Specification

Field of the invention

The invention relates to Bi2212 cuprates with an energy gap as a measure of pairing instability and Bogoliubov quasiparticles as electrons excited by depleted phonons.

Background of the Invention

In a previous paper ^[1] , discussions were made to antinodal gap features of Bi2212 with respect to the Angle-resolved photoemission spectroscopy (ARPES) results of Gromko et al ^[2] , with the application of a model of electron pairing based on non- stationary steady state (NSS state) ^[3] . According to the model, if two occupied stationary electron states (E ^ ) and (E ₂ ,fc ₂ ) matches a lattice mode (hv, q) with hv= E _J -E _J and q = k ₂ - k _l , electrons on the two states are tuned by the lattice mode and are set into NSS state, in which the probability distribution of the measured energy of each of the two electrons depends on the average phonon number n of the lattice mode, and when n ^→ 0 the probability that any of the electrons is measured at E ₂ effectively goes to zero.

Thus, as shown in Fig. 1 from Gromko et al (we add reference numbers 101-105 and the lines connecting them), states on the imagined antibonding band (AB) part from 104 to 105 and states on the bonding band (BB) part from 101 to 102 match their corresponding lattice modes respectively, so at sufficiently low temperature (when n ^→ 0 for these lattice modes) the measured energy (and wavevector) of each of the electrons associated with states on AB part from 104 to 105 is basically that of the respective lower state on BB part from 101 to 102. The same mechanism holds true for states on BB part from 102 to 103 with respect to the states on BB part from 101 to 102. In other words, electrons on states on AB part from 104 to 105 and BB part from 102 to 103 are measured as if they "sink" to their respective matching states on BB part from 101 to 102. However, with regard to existing nodal ARPES results for bilayer Bi ₂ Sr ₂ CaCu ₂ 0 ₈₊ 6 (Bi2212) ^[4]~[7] , explanation according to the above model of electron pairing meet difficulty. ARPES results for Bi2212 are typically featured by a kink and bilayer splitting band structure including substantially parallel antibonding band (AB) and bonding band (BB) extending from the kink to the Fermi level FL'. In such a nodal bilayer splitting band structure, as schematically shown in Fig. 2, electrons on states 203 and 204 near FL' should tend to sink to their matching state 201, so below superconducting transition temperature Tc a remarkable gap should exist at or immediately below FL', which is not in conformity with the existing nodal ARPES results. In this paper, explanation is to be made to the "missing" nodal gap, with respect to some existing nodal ARPES results of Bi2212, by application of the above-mentioned model of electron pairing based on NSS state.

Existing method for determining Fermi level by ARPES

Conventionally ^[8] , determination of Fermi level by ARPES was realized by comparing the photoelectron energies from a reference metal to those of the sample under study, where the reference metal and the sample are electrically connected.

Summary of the Invention

The present invention relates to a cuprates system comprising:

bilayer splitting band structure at the nodal and antinodal regions; wherein interband electron pairing mediated by lattice modes having phonon energy of about 70meV is realized at the nodal region, while interband electron pairing mediated by lattice modes having phonon energy of about 30-40 meV is realized at the antinodal region,

the interband electron pairing at the node is the most stable pairing in the system, so that electron pairing at other locations than the node can only be stabilized at an energy below the measured chemical potential of said cuprates system, depending on the relative stability of said electron pairing.

Brief Description of the Drawings

Fig. 1 is taken from Gromko et al. for showing electron pairing and band structure at the antinode of a Bi2212 system.

Fig. 2 schematically shows a typical band structure at the node of a Bi2212 system.

Fig. 3 is taken from Gromko et al. for showing doping dependence of band structure of Bi2212 systems.

Fig. 4 is taken from Gromko et al. for showing momentum dependence of band structure of Bi2212 systems.

Fig. 5 is taken from W. S. Lee et al for showing momentum and temperature dependence of band structure of Bi2212 systems.

