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Formation of hole-pairs. All the squares A.B.C.D.E.F.G.H.I are the unit cells of the two-dimensional CuO 2 plane. Both the holes traverse the same path but at any instant they are on the opposite sides of the central cell.
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A model of preformed hole-pairs in cuprate superconductors has been proposed based on some experimental results i.e., 1) electron paramagnetic resonance spectra of quenched superconductors which show very frequently the fragment (CuO)4 broken off from the CuO2 layer in the structure, 2) 41 meV peak observed in neutron diffraction and nuclear magnet...
Contexts in source publication
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... se- quence of well defined spin states will be found in (CuO) 4 units at fixed distances between them. The jour- ney of the hole through one round of these well defined spin states is completed when it traverses a length of ten (CuO) 4 units as shown in the Figure (3). It means that the successive well defined spin states will come after the hole crosses two and a half plaquettes [see Fig- ure (3)]. ...
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... jour- ney of the hole through one round of these well defined spin states is completed when it traverses a length of ten (CuO) 4 units as shown in the Figure (3). It means that the successive well defined spin states will come after the hole crosses two and a half plaquettes [see Fig- ure (3)]. It also means that a hole will take 10 -14 sec. ...
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... analogy with the reference [20], the binding be- tween two holes seems to be through the Heisenberg exchange interaction because conditions of binding in the two cases are quite similar. There are a large number of lattice holes wandering in the two-dimensional CuO 2 plane When two holes traveling in the opposite direc- tions in the same column or row .of the CuO 2 continuous sheet come at a distance of nearly four (CuO) 4 units as shown in the Figure (3) they might feel a mutual force of attraction due to Heisenberg exchange interaction The separation of four (CuO) 4 units has been chosen because the coherence length is known to be 15 -20 A or nearly equal to the length of four (CuO) 4 plaquettes kept side by side. ...
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... will be strong exchange interaction. But in a very short time (≈10 -14 sec), the hole from the A-side will cross over to B-cell and that from E-side to D-cell [ Figure (3 ...
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... the Figure (3), the squares A,B,C,D,E,F,G,H,I are the unit cells of the two-dimensional CuO 2 lattice, each cell being a square of side = 3.84 A which is approxi- mately equal to the size of (CuO) 4 plaquette or unit cell of the two-dimensional CuO 2 plane in Y-123 supercon- ductor. When two holes enter the Figure 3 from opposite sides, one from the A side and the other from the E side, they feel an attractive force due to exchange interaction between them and continue moving towards each other with thermal velocity. ...
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... the Figure (3), the squares A,B,C,D,E,F,G,H,I are the unit cells of the two-dimensional CuO 2 lattice, each cell being a square of side = 3.84 A which is approxi- mately equal to the size of (CuO) 4 plaquette or unit cell of the two-dimensional CuO 2 plane in Y-123 supercon- ductor. When two holes enter the Figure 3 from opposite sides, one from the A side and the other from the E side, they feel an attractive force due to exchange interaction between them and continue moving towards each other with thermal velocity. Because they are charged particles, their motion will be guided by the magnetic field pro- duced by the Cu 2+ holes of the (CuO) 4 plaquettes in which they are situated at any instant. ...
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... Under the effect of exchange interaction and mag- netic field generated by the Cu 2+ holes and its own ther- mal velocity a lattice hole (numbered 1) starting from A-cell goes to C, then to I, back to C, then to E. In the meantime, the spins of the Cu 2+ holes start from U-state at A goes to Uo at C, then to D at I, then to Do at C and to U again at E. We see from the Figure (3) that the geo- metrical angle from A to E is 180˚, but the spins of the Cu 2+ complete 360˚in360˚in going from U to U state. To dif- ferentiate between the two, the spin angles will be de- noted by ω and the geometrical angle by ω'. ...
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... V has now two com- ponents Vx and Vy. In the Figure (3), X-axis is from the origin O (center of the cell C) towards I and Y-axis is from O towards A. ...
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... values of RHS of (21') have been shown in the Table 1. The positions of the lattice holes at different spin angles (ωt) have been shown in the Figure (3). In Table 1, in the range of spin angles 180˚-180˚-360ånd 540˚-540˚-720˚, the values of RHS of (21') comes to be negative. ...
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... now, we have mainly discussed the motion of the hole1. The conditions governing the motion of the hole 2 is identical to that of the hole1 and they execute the same kind of motion, only difference being that the hole 1 starts from the A-cell and the hole 2 starts from the E-cell at the same time, Both the holes repeatedly trav- erse the four lobes in the Figure 3 in the same time but are always situated diametrically opposite to each other. In the Figure 3 we see that the path of the pair of lattice holes (1 and 2) has four lobes around the center which is like the orbitals of electrons in 2 2 x y d configuration. ...
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... conditions governing the motion of the hole 2 is identical to that of the hole1 and they execute the same kind of motion, only difference being that the hole 1 starts from the A-cell and the hole 2 starts from the E-cell at the same time, Both the holes repeatedly trav- erse the four lobes in the Figure 3 in the same time but are always situated diametrically opposite to each other. In the Figure 3 we see that the path of the pair of lattice holes (1 and 2) has four lobes around the center which is like the orbitals of electrons in 2 2 x y d configuration. ...
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... y d type and developed a model which corroborates it, demonstrates the correctness of our logic. On examining the Figure 3, two important questions arise, 1) why the hole 1 coming from A on reaching C is deflected towards I-cell and the hole 2 towards the F-cell and 2) why the two holes on reaching extreme ends of the figure bounce back. To answer these questions, we will examine the Figure 3 and the Table 1 in detail. ...
