Luiz A.M. (ed.) Superconductor

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A Model to Study Microscopic Mechanisms in High-T

Superconductors

(1/3) for Cu(+I) ions and (2/3) for Cu(+III) ions, we may write the formula unit:

YBa

(+I)Cu

(+III)O

. Considering the oxidation states Y(+III), Ba(+II) and O(-II) and

using the charge neutrality condition, we get:

3 + (2 × 2) + (1 × 1) + (2 × 3) – 2x = 0 (4)

From Equation (4) we obtain:

x = 7.0 (5)

The result (5) is in good agreement with the result (x = 6.9) reported in (Kokkallaris et al.,

1999).

In the next section, using the above method, we estimate the oxygen content for optimal

doping of the most important p-type copper oxide superconductors.

11. Results

Using the simple model described in the previous section, we estimate the necessary oxygen

content to obtain the optimal doping of the most relevant p-type cuprate superconductors. It

is important to note that the experimental determination of the oxygen content is a very

difficult task. In Table 3 we have selected a number of works containing this experimental

information.

Superconductor Predicted Measured REFERENCE

0.15

1.85

CuO

x = 4.1 x = 4.0 Bednorz & Müller, 1986

CuO

x = 4.2 x = 4.1 Schirber et al., 1988

YBa

x = 7.0 x = 6.9 Kokkallaris et al.,1999

YBa

x = 8.2 x = 8.0 Rao et al., 1993

CuO

x = 3.17 x = 3.16 Hiroi et al., 1993

CaCu

x = 8.3 x = 8.3 Babaei et al., 2003

CuO

x = 6.2 x = 6.0 Rao et al., 1993

TlCa

x = 9.0 x = 9.0 Martin et al., 1990

HgBa

x = 8.5 x = 8.4 Hung et al., 1997

Table 3. Comparison between the values of oxygen content predicted by our simple model

and the experimental values reported in the literature

According to our model, we have used for the copper ions the following relative values:

(1/3) for Cu(+I) ions and (2/3) for Cu(+III) ions. For the other elements in Table 3, we have

considered the following stable oxidation states: La(+III), Y(+III), Ba(+II), Sr(+II), Bi(+III),

Ca(+II), Tl(+III), Hg(+II) and O(-II). We verify that the results predicted by the simple model

proposed here are in good agreement with the experimental results listed in Table 3.

In Table 3 we have considered only copper oxide superconductors. Our model may be

extended to estimate the optimal doping of p-type oxide superconductors that do not

contain Cu. For example, consider the material Ba

0.6

0.4

BiO

, a famous superconductor

without copper, with T

approximately equal to 30 K (Cava et al., 1988). We shall suppose

for the Bi ions the same proportionality assumed in the model just suggested for the cuprate

superconductors, that is, for optimal doping, we assume that the relative concentrations

Superconductor

should be given by: (1/3)Bi(+III) and (2/3)Bi(+V). Considering the oxidation states Ba(+II)

and K(+I) and using the charge neutrality condition, we have:

1.2 + 0.4 + (1/3)(3) + (2/3)(5) – 2x = 0 (6)

From Equation (6) we obtain the result:

x = 2.95 (7)

The result (7) is in good agreement with the value (x = 3) reported in the reference (Cava et

al., 1988).

12. Discussion

We believe that the simple model proposed in this paper in the case of p-type oxide

superconductors could also be extended to estimate the optimal doping of n-type oxide

superconductors. However, in the case of n-type oxide superconductors, the reaction

produced by oxygen doping is a reduction reaction instead of an oxidation reaction that

occurs in p-type oxide superconductors. Since we have not found in the literature any

experimental determination of the oxygen content in the case of n-type oxide

superconductors we shall not discuss this issue here. This question will be addressed in a

future work.

We have proposed a simple model to estimate the relative concentrations of the ions

involved to estimate the oxygen content for optimal doping of p-type oxide

superconductors. The predictions based on this model are in good agreement with

experimental results reported in the literature (Table 3). However, we emphasize that this

simple model is not a theoretical model, it is a phenomenological model. In Sections 5, 6, 7

and 8 we have discussed some questions in order to give theoretical support for this model.