Fig. 6 schematically shows a typical band structure at the node of a Bi2212 system.

Fig. 7 is taken from Matsui et al for showing Bogoliubov

quasiparticles in a Bi2223 system.

Fig. 8 is taken from Matsui et al for showing the relationships of Bogoliubov quasiparticles and a dip in the spectra in a Bi2223 system.

Fig. 9 is for explaining the measured intensity of Bogoliubov quasiparticles with respect to the intensity of the corresponding dip.

Fig. 10 schematically shows the band structure at a location near the node in a Bi2223 system.

Fig. 11 is taken from Alexander V. Balatsky for showing the distribution of Bogoliubov quasiparticle.

Detailed Description of the Invention

We would argue that the applicability of this method is

model-dependent. To a model of electron pairing in which a

superconducting gap (SG) or a pseudogap (PG) opens symmetrically with respect to Fermi level, application of the method can be justified.

However, to the above-mentioned model of electron pairing based on NSS state, the method would not be applicable. As schematically shown in Fig. 2, if electrons on states 203 and 204 at the "original" Fermi level FL' sink to state 201 , and electrons on states between 201 and 203 sink to corresponding states below 201 , state 201 would become the lower edge of gap (for simplicity we omit the effect of thermal excitation here), and the chemical potential (CP) of electrons in a reference metal electrically connected to the system of Fig. 2 would sink to the level of state 201 and be measured at lowered level FL, that is, the measured chemical potential would be aligned with the lower edge of the gap. Insofar that the system shown in Fig.2 resembles nodal bilayer splitting band structure typically shown in existing ARPES data of Bi2212, the above analysis may explain why no remarkable nodal gap is apparent in ARPES measurements of superconducting Bi2212 sample.

Then, why antinodal gap is apparent in existing ARPES results of Bi2212? Band topological features seem to decide the lower edge of the antinodal gap. As shown in Fig. 1, electrons on the AB part between states 104 and 105 and on BB part between states 102 and 103 sink to respective states on BB part between states 101 and 102, so none of the states on AB part from state 104 to the Fermi level (zero energy) and states on BB part from 102 to the Fermi level can be the "base" state of electron pairing of our model, for all these states are upper states pairing with respective lower states on BB part from 101 to 102. Thus, it could be said that the magnitude Δ _Α of the antinodal gap is determined by the energy E _k of the antinodal kink (that is, the energy of state 101 in Fig. 1) as:

^Δ Α= E _k -hv ,

with v being the frequency of the lattice mode mediating pairing between states 101 and 102.

Then, what decides the E _k the energy antinodal kink? We would propose that it is the competition between electron pairing at the node and that at the anti-node, which competition could be characterized by the difference in stabilities of electron pairing at these two sites. In the anti-nodal scenario of Fig. 1 , state 102 is associated with the double pairing of between 103 and 102 and between 105 and 102; similarly, in the nodal scenario of Fig. 2, state 201 is associated with the double pairing of between 203 and 201 and between 204 and 201. As the pairing at the node and that at the anti-node compete with each other, the less stable pairing can only be realized at an energy level further below the chemical potential of the system. This interpretation agrees with the results of Gromko et al that the antinodal gaps of OD58, OD75, and OP91 Bi2212 samples at T=10K increase in this order, as can be seen clearly in Fig. 3.

Although that the spacing between states 101 and 102 in Fig. 1 corresponds to the energy (hv) of the lattice mode mediating the intraband pairing in BB is a very strong limitation, such confinement of the length of the apparent BB section seems to agree very well with existing experimental results. As shown in Fig. 4 from Gromko et al, even at (0.7π,0) the length of the apparent BB section above the kink is still confined very well. While data for momentum cut further closer to the node is not available in Reference 2, one may roughly identify

