Mourachkine A. Room-Temperature Superconductivity

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274 ROOM-TEMPERATURE SUPERCONDUCTIVITY

a complex phase diagram,

the moderately strong and nonlinear electron-phonon interaction,

an unstable lattice,

charge-donor or charge-acceptor sites (charge-reservoirs), and

a complex structure (with the exception of hydrides, deuterides and a few

heavy fermions).

In the third group:

the T

value of hole-doped superconductors is on average a few times

higher than that of electron-doped superconductors.

superconductors with T

> 20 K have no metal-metal bonds (only heavy

fermions have metal-metal bonds).

oxides and organic superconductors represent an absolute majority of this

group.

Considering the common features of superconductors of the third group,

one must however realize that some of these features are direct consequences

of the other. For example, the anisotropic character of transport and magnetic

properties of superconductors of the third group is a direct consequence of a

low-dimensional structure of these superconductors. The strong and nonlinear

electron-phonon interaction results in a large value of the pairing energy gap

and, therefore, in a large value of the gap ratio 2∆

/(k

). Since in super-

conductors of the third group, the Cooper pairs are represented by bisolitons

havinga small size (a consequence of the strong and nonlinear electron-phonon

interaction) and a low density, this leads to the penetration depth and, conse-

quently, the ratio λ/ξ being large. Therefore, all superconductors of the third

group are type-II. The presence of strongly correlated electrons in these super-

conductors results in a complex phase diagram, and so on. Hence, some of

these common features of superconductors of the third group are more impor-

tant than others.

2. Requirements for high-T

materials

We are now in a position to discuss requirements for materials that super-

conduct near room temperature. In this section, we shall ﬁrst consider the

characteristics of room-temperature superconductors that are important for (i)

electron pairing and (ii) phase coherence. Then, we shall discuss (iii) the crys-

tal structure and (iv) materials of room-temperature superconductors.

Room-temperature superconductors 275

2.1 Electron pairing

From Chapter 8, we know that, in room-temperature superconductors, the

Cooper pairs should be represented by positively-charged bisolitons. On the

basis of the analysis of the properties of superconducting materials presented

in the previous section and Chapter 8, for the presence of positively-charged

bisolitons, room-temperature superconductors must be

hole-doped,

low-dimensional,

with strongly correlated holes,

near a metal-insulator transition,

with the moderately strong and nonlinear hole-phonon interaction,

with an unstable lattice, and

most likely, organic.

The electrosolitons and bisolitons appear in low-dimensional systems hav-

ing strongly correlated electrons and the moderately strong, nonlinear electron-

phonon interaction. These systems are in a state near a metal-insulator tran-

sition and have an unstable lattice. (In fact, the expression “systems with

strongly correlated electrons” partially assumes that the electron-phonon inter-

action in these systems is strong and nonlinear.) Experimentally, the bisolitons

exist above room temperature in organic compounds.

2.2 Phase coherence

From Chapter 9, we know that, in room-temperature superconductors, the

mechanism of phase coherence should most likely be magnetic. On the basis of

the analysis of the properties of third-group superconductors presented in the

previous section and Chapter 9, for the onset of long-range phase coherence

due to spin ﬂuctuations, room-temperature superconductors must

be magnetic or, at least, have strong magnetic correlations,

have the localized states with a spin of 1/2,

have dynamic spin ﬂuctuations,

be in a state near a quantum critical point,

most likely follow the Uemura relation T

∝ n

∗

(see Fig. 9.2), and

most likely be antiferromagnetic.

276 ROOM-TEMPERATURE SUPERCONDUCTIVITY

The last constraint is based on experimental facts accumulated at the time of

writing. However, ferromagnetic materials should also be examined in the near

future (see the discussion in Chapter 9). The other requirements have already

been discussed in Chapter 9.

2.3 Structure

On the basis of the analysis of the properties of superconducting materials

presented in the previous section, the structure of room-temperature supercon-

ductors must

be low-dimensional,

be complex (with more than two sites per unit cell),

have an unstable lattice,

have electron-acceptor sites, and

have no metal-metal bonds.