13. Concluding remarks

In this chapter we have studied the most relevant questions about the microscopic

mechanisms of superconductivity in oxide materials. Parts of our arguments may be found

in the list of references in the next section. However, we believe that our ideas have been

expressed in a clear form for the questions at hand.

Our conjectures can be used to explain some remarkable properties of high-T

superconductors mentioned in Section 2: (a) the anisotropy is explained considering that the

electrons involved in the hopping mechanisms are 3d-electrons (see Section 5); (b) the order

of magnitude of the coherence length (the mean distance between two electron pairs) is in

accordance with the order of magnitude of the distance between the electron clouds of two

neighboring ions (see Section 2); (c) the nonmonotonic dependence of T

on the carrier

concentration is explained by the hypothesis of double charge fluctuations and optimal

doping (Sections 3 and 11).

The theory of bipolaronic superconductivity (Alexandrov & Edwards, 2000) is similar to our

phenomenological model. In the theory of bipolaronic superconductivity, bipolarons are

formed supposing a mechanism to bind two polarons. However, by our hypothesis, it is not

necessary to suppose the formation of bipolarons by the binding of two polarons. We have

assumed that the preformed pairs are just pairs of electrons existing in the electronic

configurations of the ions or atoms involved in double charge fluctuations. These pairs

A Model to Study Microscopic Mechanisms in High-T

Superconductors

should be, for example, lone pairs in atoms or ions or pairs of electrons in the electronic

configurations obtained when Hund’s rule is applied.

The simple model described here is not a theoretical model and cannot be used to account

quantitatively for the microscopic mechanisms responsible for superconductivity in oxide

materials. However, we believe that our assumptions are helpful to the investigations of the

microscopic mechanisms in oxide superconductors. We expect that this simple model will

also be useful to encourage further experimental and theoretical researches in

superconducting materials. It is worthwhile to study the details of the role of double charge

fluctuations in the microscopic mechanisms responsible for superconductivity in oxide

materials.

Finally, we suggest some future researches. It is worthwhile to make experiments to verify if

this model is correct. Supposing that this simple model works, it would be possible to

calculate stoichiometric compositions in order to obtain the optimal doping in the researches

to synthesize new oxide superconductors. It is well known that the most important method

in semiconductor technology is obtained by ion implantation techniques. Similarly, we

believe that ion implantation techniques probably will be important in superconductor

technology as well. Thus, we hope that future researches based on ion implantation

techniques could open a new route in the synthesis of high-T

superconductors. These future

researches, using ion implantation, should take advantage of the possibility of double

charge hoping mechanisms, instead of single charge hoping mechanisms existing in the case

of ion implantation in the semiconductor technology.

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pp. 659-663

The Discovery of Type II Superconductors

(Shubnikov Phase)

A.G. Shepelev

National Science Center «Kharkov Institute of Physics and Technology»

Ukraine

“It is a fascinating testament to Shubnikov’s great originality and to the terrible times

that deprived him of his life and we all of the fruits of the science for so long. Even

now, many do not really understand the breakthrough made in Kharkov.”

From the letter of 31 December, 2008, written by Shubnikov Professor D.

Larbalistier, Director of Applied Superconductivity Center, USA,

on reprinting in English the article (Shubnikov et al., 1937) in 2008.

1. Introduction

At present, Type II superconductors enjoy wide applications in science and technology. It is

worth noting that all the superconductors, from Nb

Sn to cuprates, fullerenes, MgB

, iron-

based systems that have been discovered for the last 50 years, are Type II superconductors.

