In 1986, J. Bednorz and K. Müller reported copper-oxide superconductor in "Possible High T_c Superconductivity in the Ba-La-Cu-O System". Now a lot of 100 K grade copper-oxide superconductors are discovered. The name of "a copper oxide" comes from CuO₂ plane made up of copper and oxygen in the crystal structure.Fig.2 indicates crystal structure in "La_2-xBa_xCuO₄", the first copper-oxide superconductor.This structure is called K₂NiF₄ type, and perovskite structure and rock salt type structure are stacked alternately. An arrow shows CuO₂ plane in this figure. The CuO₂ plane plays an important role in superconductivity in copper-oxide superconductors.

Key factors in superconductivity mechanism ~ electronic state and carrier dope in CuO₂ plane ~

Copper oxide superconductor has high T_c. but the mechanism has not been understood for 20 years. There are some common points. The mother materials are anti-ferromagnetism insulators which have CuO₂ plane, and realize superconductivity by carrier dope. Here, let us introduce the most famous material, "La₂CuO₄" which is mother material of the first copper-oxide superconductor La_2-xBa_xCuO₄.

Electronic state of CuO₂ plane (1) ~ Mott insulator and anti-ferromagnetism order correlation ~

Copper-oxide superconductor has two-dimensional plane (CuO₂ plane) made up of copper and oxygen in the crystal structure. This CuO₂ plane greatly contributes to the superconductivity. Mother material consists of following ions, (La³⁺)₂(Cu²⁺)(O^2-)₄. Focusing on the crystal structure, CuO₂ plane and (LaO)₂ layer made up of La³⁺ and O^2- piled up in turn. CuO₂ plane is totally -2 values. (LaO)₂ layer is +2 values. Therefore the system keeps neutral.

In the CuO₂ plane, electronic states in Cu²⁺ and O^2- are (3d)⁹ and (2p)⁶ respectively, so 3d_x2-y2 orbital in Cu lacks one electrons. Fig.3 shows energy level in Cu²⁺ in La₂CuO₄. 3d orbital of Cu²⁺ is degenerate to five fold, so five orbits are called 3d_xy (x-y plane), 3d_yz (y-z plane), 3d_zx (z-x plane), 3d_x2-y2 (x axis and y axis direction), 3d_z2-r2 (z axis direction). The five orbital are the same energy level, but they are affected by eight oxygen around Cu, and 3d_x2-y2 and 3d_z2-r2 become higher energy level because of of oxygen position. Therefore, 3d orbital which degenerates to five fold are divided to two energy level in t_2g orbital (3d_x2-y2, 3d_z2-r2) and e_g orbital (3d_xy, 3d_yz, 3d_zx). We call it "crystal field". Furthermore, in the case of La₂CuO₄, CuO₆ octahedron expands to z axis direction (because this structure is energetically stable), so 3d_x2-y2 influenced more than 3d_z2-r2. This is why energy level of 3d_x2-y2 is highest. (dividing energy level caused by distorted ochtahedron is called "Jahn-Teller effect".) As a result, in the case of electronic condition in Cu²⁺, only one electron exists in 3d_x2-y2. We show the state of orbital in CuO₂ plane in Fig.4, 3d_x2-y2 orbit of Cu and 2p orbit of O forms hybridized orbital. The electronic state in CuO₂ plane (3d)⁹ and half filled state in 3d_x2-y2 (Fig.5(a)), so it should show metallic property. But it has no conductivity, and mother maternal behaves as an insulator. This comes from strong correlation between electrons. (The system is called "strong correlation electronic system".) Under the conduction, an electron of 3d_x2-y2 must jump between Cu sites. However U, strong Coulomb interaction between electrons, prevents it when there are two electrons. In other words, when two electrons occupy one Cu site, it needs the extra energy U. Therefore conduction electron is suppressed and localized in each Cu site. Therefire the band state in CuO₂ plane is Fig.5(b). Thanks to the effect of big electronic correlation, 3d band in Cu is divided to lower Hubbard band. That is occupied by electron and upper Hubbard band is empty. Then the gap (Mott-Hubbard gap) is formed between these bands. Therefore, mother material in the copper oxide superconductor is an insulator. The insulator originated from strong electronic correlation is called "Mott insulator". As a result, an electron with the spin of S=1/2 and one hole localize in Cu sites, so Cu ion becomes a magnetic ion. That is why the mother material shows anti-ferromagnetiv ordering. In mother material, the spin of S = 1/2 on a Cu site orders antiferromagnetically. This is caused by spin in a Cu site and two electrons in the O site. An arrow in Fig.4 expresses a spin of an electron in each site. As electrons are occupied entirely in the O site, there are two spins. Thanks to correlation of anti-ferromagnetism order in a copper oxide, spins of a Cu sites between the neighbors interacts through a spin of this O site. This interaction is called "super exchange interaction".