In materials able to superconduct at room temperature, the unit cell must

have at least two interacting subsystems: one subsystem is quasi-metallic, and

the other is magnetic. The electron pairing takes place in the ﬁrst subsystem,

whilst the onset of long-range phase coherence occurs with the participation of

the second subsystem. For example, in the cuprates, the unit cell has three sub-

systems. In addition to the quasi-metallic and magnetic subsystems mentioned

above (see Fig. 6.2), the third subsystem represents charge reservoirs. The

charge reservoirs in the cuprates are the layers that intercalate the CuO

lay-

ers. They are usually insulating or semiconducting. In contrast, in organic

superconductors the second and the third subsystems coincide: the charge

reservoirs, after donating/accepting electrons to/from organic molecules, be-

come magnetic. Thus, in organic superconductors, one subsystem performs

two functions: to donate/accept electrons and to mediate the phase coherence.

To conclude, a room-temperature superconductor must have:

1) a subsystem with bisolitons,

2) charge reservoirs, and

3) magnetic atoms/molecules.

Experimentally, the second and the third subsystems can be represented by the

same atoms/molecules.

2.4 Materials

From Chapter 8 and the analysis of the properties of superconducting com-

pounds presented in the previous section, the material of room-temperature

superconductors must be

Room-temperature superconductors 277

multicomponent,

most likely, organic, and

probably, oxidic.

It is an experimental fact that bisolitons exist in some organic materials at

temperatures much higher than room temperature.

In Chapter 1, we have discussed the requirements for materials that super-

conduct at high temperatures, presented by Geballe in 1993 [22]. One can now

compare these requirements with those itemized in this section. The require-

ments summarized in this section include the Geballe constraints.

3. Three basic approaches to the problem

In this section, we discuss the basic approaches to the problem of room-

temperature superconductivity. In general, one may suggest three approaches

to the problem.

The ﬁrst approach: synthesis. The basic idea for synthesizing a compound

able to superconduct above room temperature is straightforward. One should

take a material containing bisolitons above room temperature and dope (inter-

calate) it with atoms/molecules able to accept electrons and having an unpaired

electron after the intercalation. In this case, the intercalant atoms/molecules

will be magnetic. For instance, the structure of a Bechgaard salt shown in Fig.

3.15 is a good example. Alternatively, a material containing bisolitons can

be doped by atoms/molecules of two types. The atoms/molecules of one type

stands duty exclusively as charge reservoirs. This basic idea is more or less

obvious; the main question is what materials to use and how to achieve a right

intercalation. That is all.

The second approach consists in improving the performance of known su-

perconducting materials, for example, the cuprates. This approach is also ob-

vious.

The third approach. We already know that, by deﬁnition, the density of

bisolitons in a system cannot be large; otherwise, the system will become

metallic. As a result, the bisolitons cannot condense due to the overlap of

their wavefunctions because, in general, the average distance between bisoli-

tons is larger than the size of a bisoliton. Theoretically, this obstacle can be

overcome by creating a train of bisolitons in a specially-prepared polymer. Let

us call it the bisoliton overlap approach.

It is worth noting once more that some ideas presented in the following

sections cannot be realized at present because of technological difﬁculties but

can surely be realized in the near future.

278 ROOM-TEMPERATURE SUPERCONDUCTIVITY

4. The ﬁrst approach

In order to synthesize a room-temperature superconductor, one needs to

know what materials to use. As was discussed above, the structure of every

superconductor of the third group has at least two interacting subsystems: the

electron pairing takes place in one subsystem, whilst the onset of long-range

phase coherence occurs with the participation of the second subsystem. In

spite of the fact that these two subsystems are interacting, we shall consider

materials of one subsystem independently of materials of the other. This is

because a number of various combinations between the materials of one sub-

system and the materials of the other is very large, and an attempt to analyze

all these combinations is simply impractical. On the other hand, discussing

these two groups of materials independently of one another, one should take

into account that, in practice, certain materials of the two subsystems can be

incompatible, i.e. cannot be used together.

We shall discuss ﬁrst “pairing” materials and then “magnetic” materials

which can be used to intercalate the “pairing” ones.

4.1 Materials for electron pairing

In this subsection, we shall consider materials containing bisolitons above

room temperature intrinsically. For simplicity, let us classify the materials for

electron pairing as

organics,

living tissues, and

oxides.

Such a sorting is conventional because these three groups, in fact, overlap. For

example, the living tissues are organic and contain often oxygen.

4.1.1 Organic materials

Let us start this “journey” by trial and error with organic materials which

are well studied and commercially available.

