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Main factors determine Tc in superconducting copper-oxides
PHYSICA@ ELSEVIER
Physica C 282-287 (1997) 1693-1694
Main factors determine Tc in superconducting copper-oxides Ming-Liang Zhang National Laboratory for Superconductivity Institute of Physics, Academia Sinica, P. O. Box 603, Beijing 100080, China Tcs of cuprate superconductors are determined by following three structure factors: (1) Cu-O plane: la) orthorhombic distortion degree from square, lb) deviation degree from fiat plane, lc) the length of Cu-O bond; (2) carrier reservoir: 2a) ability to polarize other ions of metallic charge source ions and their polarized ability, 2b) connection manner of component ions; (3)the distance d between charge source and Cu-O plane. Let us first consider La2_~Sr~CuO4, local charge equilibrium means that total charges included in a micro-size volume enclosed Sr 2+ are exactly zero. Sr 2+ ion has tendency to hold a hole in its neighouring region and to maintain local charge equilibrium. The motion of hole in Cu-O plane will break local charge neutrality. Because Sr 2+ and holes are in different space regions, the motion of holes can not completely screen Sr 2+ ions, usual complete sum rule is not able to use. The ioncores in ordinary 3D metal or alloy are immersed in electron sea, are well screened by the electron motion and complete sum rule is correct. The potential of a ion-core is exponential small when distance is larger than Debye screen length gD, local charge equilibrium is always maintained in a sphere with radius gD. Whereas, when the distance between hole and projective point of Sr2+(1) ion is bigger than a characteristic length (name it affection length) A, the static-electric attractive energy between hole and Sr 2+ is smaller than the kinetic energy of hole. Just like La2_zSr~CuO4, all cuprates are very different from 3D metal or alloy in keep of local charge equilibrium. Charge source ions and holes are in different space regions is common character of all cuprates. Carrier reservoir layers play important roles in keep of local charge equilibrium. The geometry characters of Cu-O plane can be described by coordinate number of Cu atom and following three parameters: 1) orthorhombic distortion
b-a
degree:b+ a'
constants respectively;
a and
b are lattice
2) devfation degree of
0921-4534/97/$17.00 © Elsevier Science B.V. All rights reserved. PII S0921-4534(97)00956-8
flat plane:180°-L Cu-O1-Cu; 3) bond length of b Cu-O,~ ~ and ,-~ 7. Let us first consider a fiat and square Cu-O plane with a fixed carrier concentration. About its electron state, according to different doping concentrations, Cu-O plane is divided into fragments Cu(2n+l)~O2(2,,+l)2 (where n = 0, 1, 2, 3, 4 . . . is non-negative integer), which have C4v symmetry and a Cu atom on their center (fragment symmetry). Any depression of fragment symmetry will restore Coulomb interaction W between holes [3], therefore lower effective net attraction between carriers and depress To. Therefore to keep maximal effective net attraction between carriers, orthorhombic distortion degree from square Cu-O plane should be as small as possible. Orthorhombic distortion and element substitution in Cu-O plane are two manners to depress fragment symmetry. These symmetry depression will restore some Coulomb interaction W between holes and decrease effective net attraction between carriers, therefore lower To. In addition, although deviation from a fiat and square plane does not depress the fragment symmetry; the holes motion will be in smaller range than in a fiat Cu-O plane, Coulomb interaction can not be effectively removed, effective net attraction between carriers is decreased and Tc are depressed too. So that high Tc compound should satisfy following conditions [2] (1) the carrier concentration in the CuO2 plane must be adjusted to the optimal level; (2) there are no defects in or near the CuO2 layers; (3)fiat, square CuO2 plane. In some cuprates which have more than one
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M.-L. Zhang/Physica C 282-287 (1997) 1693-1694
Cu-O planes, there are such Cu-O planes which do not directly connect with any carrier reservoir layers. The Cu-O planes directly connected with carrier reservoir layers (directly connected CuO planes) have much more carriers than the Cu-O planes non-directly connected with carrier reservoir layers (non directly connected Cu-O planes), are very important for superconductivity and other properties. Non directly connected CuO planes are screened by directly connected CuO planes with large amount of carriers, are very weakly affected by carrier reservoir layers and nearly only play the role of structure frame. In the following we only consider the roles of directly connected Cu-O planes. For fixed Cu-O plane and fixed carrier reservoir, the shorter distance d, the more carriers produced by charge sources, the better to screen charge source ions and the easier to keep local charge equilibrium, so that the higher Poptimat and higher To,max, the existence of superconductivity in higher hole concentration is allowed. According to the composition of carrier reservoir layers, the properties of charge source ions and connection manner, we divide the cuprates into two classes. The two classes cuprates are very different in keep extent of local charge equilibrium. The carrier reservoir of first class cuprates has following characters: the valence of metallic charge source ions is not variable, the metallic charge source ions has very weak ability to polarize other ions and is very difficult to polarize itself, the bond connecting component ions of carrier reservoir is ionicity bond. Whereas, the carrier reservoir of second class cuprates has following characters: the valence of metallic charge source ions is variable, the charge source ion has strong ability to polarize other ion and can also be polarized itself easily, the bond connecting component ions of carrier reservoir is co-valence bond. Some examples of first class cuprates are: La2-xSrxCuO4, Nd2-xCexCuO4, etc. The examples about second class cuprates are: Y123, Y-124, Tl(Hg)-1201, 1212, 1223 (denote as Wl(Hg)l-system), Wl(Bi)-2201,2212,2223 (denofe as Tl(Bi)2-system), etc. In the first class cuprates, 1) the metallic charge source ions are at lattice positions and not movable, 2) the polarizability of metallic charge
