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We investigated quantized modes of kinks in the phase space of superconducting gaps in a superconductor with multiple gaps. The kink is described by the sine-Gordon model in a two-gap superconductor and by the double sine-Gordon model in a three-gap superconductor. A fractional-flux vortex exists at the edge of the kink, and a fractional-flux vortex will be stable in a three-gap superconductor with time-reversal symmetry breaking. The kink and fractional-flux vortex exhibit massless modes as a sliding motion. We show further that there are one zero-energy mode (massless mode) and quantized excitation modes in kinks, which are characteristic features of multi-gap superconductors. The equation of quantized modes for the double sine-Gordon model is solved numerically. The correction to the ground-state energy is calculated based on the renormalization theory., Comment: 9 pages, 8 figures

We comment on a recent paper by the LEPS2/BGOegg Collaboration [Phys. Rev. Lett. 124, 202501 (2020), arXiv:2005.03449].

Journal of physics / Conference series 1643, 012181 (2020). doi:10.1088/1742-6596/1643/1/012181, Published by IOP Publ., Bristol

Applying a radian phase shift other than 2π is a key issue for superconducting circuits, such as flux qubits. The magnetic flux is useful when generating a phase shift. However, a quantized magnetic flux accompanying a trapped vortex in a superconductor does not have a phase shifter function. The magnetic flux generated by an external field generates noise. In this study, we propose a phase bias system that does not require an external field during operation. We confirm the phase shift of a direct current superconducting interference device (SQUID) placed on an ultrathin superconducting Nb bilayer with a through-hole by cooling it to a temperature below the superconducting transition temperature with an external field. Although the cause of the phase shift in our system is unclear, we believe that it may be caused by a fractional quantum in the bilayer. When the SQUID is replaced by a qubit, the phase shift can be applied to a phase bias.

Physics letters / B 807, 135565 (2020). doi:10.1016/j.physletb.2020.135565, Published by North-Holland Publ., Amsterdam

An ultrathin superconducting bilayer creates a coreless fractional vortex when only the second layer has a hole. The quantization is broken by the hole, and the normal core disappears. The magnetic flux is no longer confined near the normal core. The divergence of the magnetic flux density is truncated around the center. We propose basic design of a practical device to realize a coreless fractional vortex.

An ultrathin superconducting bilayer can admit a monotonic magnetic field when one layer has a slit even in a Meissner state. The rotation of the superconducting quantum phase by a vector potential for the magnetic field is compensated by a phase shift accompanying an inter-layer phase difference mode which grows from the slit. This phase difference mode may grow to form a fractional vortex, and it may show a close relationship with experimentally observed fractional vortices.

We report the experimental formation of a fractional vortex generated by using a thin superconducting bi-layer in the form of a niobium bi-layer, observed as a magnetic flux distribution image taken by a scanning superconducting quantum interference device (SQUID) microscope. Thus, we demonstrated that multi-component superconductivity can be realized by an s-wave conventional superconductor, because, in these superconductors, the magnetic flux is no longer quantized as it is destroyed by the existence of an inter-component phase soliton (i-soliton).

We developed a minimal method of forming and detecting a fractional magnetic flux quantum in a two-component superconductor fabricated using an ultra-thin niobium bilayer that sandwiches a Josephson barrier. The fractional quantum created by cooling a bilayer disk in the magnetic field survived after turning off the magnetic field. The survived quantum was confirmed by the change in the critical current of a superconducting quantum interference device (SQUID) placed on the bilayer disk. By replacing a flux qubit with the SQUID, we can use the fractional flux quantum as the flux bias for the flux qubit. This method enables the investigation of fractional quantization and the related topology.

An ultra-thin superconducting bi-layer is an artificial multi-component superconductor in which the magnetic flux can be fractionally quantized. The fractionally quantized state is energetically unfavorable, so it is difficult to realize experimentally. We propose a new method to create fractional quantized states by the reaction of a unit quantized state with an externally injected inter-layer phase-difference soliton. Simulation shows that the unit quantized state splits the soliton and the soliton fragments produce fractional quanta by dissociation of the unit quantum.