Electronic state of CuO2 plane (2) ~carrier dope and superconductivity expression~

Big characteristic of a copper oxide superconductor is that property of system changes into anti-ferromagnetism → superconductivity → metal in depending on the carrier density. Here, a career is a hall or an electron introduced into CuO₂ plane. (It is substitution amount of Ln-214 system: x.) Fig.7 shows phase diagram for career concentration x of copper oxide superconductor. A right direction of a cross axle shows hall concentration x (La_2-xSr_xCuO₄, YBa₂Cu₃O_6+δ, Bi₂Sr₂CaCu₂O_8+δ etc…). A left direction of a cross axle shows electron concentration x (Nd_2-xCe_xCuO₄ etc…). In the domain where the hall density is small, doped material is anti-ferromagnetic insulator by strong property of mother material. But, as the hall density increases, it shows superconductivity. As increasing carrier concentration, there is the domain where Tc increases (underdoping region) at superconductivity phase. And, it is in the best Tc with a certain dope (optimal dope). Then, on the contrary, it become domain that Tc decreases (overdoping region). Most suitable dope amount x is around 0.15-0.20. While dope amount increasing more, it do not show superconductivity, and becomes domain that a metalic property is strong. (In the case of electron doping, anti-ferromagnetism leniently decreases rather than in the case of hall doping, and a superconductivity phase appears at the same time as decreasing anti-ferromagnetism.) In addition, with a copper oxide superconductor, there is a state such as superconductivity gap structure called "a pseudo gap" in normal state in T > T_c. Next, let's look at a band state when superconductivity develops. A model to use here is the model that is supported well when an electronic state of a copper oxide expressed. (It is influential until now, and a decisive thing is not proposed in a copper oxide superconductor.)     Superconductivity phase appears, so it is expected that a band state of mother material originally be motto insulator changed in a metal band state. As had described first, a band of CuO₂ plane in mother material seems to be Fig.8 (a).At first let's think about superconductor La_2-xBa_xCuO₄ by hall doping. Electric charges of (LaO)₂ layer decrease from +2 values by substituting La³⁺ for Ba²⁺, so an electric charge of CuO₂ plane which kept -2 values must change into a direction of -1 value from -2 in order to keep an electric charge of the whole system neutral in La_2-xBa_xCuO₄. In other words, an electron in a CuO₂ plane must be removed from there (put a hall into CuO₂ plane). As a result, it is thought that band structure of CuO₂ plane which was originally an insulator band state (Fig.8(a)) changes into a metallic band state like Fig.8(b) by removing of electron (by injecting of hall).
On the other hand, in superconductor Nd_2-xCe_xCuO₄ by electron dope, because Nd³⁺ are substituted Ce⁴⁺ for, electric charges of (NdO)² layer increase from +2 values. Therefore an electric charge of CuO₂ plane changes from -2 values in a direction of -3 values, that is, more electrons are injected into CuO₂ plane. As a result, it is thought that the band structure becomes a condition that electron entered in upper Hubbard band of 3d in Cu like Fig.8(c). Such a band model thought about in a copper oxide superconductor, from being thought in explanation of a semiconductor well, imitates semiconductor, and so a superconductor by hall doping is called "a p type superconductor" and a superconductor by electron doping is called "an n type superconductor".
In this way, both superconductors of p type and n type can be explained, so it is thought that this model is influential. However, in the hall doping type that a single crystal is easily grown in comparison with electron doping type, it is said that Fig.8 (d) which is slightly different from Fig.8 (b) is convincing.As for this model, a new state (impurity level with a semiconductor) is formed on a little above 2p band in O by hall doping, and with that, it behaves like metal.In addition, why can n type and p type be really explained (to have a gap in T_c) by the same model, in present conditions, room for various arguments is left. For this mechanism elucidation, a new experiment result and discovery of a new material are expected in future.

