The mechanism of high-temperature superconductivity (HTSC) is still controversial in spite of intensive studies since the discovery of cuprate
high-temperature superconductors. We do not still have a picture to describe various unusual properties of high-temperature superconductors.
There are many properties that should be resolved. They are as follows.
・What is the mechanism of superconductivity?
・How do we describe the anomalous metallic pahse in the underdoped region?
・What is the correct phase diagram in the underdoped region?
・Is the phase diagram symmetric between the hole- and electron-doped region?
First of all, it is important that Cooper pairs have d-wave symmetry, as established from intensive experimental studies for HTSC.
We must investigate an origin of attractive interactions that will bring about the d-wave superconductivity. A plausible candidate of the model
that describes high-temperature superconductivity is the two-dimensional model with the short-range Coulomb repulsion.
Typical models of this kind are the Hubbard model and the three-band Hubbard model model with d and p orbitals (or called d-p model).
A significant question is whether the on-site Coulomb repulsion induces superconductivity or not.
This is unresolved yet and there has been a controversy concerning this question.
Although there have been many works involving some kind of approximations such as the random phase approximation (RPA),
fluctuation-exchange approximation (FLEX), perturbation therory, and numerical works by using the variational Monte Carlo
method and quantum Monte Carlo method, a definitive conclusion is not given to this question until now.
References
[1] Attractive interaction comes from the susceptibility U²&chi(q). Please see, for example,
D.J. Scalapino, E. Loh, J.E. Hirsch: Phys. Rev. B34, 8190 (1986).
N.E. Bickers, D. J. Scalapino, S.R. White: Phys. Rev. Lett. 62, 961 (1989).
Here, the random phase approximation (RPA) or the fluctuation-exchange approximation (FLEX)
is employed.
[2] Perturbative calculations of weak coupling superconductivity for the 2D Hubbard model are in
R. Hlubina: Phys. Rev. B59, 9600 (1999).
J. Kondo: J. Phys. Soc. Jpn. 70 (2002) 808.
[3] The third-order contribution in the perturbation theory of weak coupling Hubbard model reducesTc:
T. Yanagisawa: New J. Phys. 10 (2008) 023014.
[4] Strong coupling theory of superconductivity for the Hubbard model in the internediate region of U（for example, U/t=3）is in
T. Nomura, K. Yamada: J. Phys. Soc. Jpn. 69 (2000) 3678.
[5] Variational Monte Carlo calculations for the d-p model:
T. Yanagisawa, S. Koike, K. Yamaji: Phys. Rev. B64, 184509 (2001).
T. Yanagisawa, M. Miyazaki, K. Yamaji: J. Phys. Soc. Jpn. 78 (2009) 013706.
[6] T. Nakanishi, T. Yanagisawa, K. Yamaji: J. Phys. Soc. Jpn. 66 (1997) 294.
K. Yamaji, T. Yanagisawa, T. Nakanishi, S. Koike: Physica C304 (1998) 225.
| |