The sliding motions of inter-band phase difference solitons ( i -solitons) cause time-dependent superconducting phase variations in two-band superconductors. Two different voltages cannot exist at the same spatial location, although the conventional AC Josephson effect demands the presence of a voltage difference between the two bands at the same location, if the time-variation of the phase generates the voltage, for which a physical interpretation is not possible. Instead of the conventional AC Josephson effect, a non-linear Klein-Gordon equation (sine-Gordon equation) can enable the dissipationless movement of i -solitons, without voltage generation.

Acta physica Polonica / B Particle physics and field theory, nuclear physics, theory of relativity 51(1), 39 (2020). doi:10.5506/APhysPolB.51.39, Published by Inst. of Physics, Jagellonian Univ., Cracow

We observed the atomic 1s and 2p states of π^{-} bound to ^{121}Sn nuclei as distinct peak structures in the missing mass spectra of the ^{122}Sn(d,^{3}He) nuclear reaction. A very intense deuteron beam and a spectrometer with a large angular acceptance let us achieve a potential of discovery, which includes the capability of determining the angle-dependent cross sections with high statistics. The 2p state in a Sn nucleus was observed for the first time. The binding energies and widths of the pionic states are determined and found to be consistent with previous experimental results of other Sn isotopes. The spectrum is measured at finite reaction angles for the first time. The formation cross sections at the reaction angles between 0° and 2° are determined. The observed reaction-angle dependence of each state is reproduced by theoretical calculations. However, the quantitative comparison with our high-precision data reveals a significant discrepancy between the measured and calculated formation cross sections of the pionic 1s state.

Excitation-energy spectra of $^{11}\mathrm{C}$ nuclei near the ${\ensuremath{\eta}}^{\ensuremath{'}}$-meson production threshold have been measured by missing-mass spectroscopy using the $^{12}\mathrm{C}(p,d)$ reaction. A carbon target has been irradiated with a 2.5 GeV proton beam supplied by the synchrotron SIS-18 at GSI to produce ${\ensuremath{\eta}}^{\ensuremath{'}}$-meson bound states in $^{11}\mathrm{C}$ nuclei. Deuterons emitted at ${0}^{\ensuremath{\circ}}$ in the reaction have been momentum analyzed by the fragment separator (FRS), used as a high-resolution spectrometer. No distinct structure due to the formation of ${\ensuremath{\eta}}^{\ensuremath{'}}$-mesic states is observed although a high statistical sensitivity is achieved in the experimental spectra. Upper limits on the formation cross sections of ${\ensuremath{\eta}}^{\ensuremath{'}}$-mesic states are determined, and thereby a constraint imposed on the ${\ensuremath{\eta}}^{\ensuremath{'}}$-nucleus interaction is discussed.

Prospects of experimental studies of argon and chlorine isotopes located far beyond the proton dripline are studied by using systematics and cluster models. The deviations from the widespread systematics observed in $^{28,29}$Cl and $^{29,30}$Ar have been theoretically substantiated, and analogous deviations predicted for the lighter chlorine and argon isotopes. The limits of nuclear structure existence are predicted for Ar and Cl isotopic chains, with $^{26}$Ar and $^{25}$Cl found to be the lightest sufficiently long-living nuclear systems. By simultaneous measurements of protons and $\gamma$-rays following decays of such systems as well as their $\beta$-delayed emission, an interesting synergy effect may be achieved, which is demonstrated by the example of $^{30}$Cl and $^{31}$Ar ground state studies. Such synergy effect may be provided by the new EXPERT setup (EXotic Particle Emission and Radioactivity by Tracking), being operated inside the fragment separator and spectrometer facility at GSI, Darmstadt., Comment: 10 pages, 9 figures. Chapter added, language and some figures corrected

There is a current-induced massless mode of an interband phase difference in two-band superconductors. For a thin wire, the externally applied current always invokes a finite interband phase difference when the end of the wire is terminated by a natural boundary condition, i.e., where the total current is specified but the other parameters are left as free and a finite interband phase difference is allowed. This condition can be realized by the normal state region formed by the shrinking of a cross section of the wire where the critical current density is lower than that of the other region of the wire. The interband interaction in the wire cannot completely prevent the emergence of the interband phase difference, though it reduces it somewhat. Instead, boundary conditions determine the presence of the interband phase difference. By reverting the normal state into the superconducting state at the shrunken region by decreasing the current, we may trap a rotation of integral multiples of 2π radians of the interband phase difference in the wire. After switching off the current, this rotation of integral multiples of 2π radians, which continuously spreads over the whole wire, is separated into several interband phase difference solitons (i-solitons), where one i-soliton locally generates a 2π interband phase difference.