How to search new superconductors !? ~Characteristic of a copper oxide superconductor~

In the present when many copper oxide superconductors were discovered, information that leads to solution of superconductivity mechanism was prepared, but, on the other hand, the characteristic should become an indicator of a new superconductor search have been understood. "A general idea of block layer" showed in Fig.9 is one of them. crystal structure of a copper oxide superconductor is shown in Fig.9. The other atoms layer puts CuO₂ plane, and CuO₂ plane is alone. In La_2-xSr_xCuO₄ of Fig.10, [(La,Sr)₂O₂] layer serves to isolate CuO₂ plane. Such atom layer is called "the block layer". In other words a copper oxide takes the structure that CuO₂ plane and the block layer piled up in turn. I described it in the first, the block layer plays a role in supplying of carrier for superconductivity expression whereas CuO₂ plane plays a role in superconductivity. as a one characteristic in the copper oxides, without disturbing order of CuO₂ plane(band structure etc), by adjustment of electric charge balance of the block layer, injecting of carrier for Superconductivity expression can was done. In this time, In La_2-xSr_xCuO₄, I express that CuO₂ plane is [CuO₂]^-2 and that the block layer is [(LaO)₂]⁺², and by doing Sr I can express that the block layer is [(La,Sr)₂O₂]^+2-p, CuO₂ plane is [CuO₂]^-2+p. This p becomes the carrier concentration. (p > 0 is correspond to hole doping, and p < 0 is correspond to electron doping.) In addition, an electric charge of the block layer certainly becomes an average of +2 values in mother material when I thought that the block layer is a unit lattice. (In Y-123, the block layer is Y³⁺ and [CuO chain]1+. However, when I thought in the whole unit lattice, the block layer becomes an average of +2.)

In this way I can express a copper oxide superconductor entirely by rearranging CuO₂ plane and the block layer like a puzzle. Therefore, when I develop a new copper oxide superconductor I can do it mainly by devising composition of the block layer. Some interesting laws learned by experience are proposed by a lot of discovered copper oxide superconductors. One is relation between the number of sheets of CuO₂ plane and T_c. T_c is 40 K in La2-xSrxCuO4 having one piece of CuO2 plane in a unit lattice. Tc is 90 K in YBa2Cu3O6+d having two pieces in a unit lattice. Tc is 134 K in HgBa₂Ca₂Cu₃O_8+δ having three pieces in a unit lattice. Tc tends to become surely high in much number of sheets of CuO₂ plane. Then how is CuO₂ plane in a material piling up endlessly? An answer is that it does not show even superconductivity. After all I can seem to say that the CuO₂ plane that stood alone separated with the block layer is necessary. I show a value of Tc for the number of sheets of CuO₂ side in a unit lattice in Fig.11 every each representative material. As watching this, we understand that Tc tends to become highest at three pieces of CuO₂ plane. If number of CuO₂ sides which stood alone is many, it seems to be disadvantage to develop high Tc adversely. In addition, it is also said shape of CuO₂ plane is related to Tc. Shape of CuO₂ plane of various copper oxide superconductors is shown in Fig.12. Though CuO₂ plane of Hg, Tl system having high Tc in copper oxide superconductors is flat, those of La-214 system are uneven. As watching this, CuO₂ plane is close in evenly seems to tend to expect high T_c. After discovery of La_2-xBa_xCuO₄, a copper oxide superconductor nearly 200 kinds is reported. However, in the present when there are various laws learned by experience besides, you may discover a new superconductor having more high T_c by considering the thing which I introduced here.

Unique crystal structure of a copper oxide superconductor!!

In copper oxide superconductor, there is the common point that all composition shows superconductivity has CuO₂ plane. However, it takes unique structure by the number of sheets of CuO₂ plane in unit lattice (unit cell). Here, I introduce a main material among the crystal structure that there are dozens of kinds.

Ln-214 (having one piece of CuO2 plane) system

Crystal structure of three kinds of copper oxides is shown in Fig.13. A characteristic of these materials is having one piece of CuO₂ plane in a unit lattice. These are usually called (a) T, (b) T', (c) T^* type structure. At first, first copper oxide superconductor La_2-xBa_xCuO₄ is equivalent to this T type (a). In T type, Cu and oxygen make octahedron (CuO₆ octahedron), and CuO₂ plane does the form that these CuO₆ octahedron affected aside. Next, in T’ type (b), Nd_2-xCe_xCuO₄ showing superconductivity by electron doping takes this structure. In T' type, differently from T type there is not oxygen (top oxygen) of a top part of CuO₆ octahedron. On this account CuO₂ plane of T' type becomes a square. In last, T^* type (c) takes the structure that T type and T' type were combined. Therefore top oxygen occupied only one side of CuO₂ plane and forms CuO₂ plane of a pyramid type. (Nd,Ce)_2-xSr_xCuO₄ shows superconductivity by this structure. A big characteristic in a superconductor of this system is a point to control carrier by substituting it for one part of element. In the material which I introduced here, superconductivity develops by substituting Ln³⁺ for Ba²⁺ or Ce³⁺ partly.