corresponding antinodal AB and BB band features in Fig. 5 taken from W. S. Lee et al ^[9] , to further examine how anti-nodal band pattern like that of Figs. 1 transits to two parallel bands above the nodal kink (like for example those shown in References 6 and 7). In data up to cut C4 (for T=10K) of Fig. 5, the energy range of apparent BB above the kink still seems basically confined, while the range of apparent AB band increases dramatically. Turning back to Fig. 4, we see that the range of apparent AB band indeed increases remarkably at (0.7π,0). Such widespread confinement of apparent bonding band above the kink supports our model of electron pairing based on NSS state. Another associated feature in conformity with our pairing model is Δ _Α < hv, or E _k < 2hv. The validity of these relations is evidenced by the results of Figs. 3, 4 and 5.

Thus, with the confinement of the apparent BB band above

anti-nodal kink, if anti-nodal electron pairing becomes weaker, the kink, and thus the entire BB structure as that shown in Fig. 1 , would tend to sink deeper downward with respect to the measured chemical potential (Fermi level) so that antinodal pairing can be realized at lower energy, and surplus electrons left on states above sunken states 105 and 103 would go to nodal region to build up the lower edge of nodal gap, which is basically the measured chemical potential, leading to the overall effect of enlarging the anti-nodal apparent gap.

This interpretation of interplay between nodal and antinodal pairings and resulted shift of measured chemical potential is also in agreement with an early report by D. S. Dessau et al ^[10] : "A further very interesting aspect of our data is that the amount of spectral weight that we gain in the pileup peak does not appear to be equal to the weight that we lose from other regions (the gap plus dip). Along Γ-Jwe gain more weight in the pileup, while along Γ- we gain less weight." At the node, as shown in Fig. 2, when no pairing is present, the chemical potential is measured at FL' (here again effect of thermal excitation is omitted for simplicity); but at T ^→ 0, due to complete pairing the measured chemical potential drops by the energy of the mediating lattice mode to FL. For limited

temperature around Tc, it can be anticipated that the measured chemical potential shifts toward FL' as the temperature of the system lowers, and the number of electrons associated with states above the measured chemical potential increases. But in some existing reports, contribution to the pileup of the nodal peak by these electrons associated with states above the measured chemical potential was not recognized, so when temperature lowers more and more weight in the nodal peak lost its origin. As to the antinodal situation, first, weight lost from the dip has no contribution to the pileup of the antinodal peak because weight transfer by pairing is always downward according to the model of electron pairing based on NSS state. Second, as shown in Fig. 2, electrons associated with states on AB part from 105 to the measured Fermi level and states on BB part from 103 to the measured Fermi level contribute to pileup of antinodal peak but their contribution was not recognized, so when the weight by electrons associated with these states is smaller than the weight lost from the dip, the situation "along Γ- M we gain less weight" (than the weight lose from the gap and dip) would happen. That weight transfer from the dip has no contribution to the pileup of the peak signifies the significance of the antinodal and nodal kinks: to isolate pairings above the kinks from interacting with processes below the kinks. Due to the antinodal kink, the lattice mode mediating intraband pairing in antinodal BB above the kink is kept different from the modes mediating pairings below the kink, and this is also true for nodal intraband and interband pairings above and below the nodal kink. It could be anticipated that such isolation helps to stabilize the band structure above the kinks. And, the confinement of the length of apparent BB above kink in antinodal areas seems to indicate that the isolation by antinodal kink be more effective than nodal kink.