Since the idea of a topology based on the interband phase difference was proposed for multiband superconductors without degenerate superconducting components, many feasible and interesting possibilities have been explored. The basic concepts involved are an interband phase difference soliton , the fractionalization of the unit magnetic flux quantum, and frustration between quantum phases of multiple components. The superconductivity field was be extended by introducing the idea of the fluctuation in the interband phase difference. This extension provides a bridge between superconducting condensates and other macroscopic quantum mechanical systems such as Bose–Einstein condensates with multiple components and particle physics systems governed by a nonabelian gauge field. The entropy supported by the interband fluctuation suggests a relationship between multiband superconductors and highly correlated systems. In this chapter, I comment on the past, present, and future situation of multicomponent superconductivity based on multiband superconductors .

A basic design is proposed for a classical bit element of a superconducting circuit that mimics a frustrated multiband superconductor and is composed of an array of π-Josephson junctions (π-junction). The phase shift of π provides the lowest energy for one π-junction, but neither a π nor a zero phase shift gives the lowest energy for an assembly of π-junctions. There are two chiral states that can be used to store one bit information. The energy scale for reading and writing to memory is of the same order as the junction energy, and is thus in the same order of the driving energy of the circuit. In addition, random access is also possible.

We observe oscillations in the resistivity as a function of the magnetic field at 80 K in a 5-μm-wide channel with a 100-nm-diameter hole fabricated in a multi-band superconducting (Tlx, Cu1−x)(Bay, Sr1−y)2Ca2Cu3Oz film. A phase shift is observed in the oscillations at magnetic fields around 200 mT, which is similar to previous observations in mesoscopic superconducting rings with two order parameters.

Chiral fluctuation in frustrated superconductivity unlocks the interband phase difference at the superconducting transition temperature calculated by the standard Bardeen–Cooper–Schrieffer (BCS) theory when an interband interaction is much weaker than an intraband interaction. At low temperature, a first-order phase transition locks the interband phase difference. This transition is demonstrated in degenerate chiral superconductivity, which adds a pair entropy term to the BCS theory.

Maintaining pair entropy assists in the evolution of a gap in frustrated multiband superconductors. A finite and persistent gap is always open at finite temperatures due to the fluctuation of the interband phase difference when the interband interaction is much smaller than the intraband interaction. We demonstrate this gap evolution by combining the Bardeen–Cooper–Schrieffer (BCS) free energy with an entropy contribution originating from the internal freedom of the pair.

Excitation spectra of ^{11}C are measured in the ^{12}C(p,d) reaction near the η^{'} emission threshold. A proton beam extracted from the synchrotron SIS-18 at GSI with an incident energy of 2.5 GeV impinges on a carbon target. The momenta of deuterons emitted at 0° are precisely measured with the fragment separator (FRS) operated as a spectrometer. In contrast to theoretical predictions on the possible existence of deeply bound η^{'}-mesic states in carbon nuclei, no distinct structures are observed associated with the formation of bound states. The spectra are analyzed to set stringent constraints on the formation cross section and on the hitherto barely known η^{'}-nucleus interaction.

The positive interband Josephson interaction leads to emergence of non-trivial order parameters such as a sign-reversal one for a two-band superconductor, a frustrated superconductivity for a three-band superconductor. The frustrated superconductivity appears on the way to fully incoherent state due to the Coulomb interaction. The physical background of the frustrated superconductivity is transparent and the effect can be directly examined in the fluctuation of the interband phase difference. To understand the relationship between the phase fluctuation and an emergence of the chiral superconductivity, we examine a simple situation, which is almost degenerated system using Ginzburg-Landau theory. The frustration retains the interband phase difference fluctuation and this fluctuation becomes a seed of a chiral domain.

Multiband superconductors can have several types of domains that are inhibited in conventional single-band superconductors. These domains are phase domains and chiral domains and their domain wall are an interband phase difference soliton. In a superconductor with an odd number of electronic bands (five or more) and with positive interband Josephson interactions, we find other types of domains with different interband phase differences. We call these domains configuration domains because pseudo-order parameters for each band are dispersed in the complex plain and several configurations, which have several local minima. Fractional vortices serve as hubs for phase difference solitons (configuration domain walls). The divergence of the number of configurations with local minima would pose a serious problem for the stability of superconductivity.

