the ground state is superconducting for a finite value of U unless there is some ordering. We have shown that this also holds for the three-band Hubbard model (d-p model) which is regarded as the more realistic model for high-Tc cuprates. In summary, the d-wave superconducting state is possible in the system with the on-site repulsive Coulomb interaction, and whether the superconducting state is stable or not is dependent upon a competition between superconductivity and other possible orderings such as the antiferromagnetism. Thus, as a second approach we compare the energy of several states regarded as candidates for the ground state by using the quantum variational Monte Carlo method in order to determine the phase diagram.