It is of interest to trace back the intricate research carried out for 8 years from 1929 (De Haas

& Voogd, 1929) to 1936 by experimenters in four countries out of the five, who had liquid

helium at their laboratories at the time when L.V.Shubnikov, V.I.Khotkevich, G.D.Shepelev,

Yu.N.Ryabinin (Schubnikow et al., 1936; Shubnikov et al., 1937; Shepelev, 1938) discovered

experimentally in Kharkov the phenomenon of Type II superconductivity in single-crystal,

single-phase superconducting alloys. A theoretical explanation of the phenomenon, based

on experimental results (Shubnikov et al., 1937) and the Ginzburg-Landau theory (Ginzburg

& Landau, 1950; Ginzburg, 1955), was given by A.A.Abrikosov only in 1957 (Abrikosov,

1957). The proposed publication lays out the recognition of the discovery of Type II

superconductors by leading specialists in this area and indicates a role which this

phenomenon plays in the science and technology. Unfortunately, neither L.D.Landau nor

anyone of the pioneer-experimenters lived to witness the awarding the corresponding

Nobel Prize 2003 when it was given to V.L.Ginzburg and A.A.Abrikosov.

All the superconductors are known to be of two types depending on the magnitude of the

ratio:

æ=λ/ξ ,

where æ – the Ginzburg-Landau parameter, λ - the penetration depth of magnetic field, ξ –

the coherence length between electrons in Cooper pair (Fig.1). For the typical pure

superconductors λ~500 Å, ξ~3000 Å, i.e. æ<<1. A critical value used to determine the

superconductor type is the following: æ

= 1/ 2 (Ginzburg & Landau, 1950; Ginzburg, 1955).

Superconductor

Fig. 1. Schematic diagram of interface between normal and superconducting phases: a) Type

I superconductor; b) Type II superconductor. n

– density of superconducting electrons

(After Ginzburg & Andryushin, 2006).

Magnetic properties of these two superconductor types are essentially different (Fig.2). This

phenomenon can be attributed to the fact that in the Type I superconductors (pure

superconductors), where the Ginzburg-Landau parameter æ < 1/

2 (Ginzburg & Landau,

1950; Ginzburg, 1955), the n-s interphase surface energy σ

> 0. For this reason, under the

impact of magnetic field an intermediate state, as shown by L.D.Landau (Landau, 1937;

Landau, 1943), is created in those superconductors of arbitrary shape (with the

demagnetizing factor n ≠ 0) where the layers of the normal and superconducting phases

alternate.

(a) (b)

Fig. 2. (а) The induction in the long cylinder as a function of the applied field for Type I and

Type II superconductors; (b) The reversible magnetization curve of a long cylinder of Type I

and Type II superconductor (After De Gennes, 1966)

In Type II superconductors (superconducting alloys), where æ > 1/ 2 , the n-s interphase

surface energy σ

< 0 and magnetic field penetrates these superconductors in the form of

the Аbrikosov vortex lattice (Аbrikosov, 1957). As indicated by A.A.Abrikosov (Аbrikosov,

1957), the idea about the alloys turning into Type II superconductors at the value of the

parameter æ > 1/

2 was first brought forward by L.D.Landau.

The Discovery of Type II Superconductors (Shubnikov Phase)

Yet, it took about 30 years since the pioneering experimental research on superconducting

alloys under applied magnetic field to understand fully the Type II superconductivity

phenomenon.

The theory of Type II superconductors has been expounded in detail over the past 45 years

in scores of reviews and monographs on superconductivity, the experimental side of the

discovery of these superconductors, as far as the author knows, having been discussed only

fragmentarily either at the early stages of the research (Burton, 1934; Wilson, 1937;

Ruhemann, 1937; Shoenberg, 1938; Jackson, 1940; Burton et al., 1940; Ginzburg, 1946;

Mendelssohn, 1946; Shoenberg, 1952) or later on (refer to the authoritative published papers

(Mendelssohn, 1964; Mendelssohn, 1966; Goodman, 1966; De Gennes, 1966; Saint-James et

al., 1969; Anderson, 1969; Chandrasekhar, 1969; Serin, 1969; Hulm & Matthias, 1980; Hulm

et al., 1981; Pippart, 1987; Berlincourt, 1987; Dahl, 1992

; Dew-Hughes, 2001) and also to

(Sharma & Sen, 2006; Slezov & Shepelev, 2008; Karnaukhov & Shepelev, 2008, Slezov &

Shepelev, 2009)). Therefore, the way the real events took place is, quite regrettably, largely

hidden from view to many of the International Scientific Community.