We investigate multi-component superconductors, in relation to iron pnictides, by using the Ginzburg–Landau theory. We show that a three-band superconductor exhibits several significant properties that are not found in single-band or two-band superconductors. The frustrating pairing interaction among Fermi surfaces may lead to a time-reversal symmetry broken pairing state. In fact, we have a solution with time-reversal symmetry breaking, that is, a chiral solution when there is such a frustration. The Ginzburg–Landau equation for three-component superconductors leads to a double sine-Gordon equation. A kink solution exists to this equation that results in the existence of fractional-quantum flux vortices on the domain wall.

Competition between an interband Josephson interaction and a biquadratic interband interaction can break time-reversal symmetry when the interband interactions are very weak compared with the intraband interaction. We demonstrate this using the phenomenological Ginzburg–Landau free energy, taking into account terms essential for this phenomenon. This time-reversal symmetry-breaking state peels away a sheet of an interband phase difference soliton wall. This sheet is the domain wall between two different chiral states. The peeling reduces the formation energy of the domain wall. The domain wall can simultaneously erase the Meissner effect and the specific heat jump when the entropy invokes many domain walls, and its life time is prolonged by a pinning owing to an inhomogeneity such as surface roughness.

(Cu, C)–Ba–O thin films have been deposited at low growth temperature of 450–570 °C by pulsed laser deposition method. A control of CO 2 gas pressure and the growth temperature, usage of BaCu y O x pellet target resulted in an expansion of twice c -axis length of BaCuO 2 structure (2c phase) and a significant rise of conductivity. Measurements of in-situ XPS suggest that the 2c phase should be (Cu, C)Ba 2 CuO x [(Cu, C)-1201]. The maximum temperature of onset of the superconducting transition and zero resistance state obtained so far were 60 and 47 K, respectively.

The discovery of superconductivity in MgB2 and, more recently, in iron pnictides, revived the interest in two-component and other exotic superconductors, including in the field of vortex matter, as was shown recently by the discovery of “type 1.5” superconductivity. However, even some “older” exotic cuprates grown by high-pressure techniques showed interesting anomalies related to the interplay between Josephson and magnetic coupling and/or two-gap superconductivity. Here, we will present two such examples of exotic vortex matter: magnetically-coupled pancake-vortex molecules in super-multilayered cuprates, and vortex molecules composed of fractional flux quanta glued by an interband phase difference soliton, and will discuss the major differences between MgB2 and such multilayer cuprates in terms of the relative strength of the interband interaction and, respectively, in terms of the coherence and penetration lengths.

Transport properties of (Cu, C)Ba 2 CuO x [(Cu, C)-1201] thin films have been characterized by in situ temperature dependence of resistivity, without breaking vacuum from the deposition to the measurement. In in situ transport properties measurements, the obtained results reveal that (Cu, C)Ba 2 CuO x films exhibit T c > 20 K on the cased of conductivity at 290 K ( σ [290 K] ) > 4 × 10 2 S/cm and temperature coefficient of resistivity (TCR) > 1.5 × 10 −3 K −1 , and doping level of them should be in between under-doped and optimally-doped states. Their results suggest that there would be possible to further increases of T c , and XPS data suggest that (Cu, C)-system should have the excellent dopability in their charge reservoir and the possibility of low anisotropy.

BiCr0.5Mn0.5O3, synthesized at high pressure and high temperature, has a monoclinic structure (space group C2/c) at room temperature with a = 9.4590(3) A, b = 5.5531(2) A, c = 9.6465(3) A and β = 108.149(2)°. It undergoes a structural transition from the monoclinic to an orthorhombic (Pnma) symmetry around 650 K. Magnetic measurements show three distinct anomalies at 25, 50 and 97 K. AC susceptibility measurements confirm the occurrence of the magnetic anomalies, but suggest no spin frustration. Interestingly, this oxide shows a giant dielectric constant at room temperature. Two clear relaxation processes commencing around 200 K and 300 K are exhibited by this material. The first relaxation process is due to Maxwell-Wagner polarization at the grain boundary whereas the second relaxation may arise from hopping of electrons in the B-site.

We observed the disappearance of the Meissner effect and the specific heat jump in Ba0.2K0.8Fe2As2. A crossover of the type of superconducting order parameter can be a source of these phenomena. A quantum phase disorder provides a possible explanation.