As explained in References 1 and 3, our model of electron pairing is entirely based on traditional time-dependent perturbation equation for electron-lattice scattering. But a scattering interpretation emphasizes transitions among stationary states. In our model, however,

time-dependent perturbation for electron-lattice interaction is interpreted as representation of a non-stationary electron state in crystal by stationary states (E _n ,k _n ) , as lattice modes leading to time-dependent term in the

Hamiltonian for the perturbation equation are intrinsic to crystal; each such non-stationary electron state is typically associated with two stationary states (E _[ ,^ ) and (E ₂ ,fc ₂ ) matching a mediating lattice mode

(hv, q) with h ^ E _j -E _j and q = k ₂ - k , and whether such a non- stationary electron state can be "realized" depends on its competition with other available non-stationary electron state(s) (and it may also depends at the first place on whether sufficiently well-defined or stabilized upper and lower stationary states (E^fc^ and (E ₂ ,k ₂ ) and mediating lattice mode are available.) The non- stationary electron state is a steady state. An electron in such a non-stationary electron state can be measured either at (E _t ,k ) or (E ₂ ,k ₂ ) . When the number of (real) phonon of the mediating lattice mode goes to zero, the probability that the electron is measured at (E ₂ ,fc ₂ ) also goes to zero. As one such non-stationary electron state is associated with two stationary states, it is 2-fold "degenerate". The 2-fold degeneracy results in "pairing", and the vanishing probability that the electron is measured at (E ₂ ,k ₂ ) leads to "binding energy".

Some details of transition from antinodal pairing to nodal pairing could be identified in the data of Fig. 5, particularly in the data of cuts C2-C5 for 10K. The confined apparent antinodal BB part (corresponding to the part from 101 to 102 in Fig. 1) can still be traced even in cut C2, but increasing weight adds as its lower extension, and finally the added weight becomes indistinguishable from the antinodal BB part, and transforms into nodal BB part above the nodal kink together with the antinodal BB part; the confinement never collapses, it merely thins out. Insofar the gap seems to vanish with the transformation as evidenced in Fig. 5, an enlarged antinodal gap would retard such a transformation and extend the range in which the antinodal structure persists, in favor of stability of the entire band structure above the nodal and antinodal kinks. As such, the kinks function as spacers, and the stable nodal pairing, by its domination over antinodal pairing, enlarges the effective range of the antinodal spacer in k-space, which may in turn promote the stability and domination of the nodal pairing.

Moreover, this transformation suggests a switch of the

pair-mediating lattice mode from the antinodal mediating mode(s) to the nodal mediating mode (Details concerning the transformation and the onset of the gap at the nodal region are to be discussed later in this paper.) Scenarios in which apparent AB and BB parts stay in juxtaposition are already shown in the existing results for OP91 of Fig. 3 and for cut at (0.7π,0) of Fig. 4, where pairing is considered as being "based on" the apparent BB part, although these parts are not "parallel". Another experimental evidence is a nodal peak of about the same width as its antinodal counterpart (about 30-35 meV as identified in Fig. 1) ^[10] , which indicates that a mode of this energy is involved in mediating nodal pairs (it is noted, however, that this peak is a result of integration over a nodal area).

With these, we would anticipate a scenario of nodal pairing as schematically shown in Fig. 6, in which some "main" interband pairs are mediated between BB states below measured chemical potential FL and AB states above FL by modes of relatively great energy (70 meV or so ^[11][12] ) so that all AB states in interband pairs "based on" BB states are above FL, intraband pairs like that between 601 and 602 are mediated by modes of 30-35 meV or so and lead to a nodal peak ^[10] , and some interband pairs "based on" AB states might be realized between AB states 607 and BB states 608. Such a picture could be in conformity with the results of Figs. 4 and 5 and References 5-7 and 10.

In the scenario shown in Fig. 6, not all the states below 603 are occupied. A pair like that between states 601 and 603 or states 604 and 605 has to be stable for the corresponding upper state 603 or 605 to be occupied. Thus, a pair on a "base state" near FL like state 601 may not be guaranteed of a binding energy corresponding to the energy (hv) of its mediating lattice mode; but at sufficiently low temperature, a pair with a base state below FL like state 604 should have a binding energy basically no smaller than the energy of the base state and no greater than the energy of the base state plus hv.