source ions is small and the ability to polarize other ions is also small, 3) component ions in carrier reservoir are connected by ionicity bonds. therefore 1) when holes move in Cu-O plane, there are no corresponding electron motion in carrier reservoir to compensated the motion of holes, will produce large static electric separation energy. 2) charge source ions can not lower their bare charges because mutual polarization in c~rrier reservoir layers is very weak. 3) the charge source ions can not well be screened by the motion of carriers, because charge source ions and carriers are in different space regions, their distance d is longer. These not well screened charge source ions tend to hold local electric neutrality and any motion of holes will break local charge equilibrium. Due to above reasons, the effective masses of hole m* are bigger, Poptirnat and Pmax are smaller. In second class cuprates, charge sources are higher valence metallic ions and over-full oxygens. Higher valence metallic ions are charge sources due to the instability of these ions and the valence is variable. These higher valence ions mainly take away electrons from Cu-O plane rather than else 0 2- ions which are not in directly connected CuO plane, because Cu-O plane make the charge dispersing in a large region, thus the loss of Madelung energy is smaller than fetching electrons from else 0 2- ions. In a summary, fragment symmetry determines how much Coulomb repulsion is removed, breakage of local charge equilibrium leads to static-electric separation energy. Both two factors affect effective net attraction between carriers and therefore affect Te.
REFERENCES 1. H.Shaked, et al., Physica C , Crystal Structure of the High-To superconducting copperoxides. 2. J.D.Jorgensen, et al., Invited paper for the First Polish-US Conference on High Temperature Superconductivity, 11-15 September 1995; Y.J.Uemura, et al., Phys. Rev. Lett. 66, 2665 (1991); H.Zhang, et al., Phys. Rev. Lett. 70, 1697 (1993). 3. M.Cini, et al., preprint 1996; M.L.Zhang, et al., preprint, June, 1996.
Physica C 282-287 (1997) 1693-1694
Main factors determine Tc in superconducting copper-oxides Ming-Liang Zhang National Laboratory for Superconductivity Institute of Physics, Academia Sinica, P. O. Box 603, Beijing 100080, China Tcs of cuprate superconductors are determined by following three structure factors: (1) Cu-O plane: la) orthorhombic distortion degree from square, lb) deviation degree from fiat plane, lc) the length of Cu-O bond; (2) carrier reservoir: 2a) ability to polarize other ions of metallic charge source ions and their polarized ability, 2b) connection manner of component ions; (3)the distance d between charge source and Cu-O plane. Let us first consider La2_~Sr~CuO4, local charge equilibrium means that total charges included in a micro-size volume enclosed Sr 2+ are exactly zero. Sr 2+ ion has tendency to hold a hole in its neighouring region and to maintain local charge equilibrium. The motion of hole in Cu-O plane will break local charge neutrality. Because Sr 2+ and holes are in different space regions, the motion of holes can not completely screen Sr 2+ ions, usual complete sum rule is not able to use. The ioncores in ordinary 3D metal or alloy are immersed in electron sea, are well screened by the electron motion and complete sum rule is correct. The potential of a ion-core is exponential small when distance is larger than Debye screen length gD, local charge equilibrium is always maintained in a sphere with radius gD. Whereas, when the distance between hole and projective point of Sr2+(1) ion is bigger than a characteristic length (name it affection length) A, the static-electric attractive energy between hole and Sr 2+ is smaller than the kinetic energy of hole. Just like La2_zSr~CuO4, all cuprates are very different from 3D metal or alloy in keep of local charge equilibrium. Charge source ions and holes are in different space regions is common character of all cuprates. Carrier reservoir layers play important roles in keep of local charge equilibrium. The geometry characters of Cu-O plane can be described by coordinate number of Cu atom and following three parameters: 1) orthorhombic distortion
b-a
degree:b+ a'
constants respectively;
a and
b are lattice
2) devfation degree of
0921-4534/97/$17.00 © Elsevier Science B.V. All rights reserved. PII S0921-4534(97)00956-8