There are four topologically different paths to interchange two single-component winding vortices in a two-band superconductor having a weak inter-band interaction, where each band has its own superconducting component and its own phase, θν, other than the ordinary quantum phase, Θ (ν is the index of the band and Θ is defined at the region of θ1=θ2.). The acquired phase for the interchange of two single-winding vortices depends on the path, and three values, Θsoliton, −Θsoliton and 0, are observed. Θsoliton is the phase-slip accompanying the inter-band phase difference soliton (i-soliton). The interchange requires the creation and annihilation of the i-soliton and gives rise to an ambiguity in the statistics.

HgBa 2 Ca n −1 Cu n O y (Hg:12( n − 1) n ) phases have the same T c independent of n and the same vortex melting line for n ⩾ 6. In these materials, there are two types of pancake pairs: those separated by the thick block of ( n − 2) inner CuO 2 planes, which are weakly coupled by the magnetic interaction, and, respectively, those separated by the thin HgBa 2 O x charge reservoir layer, which are much stronger coupled by the Josephson coupling. The vortex melting line common to all Hg:12( n − 1) n phases ( n ⩾ 6), separates two new vortex phases, pancake-molecule-glass, and pancake-molecule-liquid.

Change of electronic structure of superconducting (Cu, C)-1201 thin films grown by pulsed laser deposition with superconducting critical temperature Tc has been characterized by means of in situ photoemission spectroscopy. The finite spectral weight at the Fermi level in the valence band of (Cu, C)-1201 superconducting thin films and a rigid-band-like approach of the main peak of the valence band toward the Fermi level with a rise of Tc has been observed, which reveals hole-doping-induced superconductivity of this system. The obtained Ba 4d and Cu 2p signals with an increase of Tc suggest excess oxygen should be introduced around Ba ions in the early stage of the emergence of superconductivity. Then, they should be preferentially introduced around Cu ions. The changes of core signals with Tc and comparisons of the obtained data with infinite-layer and other cuprate superconductor compounds suggest that the (Cu, C)–O charge reservoir in this system is in the heavily hole-doped state, similar to that of the Cu–O chain in YBa2Cu3O7−δ.

Superconducting (Cu, C)?Ba?O thin films have been epitaxially grown on (100) SrTiO3 at a low growth temperature of 500?600??C by pulsed laser deposition. The dependences of their crystallinity and transport properties on preparation conditions have been investigated in order to clarify the dominant parameters for carbon incorporation and the emergence of superconductivity. It has been revealed that the CO3 content in the films increases with increasing both the parameters of partial pressure of CO2 during film growth and those of growth rate and enhancement of superconducting properties. The present study has also revealed that the structural and superconducting properties of the (Cu, C)?Ba?O films are seriously deteriorated by the irradiation of energetic particles during deposition. Suppression of the radiation damage is another key for a high and uniform superconducting transition. By these optimizations, a superconducting onset temperature above 50?K and a zero-resistance temperature above 40?K have been realized.

Zero- and longitudinal-field muon-spin rotation (ZF-μSR and LF-μSR) measurements were carried out on a multi-layered HgBa 2 Ca 4 Cu 5 O y (Hg-1245) superconductor with T c of 108 K. With decreasing temperature, the observed ZF-μSR function changed from a Gaussian-type to an exponential-type below 60 K and zero field muon precession was also observed below 45 K. These μSR signals are attributed to the development of the antiferromagnetic ordering in inner CuO 2 planes with a low carrier concentration. These results seem to indicate clear evidence that antiferromagnetism microscopically coexists with superconductivity in the Hg-1245 superconductor below 60 K.

The magnetic torque of ( Cu , C ) Ba 2 Ca 3 Cu 4 O y ( ( Cu , C )-1234) aligned samples with various carrier concentrations has been measured under a magnetic field of 9 T at 80 K and 90 K. The carrier concentration was determined by Hall effect measurements. From angular dependent torque measurements, the anisotropy ratio γ was estimated using the 3D anisotropic London model. The γvalues decreased from 23 to 10 with an increase in the average Hall number per CuO 2 plane ( n H); however, these samples showed a nearly constant Tc of about 117 K. These results indicate that the anisotropy of ( Cu , C )-1234 strongly reflects the doping levels of the outer planes.