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... examining the Figure 3, two important questions arise, 1) why the hole 1 coming from A on reaching C is deflected towards I-cell and the hole 2 towards the F-cell and 2) why the two holes on reaching extreme ends of the figure bounce back. To answer these questions, we will examine the Figure 3 and the Table 1 in detail. At 62˚, the position of the hole 1 is just at the upper bound- ary of the cell C. From 62˚to62˚to 74.6˚, the position of this hole is inside the cell. ...
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... at 90˚, the hole seems to go to infinity (see the table 1). At 118˚, the position of the hole is at the RHS boundary of the cell C. At 180˚the180˚the position of the hole is at the extreme right at the center of the cell I. On reach- ing 180˚, it turns back and the path between 180ånd 360 0 is of similar nature to that between 0ånd 180˚but180˚but in different quadrant of the circle (see Figure 3). Now we consider the motion of the hole 2 which starts its journey from 360˚where360˚where as the hole 1 had started its journey from 0˚The0˚The position of the hole 2 at an angle (360 + θ)˚ is equivalent to the position of the hole 1 at an angle θ, but always in opposite quadrants. ...
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... time advances, both the holes navigate the full circle but always re- maining opposite to each other. Both of them bounce back when they reach the four extreme positions shown in the Figure 3. ...
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... 90˚to90˚to 118˚, the hole 1 ex- periences the same kind of repulsion and push back as from 90˚to90˚to 62˚. The hole 1 takes the path MTN [see Fig- ure 3] and at 118˚enters118˚enters the cell H on the right hand side. Similarly the hole 2 takes the path KLJ from 422˚to422˚to 478ånd478ånd enters the cell G on the left hand side. ...
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... FM coupling, Cu 2+ spin directions both in A and E cells ini- tially will be along (+z or upward of the CuO 2 plane ) direction , but in AFM coupling, initially the spin direc- tion in A will be along (+z) direction and in E along the (-z) direction. But the trajectory of the two holes in both the cases will remain the same as shown in the Figure 3. This is due to the direction of force exerted by magnetic field on a conductor carrying current due to hole (+ charge). ...
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Citations
... We have proposed models of preformed hole-pairs [3]- [5] for resistanceless current flow in the a-b plane and along c-axis of cuprate superconductors. For better understanding of this paper, it should be read in conjunction with the paper in Ref. [4] because the detailed treatment given in [4] cannot be reproduced here. However, some salient points of the paper [4] are given here which may be of help to readers. ...
... We have proposed models of preformed hole-pairs [3]- [5] for resistanceless current flow in the a-b plane and along c-axis of cuprate superconductors. For better understanding of this paper, it should be read in conjunction with the paper in Ref. [4] because the detailed treatment given in [4] cannot be reproduced here. However, some salient points of the paper [4] are given here which may be of help to readers. ...
... For better understanding of this paper, it should be read in conjunction with the paper in Ref. [4] because the detailed treatment given in [4] cannot be reproduced here. However, some salient points of the paper [4] are given here which may be of help to readers. As prepared, cuprate superconductors are electron paramagnetic resonance (EPR) silent because of antiferromagnetic (AFM) coupling of Cu 2+ ions in the all-important CuO 2 plane. ...
La2-xNdxCuO3.5 (x ≤ 0.5) compounds have been synthesized by a topotactic reduction reaction with calcium hydride at 280 °C for 48 h. Structural, thermal, vibrational and magnetic properties of La2-xNdxCuO3.5 (x ≤ 0.5) were studied by X-ray powder diffraction (XRD), by differential thermal analysis (DTA) and temperature dependent powder X ray diffraction (TDXD), by Raman spectroscopy and by electronic paramagnetic resonance. The oxidation of the compounds La2-xNdxCuO3.5 (x ≤ 0.5) at 400 °C for 24 h kinetically stabilizes the compounds La2-xNdxCuO4 (x ≤ 0.5) with an I4/mmm type structure. The phase relationship between T’ and T, ensured at high temperature, was followed and discussed by thermal and structural analysis.
In the order parameter of hole-doped cuprate superconductors in the pseudogap phase, two holes enter the order parameter from opposite sides and pass through various CuO2 cells jumping from one O2− to the other under the influence of magnetic field offered by the Cu2+ ions in that CuO2 cell and thus forming hole pairs. In the pseudogap phase of electron-doped cuprates, two electrons enter the order parameter at Cu2+ sites from opposite ends and pass from one Cu2+ site to the diagonally opposite Cu2+ site. Following this type of path, they are subjected to high magnetic fields from various Cu2+ ions in that cell. They do not travel from one Cu2+ site to the other along straight path but by helical path. As they pass through the diagonal, they face high to low to very high magnetic field. Therefore, frequency of helical motion and pitch goes on changing with the magnetic field. Just before reaching the Cu2+ ions at the exit points of all the cells, the pitch of the helical motion is enormously decreased and thus charge density at these sites is increased. So the velocity of electrons along the diagonal path is decreased. Consequently, transition temperature of electron-doped cuprates becomes less than that of hole-doped cuprates. Symmetry of the order parameter of the electron-doped cuprates has been found to be of 3dx2−y2 + iS type. It has been inferred that internal magnetic field inside the order parameter reconstructs the Fermi surface, which is requisite for superconductivity to take place. Electron pairs formed in the pseudogap phase are the precursors of superconducting order parameter when cooled below Tc.