Y-Ba-Cu-O system

YBa₂Cu₃O_6+δ (Y-123) to have recorded T_c of 90 K grade more than liquid nitrogen temperature for the first time are showed in Fig.14. What carrier doping by Sr doping than Ba doping appeared high T_c and T_c having risen when pressure is impressed in La_2-xBa_xCuO₄ lead to discover of Y-123. In other words it is an idea that an ion radius which is smaller makes high T_c. As a result, Y-123 realized high T_c more than 2 times of La_2-xSr_xCuO₄.In this system, materials have two pieces of CuO₂ plane in a unit lattice. Whereas La_2-xBa_xCuO₄ had CuO₂ plane of octahedron, in Y-Ba-Cu-O system, octahedron is divided into up and down, and CuO₂ plane of top and bottom prevent connecting directly through top oxygen by Y entering between it. Therefore two pieces of CuO₂ plane takes a pyramid type. In addition, a big characteristic of crystal structure in this system is existence of a CuO chain that connects a top of a pyramid. This chain site just was formed because oxygen of an aspect direction of CuO₂ plane suffers a loss. (If this part were CuO₂ plane, three perovskites connects through top oxygen.) At this point, it can be said that Y-Ba-Cu-O system has the most unique crystal structure in a copper oxide. A CuO chain gives big influence for superconductivity expression of Y-Ba-Cu-O system. Though in Ln-214 system, superconductivity develops by substituting the other element for a Ln site, in this system, superconductivity develops by an oxygen ion entering in a chain site. (Mother material of Y-123 system becomes YBa₂Cu₃O₆ of the state that all the oxygen of a chain site fell out.) In superconductor of Y-Ba-Cu-O system, there is YBa₂Cu₄O₈(Y-124) that a chain site repeated double, and Y₂Ba₄Cu₇O₁₄(Y-247) which repeated Y-123 and Y-124 structure every one period other than Y-123. In addition, in the system that replaced these Y sites with Ln superconductivity also develops.

Bi, Tl, Pb, Hg system

[1]   J. G. Bednorz and K. A. Müller, Z. Phys. B64 (1986) 189
[2]  BKBO
[3]  S. Uchida, H. Takagi K. Kitazawa and S. Tanaka, Jpn. J. Appl. Phys. 26 (1987) L1
[4] M. K. Wu, J. R. Ashburn, C. J. Thorng, P. H. Hor,  R. L. Meng, L. Gao, Z. J. Huang, Y. Q. Wang and C. W. Chu, Phys. Rev. Lett. 58 (1987) 908
[5]  H. Maeda, Y. Tanaka, M. Fukutomi and T. Asano, Jpn. J. Appl. Phys. 27 (1988) L209
[6]  Y. Tokura, H. Takagi and S. Uchida, Nature 337 (1989) 345
[7]  十倉好紀, パリティ 5 (1990) 34
[8]  A. Schilling, M. Cantoni, J. D. Guo and H. R. Ott, Nature 363 (1993) 56
[9]  J. Akimitsu, S. Suzuki, M. Watanabe and H. Sawa, Jpn. J. Appl. Physics. 27 (1988) L185
[10] A. F. Marshall, R. W. Barton, K. Char, A. Kapitulnik, B. Oh, and R. H. Hammond, Phys. Rev. B 37 (1988) 9353
[11] D. B. Currie, M. T. Weller, P. C. Lanchester and R. Walia, Physica C 224 (1994) 43
[12] D. E. Morris, N. G. Asmar, J. Y. T. Wei, J. H. Nickel, R. L. Sid, J. S. Scott and J. E. Post, Phys. Rev. B 40 (1989) 11406
[13] J. Akimitsu, A, Yamazaki, H. Sawa and H. Fujiki, Jpn. J. Appl. Phys. 26 (1987) L890
[14] S. N. Putilin, E. V. Antipov, O. Chamaissem and M. Marezio, Nature. 362 (1993) 226