We report the tunneling conductance on a quadruple-layered cuprate, Ba 2 Ca 3 Cu 4 O 8( O 1-x F x)2 (2x~1.4, Tc~100 K ) that includes inequivalent outer (OP) and inner (IP) CuO 2 planes in a unit cell. Typical tunneling conductance displays the spectral dip structures as well as the superconducting gap (SCG) with clear coherence peaks. However we sometimes observe a pseudogap (PG) like structure without coherence peak at 4.2K. The magnitude of PG at 4.2K is larger than that of SCG at 4.2K and its conductance curve displays a faint structure at low energy. Therefore its origin would be different from that of small-PG observed at above Tc. In addition, we find that there are two kinds of SCGs that originate from IP and OP, and this result suggests that the superconducting property at IP is different from that at OP because of the imbalance of doped carrier between IP and OP. The observation of large PG at low temperature suggests the existence of some form of hidden ordered state at Tc and it would coexist with superconductivity.

An AC magnetic field can rotate a vortex-molecule composed of two fractional vortices in a multiband type of multicomponent superconductor, where two components couple with each other through the intercomponent Josephson interaction. It may directly relate to an abnormal AC loss peak, which we have found recently in the multilayer cuprate supercondutor CuxBa2Ca2Cu3Oy (Cu-1223).

Previously unknown isotopes Ar-30 and Cl-29 have been identified by measurement of the trajectories of their in-flight decay products S-28 + p + p and S-28 + p, respectively. The analysis of angular correlations of the fragments provided information on decay energies and the structure of the parent states. The ground states of Ar-30 and Cl-29 were found at 2.25(-0.10)(+0.15) and 1.8 +/- 0.1 MeV above the two-and one-proton thresholds, respectively. The lowest states in Ar-30 and Cl-29 point to a violation of isobaric symmetry in the structure of these unbound nuclei. The two-proton decay has been identified in a transition region between simultaneous two-proton and sequential proton emissions from the Ar-30 ground state, which is characterized by an interplay of three-body and two-body decay mechanisms. The first hint of a fine structure of the two-proton decay of Ar-30*(2(+)) has been obtained by detecting two decay branches into the ground and first-excited states of the S-28 fragment.

The $\ensuremath{\beta}$ decay of $^{31}\mathrm{Ar}$, produced by fragmentation of an $^{36}\mathrm{Ar}$ beam at 880 MeV/nucleon, was investigated. Identified ions of $^{31}\mathrm{Ar}$ were stopped in a gaseous time projection chamber with optical readout allowing us to record decay events with emission of protons. In addition to $\ensuremath{\beta}$-delayed emission of one and two protons we clearly observed the $\ensuremath{\beta}$-delayed three-proton branch. The branching ratio for this channel in $^{31}\mathrm{Ar}$ is found to be $0.07\ifmmode\pm\else\textpm\fi{}0.02$%.

The possible existence of \eta'-nucleus bound states has been put forward through theoretical and experimental studies. It is strongly related to the \eta' mass at finite density, which is expected to be reduced because of the interplay between the $U_A(1)$ anomaly and partial restoration of chiral symmetry. The investigation of the C(p,d) reaction at GSI and FAIR, as well as an overview of the experimental program at GSI and future plans at FAIR are discussed., Comment: 7 pages, 3 figures; talk at the International Conference on Exotic Atoms and Related Topics (EXA2014), Vienna, Austria, 15-19 September 2014. in Hyperfine Interactions (2015)

The multilayered cuprates of HgBa 2 Ca n −1 Cu n O y (Hg-system) and Ba 2 Ca n −1 Cu n O 2 n (O, F) (F-system) ( n = 5–9) have been synthesized under high-pressure to investigate the variation of T c . The a - and c -parameters showed reasonable behavior: as the n increases from 5 to 9 the a -parameter approached that of an infinite layer CaCuO 2 (IL) and the average interval of c (or c /2) was close to the c -parameter of the IL. All the samples showed high T c values of about 100 and 80 K for Hg- and F-system, respectively. In addition, the T c was almost constant for n ⩾ 5 for both systems. We have shown that the T c variations can be explained using inhomogeneous charge distribution model as follows. The high T c value is maintained because the charge reservoir layer supplies enough carriers for superconductivity to the adjacent CuO 2 planes (OP) even for large n . The T c is independent of n because the carrier concentration of OP is insensitive to n for large n .