Of special interest are reported Bogoliubov quasiparticles (BQP) detected by ARPES ^[9][13][14] and interpreted as thermally excited electrons in an upper branch of a superconducting binding-back band. We propose, however, that BQPs are paired electrons measured at the upper state

(E ₂ ,fc ₂ ) of the pair due to excitations by concentrated phonons in its mediating lattice mode. In an earlier paper by this author, a mechanism of phonon depletion from lattice modes mediating electrons at the nodal region in superconducting cuprates was proposed. ^[15] It is to be noted that phonon transfer as proposed in Ref. 15 can be along various directions, and the electron states involved are not necessary in spatially

communicated in k-space. Generally, electron pairs based on NSS states need not to be confined in one plane as shown in Fig. 6, but due to symmetry restriction, stabilized pairs at the node could only be realized along T-X. Thus, for a lattice mode mediating pairing at the node to be depleted, the destination mode(s) of the phonon depletion/transfer should not deviate too much from T-X.

BQPs in Bi2212 were reported in a region near the node. As shown in (b) and (d) of Fig. 5, at cut CI , which is the closest to the node, BQPs seem to damp. We propose here that these BQPs in Bi2212 are due to excitation by phonons of destination modes of phonon depletion suffered by lattice modes mediating interband pairings "based on" BB states at the node; such interband pairings are schematically shown in Fig. 6 as pairing between 604 and 605 and between 601 and 603. While the slope of the band decreases upon moving from the node to the antinode, the

separation of the band bilayer splitting tends to increase ^[6] . Interband pairing between bilayer band structures of various slopes can be mediated by the same mode, so long as the bilayer separation varies accordingly. Thus, it could be anticipated that the lattice modes mediating interband pairings at cuts C1-C4 in Fig. 5 are just slightly different from the modes mediating interband pairings at the node, so these slightly different modes compete, possibly through some intermediate modes, for real phonons, with the modes mediating at cuts C1-C4 being the winning modes and the modes mediating at the node suffer phonon depletion. This mode competition is essentially the same as that in a laser, and the modes mediating at cuts C1-C4 correspond to laser modes that generate radiation output. While phonons concentrated to the winning lattice modes are not for output from the crystal of superconducting cuprates, they do lead to excitation of paired electrons from their "base" states as schematically- shown in Fig. 6 at 604 to their "upper" states as schematically shown at 605, where they are be detected by ARPES as BQPs.

As explained above, some (typically a small portion) of the states from FL to the upper limit of BQPs' distribution are not occupied, allowing phonon to be dissipated by transitions of BQPs to these non-occupied states. At limited temperature, as processes like anharmonic interactions or so may lead to an inlet flow of phonons to the depleted modes, such phonon dissipation, or "phonon sink", would allow a corresponding flow of depleted phonons to balance the inlet flow. The phonon depletion suffered by lattice modes mediating BB-based interband pairs at the node leads to greatly enhanced stability of these pairs, since it will be far less probable for electrons in these pairs to be "measured" as at their upper states. It is the losing modes that are capable of leading to high- temperature superconductivity.

In such an interpretation, BQPs would be associated with a

corresponding dip immediately above the nodal kink; the dip is separated from the BQP peak by one phonon energy (about 70meV). As shown in Fig. 5, in cut CI a seemingly slight dip could be identified at 50-60 meV but no dip is apparent in cuts C2-C4. But first, cuts C1-C4 are not along T-X, so the dip in cut CI should largely correspond to BQPs in cut C2, and so on. Second, due to dispersion, the weight of the main part of BB at around 70meV might have not been included in the data of Fig. 5, as can be seen from Figs. 4 and 5 of Ref. 14, where the main part of BB at 70meV is clearly excluded from the data-collecting (shade) area.

However, in Fig. 7(b) of Ref. 14, a clear dip is seen at the energy of >70 meV while a BQP peak centers at about 20 meV; the energy of this dip is not easy to be determined as it is partly at the shoulder of the steep peak.