We shall remind that H.Kamerlingh Onnes (Physical Laboratory, University of Leiden), an

outstanding physicist of those times, who discovered the phenomenon of superconductivity

in pure metals in 1911 (Kamerlingh Onnes, 1911), was the first with his co-workers to take an

interest beginning from 1914 in the effects of magnetic field on those superconductors

(Kamerlingh Onnes, 1914; Tuyn & Kamerlingh Onnes, 1926; Sizoo et al., 1926; De Haas et al.,

1926, De Haas & Voogd, 1931a). In particular, it was found that superconductivity in pure

metals got suddenly disrupted when impacted by an applied magnetic field with a critical

value Н

(in the case of the demagnetizing factor n = 0), which manifested itself in a sudden

restoration of electrical resistance of the samples from zero to such value that corresponded

to Т>Т

(Fig.3).

Fig. 3. Sudden change of electrical resistance of wire sample of single crystal tin at Т<T

, as

caused by longitudinal magnetic field (After De Haas & Voogd, 1931a).

In the interesting book, Dahl (Dahl, 1992) has erroneously ascribed the discovery of Type II superconductors

to some other article from Kharkov. In reality, as is well known (see 4. Recognition), the world’s leading

specialists in superconductivity unanimously relate this discovery to the articles by L.V.Shubnikov

V.I.Khotkevich, G.D.Shepelev, Yu.N.Ryabinin. (Schubnikow et al., 1936, Shubnikov et al., 1937).

Superconductor

It should be said that, aside from the feature of electric properties of Type I superconductors

upon decreasing temperature below Т

(the steep fall of electrical resistance down to such

resistivity which was smaller than 10

-23

Ω·cm), the second fundamental characteristic of pure

superconductors (magnetic properties) also had a peculiarity that was out of the ordinary. In

1933 W. Meissner and R. Ochsenfeld (Physikalische Technische Reichsanstalt) found

(Meissner & Ochsenfeld, 1933) that a magnetic field which was smaller than Н

did not run

through a pure superconductor, the magnetic induction in it being В = 0 (with the exception

of a very thin surface layer ~ λ). Under the impact of an applied magnetic field with the

value Н

the pure superconductor magnetization M and induction B also changed with a

jump (Fig.4). These values are related via the following ratio:

М = (В - Н) / 4π.

The exclusion of flux from the bulk of pure superconductor is called the Meissner effect.

Any discovery is generally preceded by a preparatory period. Then, some day or other,

following the actual discovery the recognition is accorded. Some time after that one can look

at final results and evaluate the prospects.

(a) (b)

Fig. 4. a) Magnetization curve of a pure superconducting long cylinder in longitudinal

magnetic field; b) B-H curve of a pure superconducting long cylinder in longitudinal

magnetic field (After Shoenberg, 1938).

2. Preliminary stage

Interestingly enough, even before the Meissner effect was discovered, W.J.De Haas, J.Voogd

(Kamerlingh Onnes Laboratory, University of Leiden) had discovered (De Haas & Voogd,

1929) a distinction between the behavior in applied magnetic field of electrical resistance of

polycrystals of superconducting alloys and that of pure superconductors. It appeared that in

rod specimens of the alloys Bi + 37.5at%Tl, Sn + 58wt%Bi, Sn +28.1wt%Cd (the latter two

being close to the eutectic alloy) (De Haas & Voogd, 1929), in the alloy Pb + 66.7at%Tl, the

eutectic Pb + Bi and in the alloys Pb-Bi (7wt%; 10wt%; 20wt%), Sn + 40.2wt%Sb (De Haas &

Voogd, 1930), in the alloys Pb + 15wt%Hg, Pb + 40wt%Tl, Pb + 35wt%Bi, the eutectic Au-Bi

(De Haas & Voogd, 1931b) the disruption of superconductivity occurred across a broad

interval of magnetic fields irrespective of the orientation of the field running parallel, i.e. at