flat plane:180°-L Cu-O1-Cu; 3) bond length of b Cu-O,~ ~ and ,-~ 7. Let us first consider a fiat and square Cu-O plane with a fixed carrier concentration. About its electron state, according to different doping concentrations, Cu-O plane is divided into fragments Cu(2n+l)~O2(2,,+l)2 (where n = 0, 1, 2, 3, 4 . . . is non-negative integer), which have C4v symmetry and a Cu atom on their center (fragment symmetry). Any depression of fragment symmetry will restore Coulomb interaction W between holes [3], therefore lower effective net attraction between carriers and depress To. Therefore to keep maximal effective net attraction between carriers, orthorhombic distortion degree from square Cu-O plane should be as small as possible. Orthorhombic distortion and element substitution in Cu-O plane are two manners to depress fragment symmetry. These symmetry depression will restore some Coulomb interaction W between holes and decrease effective net attraction between carriers, therefore lower To. In addition, although deviation from a fiat and square plane does not depress the fragment symmetry; the holes motion will be in smaller range than in a fiat Cu-O plane, Coulomb interaction can not be effectively removed, effective net attraction between carriers is decreased and Tc are depressed too. So that high Tc compound should satisfy following conditions [2] (1) the carrier concentration in the CuO2 plane must be adjusted to the optimal level; (2) there are no defects in or near the CuO2 layers; (3)fiat, square CuO2 plane. In some cuprates which have more than one
1694
M.-L. Zhang/Physica C 282-287 (1997) 1693-1694
Cu-O planes, there are such Cu-O planes which do not directly connect with any carrier reservoir layers. The Cu-O planes directly connected with carrier reservoir layers (directly connected CuO planes) have much more carriers than the Cu-O planes non-directly connected with carrier reservoir layers (non directly connected Cu-O planes), are very important for superconductivity and other properties. Non directly connected CuO planes are screened by directly connected CuO planes with large amount of carriers, are very weakly affected by carrier reservoir layers and nearly only play the role of structure frame. In the following we only consider the roles of directly connected Cu-O planes. For fixed Cu-O plane and fixed carrier reservoir, the shorter distance d, the more carriers produced by charge sources, the better to screen charge source ions and the easier to keep local charge equilibrium, so that the higher Poptimat and higher To,max, the existence of superconductivity in higher hole concentration is allowed. According to the composition of carrier reservoir layers, the properties of charge source ions and connection manner, we divide the cuprates into two classes. The two classes cuprates are very different in keep extent of local charge equilibrium. The carrier reservoir of first class cuprates has following characters: the valence of metallic charge source ions is not variable, the metallic charge source ions has very weak ability to polarize other ions and is very difficult to polarize itself, the bond connecting component ions of carrier reservoir is ionicity bond. Whereas, the carrier reservoir of second class cuprates has following characters: the valence of metallic charge source ions is variable, the charge source ion has strong ability to polarize other ion and can also be polarized itself easily, the bond connecting component ions of carrier reservoir is co-valence bond. Some examples of first class cuprates are: La2-xSrxCuO4, Nd2-xCexCuO4, etc. The examples about second class cuprates are: Y123, Y-124, Tl(Hg)-1201, 1212, 1223 (denote as Wl(Hg)l-system), Wl(Bi)-2201,2212,2223 (denofe as Tl(Bi)2-system), etc. In the first class cuprates, 1) the metallic charge source ions are at lattice positions and not movable, 2) the polarizability of metallic charge
source ions is small and the ability to polarize other ions is also small, 3) component ions in carrier reservoir are connected by ionicity bonds. therefore 1) when holes move in Cu-O plane, there are no corresponding electron motion in carrier reservoir to compensated the motion of holes, will produce large static electric separation energy. 2) charge source ions can not lower their bare charges because mutual polarization in c~rrier reservoir layers is very weak. 3) the charge source ions can not well be screened by the motion of carriers, because charge source ions and carriers are in different space regions, their distance d is longer. These not well screened charge source ions tend to hold local electric neutrality and any motion of holes will break local charge equilibrium. Due to above reasons, the effective masses of hole m* are bigger, Poptirnat and Pmax are smaller. In second class cuprates, charge sources are higher valence metallic ions and over-full oxygens. Higher valence metallic ions are charge sources due to the instability of these ions and the valence is variable. These higher valence ions mainly take away electrons from Cu-O plane rather than else 0 2- ions which are not in directly connected CuO plane, because Cu-O plane make the charge dispersing in a large region, thus the loss of Madelung energy is smaller than fetching electrons from else 0 2- ions. In a summary, fragment symmetry determines how much Coulomb repulsion is removed, breakage of local charge equilibrium leads to static-electric separation energy. Both two factors affect effective net attraction between carriers and therefore affect Te.
REFERENCES 1. H.Shaked, et al., Physica C , Crystal Structure of the High-To superconducting copperoxides. 2. J.D.Jorgensen, et al., Invited paper for the First Polish-US Conference on High Temperature Superconductivity, 11-15 September 1995; Y.J.Uemura, et al., Phys. Rev. Lett. 66, 2665 (1991); H.Zhang, et al., Phys. Rev. Lett. 70, 1697 (1993). 3. M.Cini, et al., preprint 1996; M.L.Zhang, et al., preprint, June, 1996.