Results of Matsui et al are of triple-layered Bi2223, with a striking feature that BQPs are measured at locations closer to antinode than to node, as shown in Fig. 7 taken from Ref. 13. But triple-layered system is more flexible in pairing match because switch between different pairs of layers is possible. For example, a mode that mediates pairing between the upper and lower bands at the node may switches to mediate pairing between the middle and the lower bands. Such a switch would allow a phonon sink located much farther away from the node and possible multiplicity of phonon-dissipating areas. Details of pairing mechanism in triple-layered Bi2223 still need investigation.

In Fig. 8 from Matsui et al, dips occur in the spectra at points B and C at energy slightly lower than 50 meV, together with BQP peaks slight over -20 meV. These dips are obvious, and at the right energy as expected in an interpretation based on our pairing model. Moreover, we can even identify a slight dip and a corresponding BQP peak in the spectrum at point A, and while the BQP peaks are seen to slightly shift toward lower energy from point C to point A, the dips exhibit substantially the same energy shift. The strength of the dip at point C, however, seems much weaker than that of its BQP peak. But this deviation can be explained in our framework of pairing mechanism. As shown in Fig. 9 in view of the inlet of Fig. 7 taken from Matsui et al, line 901 represents the central line of the Fermi arc in the area to be detected, the (Ο,Ο)-(π,π) direction is shown by the arrow, and the detected area can be represented by a horizontal stripe schematically shown at 902; thus, points A, B, and C are schematically shown here as three locations A, B, and C along stripe 902, and points A, B, and C correspond to points 1, 2, and 3 on line 901 respectively. According our interpretation, BQPs at point C are "based on" an area schematically shown at 903 C, located directly upward with respect to point 8, and so are BQPs at points B and A with respect to areas 903B and 903 A respectively. While points 1 , 2 and 3 along the central line 901 of the Fermi arc were well covered by stripe 902, part of area 903 C might have been left out, leading to a weakened dip at point C.

One more question is why BQPs' peak appears at certain energy. It is known in the art that "strong electron coupling with other

excitations concomitantly makes the electron appear as a heavier and slower quasiparticle", ^[7] and that these interactions or correlation effects give electrons "an enhanced mass or flatter E vs. k. dispersion". ^[2] We would propose that the "strong electron coupling with other excitations" is basically the electron-electron interaction mediated by lattice modes, which sets electrons into NSS states. It has been evidenced that "the quasiparticle peak dramatically sharpens on crossing |ω| ~ 70 meV (kink) towards the Fermi level", while at T>Tc such sharpening is not present even though a nodal kink still exists. ^[6] But whether there is a kink and/or band broadening above FL has not been known. We now try to analyze these with respect to our pairing model.

According to our pairing model as shown in Fig. 6, the above and other descriptions in Ref. 6 would indicate that interband pairs based on BB states from the nodal kink up to the Fermi level become stabilized only at T<Tc. As shown in Fig. 4 of Ref. 6, even at E>50meV and the very low temperature of 9K the band of the optimally doped sample of Tc=86K still begins to broaden at a significantly increased rate. According to our model of Fig. 6, the BB states slightly above the nodal kink (like state 604) pair with AB states slight above FL (such as state 605) and a BB state (not shown) slightly above FL, so we would propose that at the node the AB and BB parts just above FL broaden

correspondingly to the BB band part just above the nodal kink. This may indicate pairing like that between 604 and 605 and the intraband pairing based 604 are not as stable as pairing between 601 and 603. The energy of the nodal kink largely equals to the energy of the mediating lattice mode (~70meV), for a state with greater energy would not be able to find a matching state above FL to pair upward and its downward pairing might not be stable enough to result in the restricted band width evidenced above the nodal kink.

As explained above with respect to anti-nodal gap, pairing based on BB state at FL cannot be realized at a location other than the node. So, as schematically shown Fig. 10, upon leaving the node, interband pairing based on BB can only be realized below an energy level lower than FL by a gap energy Δ, and pairing relationships would require that the kink be lowered by the same amount. Although such a lowered kink might be realized in a small region near the node and/or at sufficiently low temperature, the pairing instability associated with the rapidly increased scattering rate evidenced in Ref. 6 would suggest that a lowered kink may not be practical, at least at a temperature not too low below Tc. Then, one solution for the system to reach a stabilized pairing pattern is to form a kink at the measured Fermi level (FL kink), as schematically shown in Fig. 10. The FL kink runs from Δ below FL to Δ' above FL, and we would argue Δ≠ Δ'. As shown in Fig. 10, with the FL kink, pairing relations similar to those at the node can be realized, by basically the same mediating mode, in which BB state 1001 at Δ pairs with AB state 1005, and BB state 1004 at the lower kink pairs with AB state 1006 to give rise to BQPs. Intraband pairing mediated by a 70meV mode may exist between states 1001 and 1003, which mode also mediates pairing between 1004 and 1002. Obviously, the FL kink may function in cooperation with the band slope and separation described above to support mediation of interband like that between 1004 and 1006 by modes supporting phonon depletion from the node. BQPs would appear at states near 1006 shown in Fig. 10 due to excitations by phonons of modes mediating pairing between 1004 and 1006. Thus, we have reached an explanation to the energy of the BQP peak in the framework of our pairing model.

The presence of the FL kink could be a factor leading to the seemingly dispersion of measured BQPs; ^[13][14] in fact, the BQP distribution shown in Fig. 11 taken from Ref. 14 looks more like a kink than a dispersion. Another factor would be that, since BQPs are only on AB in Bi2212, they would be measured as if they have a slight shift to the AB side when photon energy like 22.7 eV is used to allow simultaneous measurement of AB and BB.

Obviously, the gap associated with the FL kink is the embryo of the antinodal gap, which grows in magnitude upon moving toward the antinode as evidence in Fig. 5(a). As explained above, the antinodal gap is not symmetry with respect to FL, thus we may conclude that Δ = Δ' is not necessary. It is to be noted that the gap is full of occupied states, but most or almost all of electrons on these states engage in downward pairing mediated by modes of 20-30 meV and are measured as being on their respective base states. As the gap grows, pairings mediated by the 70 meV modes begin to lose their dominance over those mediated by the 20-30 meV modes, which eventually gain dominance and the pairing and gap pattern finally transit to that at antinode as shown in Fig. 1. It is not determined whether such transition is a critical one. By far, we have seen that although both antinodal and nodal pairings are dominated by pairing at the node, the antinodal kink is lowered by such dominance while the nodal kink tends to be raised by the dominance.

It is noted that a dip at nodal kink may appear in a high-temperature superconducting Bi2212 systems at a temperature far below Tc ^[16] . The origin of such a nodal dip is largely the same as the antinodal dip in Bi2212, as that the electrons at the low- temperature dip engage in downward pairing and "sink" to their base states below. But the low-temperature dip is below the nodal kink, while the dip relating to BQPs is slightly above the kink.

Thus, with respect to some typical existing experimental results on Bi2212 (and Bi2223), we have provided interpretations to antinodal and nodal features of these superconducting cuprates systems, using our model of electron pairing based on NSS state of electron. These interpretations are self-consistent and provide novel explanations to some important experimental results. The magnitude of an apparent energy gap is identified as a measure of relative instability of electron pairing at the location of the gap, for it indicates that a stabilized pairing (NSS state) of electrons can only be realized at a higher binding energy. At a

temperature under Tc or so, the chemical potential of a system like Bi2212 is determined by the most stable pairings in it, basically as the upper limit of the measured energy of electrons in these pairings. By considering phonon depletion relating to pairing at the node, we have reached a novel interpretation of Bogoliubov quasiparticles as excitations by lattice modes functioning to dissipate the depleted phonons, together with an explanation on the origin of the energy of BQP peak. It must be the depleted modes that lead to high-temperature superconductivity.

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