Polythiophene. As was already discussed in Chapter 8, polythiophene is a

one-dimensional conjugated polymer having the structure shown in Fig. 8.1a.

The dominant nonlinear excitations in polythiophene are positively-charged

electrosolitons and bisolitons [63]. In a thiophene ring, the four carbon p elec-

trons and the two sulfur p electrons provide the six p electrons that satisfy the

(4n +2)condition necessary for aromatic stabilization. From a theoretical

point of view, the bisolitons exist in polythiophene because the energy levels

of its two degenerate ground states are not equal [63]. In other words, the two

valence-bond conﬁgurations shown in Fig. 10.1a are not equivalent. Poly-

Room-temperature superconductors 279

(a)

(b)

≠

[

]

Figure 10.1. (a) Two valence-bond conﬁgurations of polythiophene shown in Fig. 8.1 are not

equivalent. (b) Chemical structure of soluble poly(3-alkylthienylenes) [63].

thiophene has a few derivatives and one of them shown in Fig. 10.1b is called

poly(3-alkylthienylenes) or P3AT for short. In contrast to polythiophene, P3AT

is soluble.

Polythiophene, its derivatives and other organic conjugated polymers are

usually doped by using the so-called electrochemical method [63]. The re-

action is carried out at room temperature in an electrochemical cell with the

polymer as one electrode. To remove electrons from organic polymers, oxida-

tion is usually used. Through doping, one can control the Fermi level or the

chemical potential. In the framework of our project, we are interested in dop-

ing polythiophene by magnetic atoms/molecules. These “magnetic” materials

will be discussed below. In practice, it is impossible to foresee the structure

of a doped organic compound, even knowing materials before the beginning

of a doping procedure. Depending on their origin, concentration and size, the

dopant species after the diffusion can take different positions relative to the

polythiophene chains.

Figure 10.2 shows several examples of possible positions of dopant species

relative to polythiophene chains. It is less likely that the dopant species will oc-

cupy positions in the planes of polythiophene chains, as sketched in Fig. 10.2a.

They will most likely intercalate the polythiophene planes, as illustrated in Fig.

10.2b. In fact, the dopant atoms/molecules are even able to induce a reversible

structural transition [63]. Upon doping, the polythiophene chains and dopant

species can for example form a checker-board pattern shown schematically in

Fig. 10.2c. For instance, in Na-doped polyacetylene, the Na

ions and poly-

acetylene chains form a modulated lattice with a “triangular” pattern depicted

in Fig. 10.2d. In Na-doped polyacetylene, such a lattice appears exclusively at

moderate doping levels.

280 ROOM-TEMPERATURE SUPERCONDUCTIVITY

(a)

(b)

(c)

(d)

- dopant species

- polymer, a view from one side

Figure 10.2. Possible positions of dopant species relative to inﬁnite polythiophene chains: (a)

in the plane of polythiophene chains; (b) between the planes; (c) a checker-border pattern, and

(d) a “triangular” pattern realized in Na-doped polyacetylene [63].

Until now we have considered polythiophene chains having the inﬁnite

length. By analogy with the structure of organic superconductors (see, for

example, Fig. 3.15), one should also try to use polythiophene chains having a

ﬁnite length. Taking into account that the width of a bisoliton is a few lattice

constants [10, 63], then, the length of pieces of polythiophene chains, , should

be then 2–3 times larger; thus  ∼ 15a, where a is the lattice constant. Since

some atoms/molecules must be attached to the free ends of polymer pieces,

the two ends of a polymer piece can be closed by one another resulting in the

formation of a ring. Upon doping these rings, the dopant species can occupy

the centers of the rings, as schematically shown in Fig.10.3. It is worth noting

that the structure shown in Fig. 10.3 is similar to that of the fullerides depicted

in Fig. 3.18.

Using various magnetic atoms/molecules, one should not forget to control

the doping level of the organic polymers. It can be done, for example, by

adding a small amount of atoms/molecules of another type, which may or

may not be magnetic after the diffusion. Undoubtedly, some of these doped

polythiophene-chain materials will superconduct. The main question is what

maximum value of T

can be attained in these organic compounds. This mainly

depends on the ability of “magnetic” materials to mediate the long-range phase

coherence.

Room-temperature superconductors 281

Figure 10.3. Possible arrangement of polythiophene rings and diffused magnetic

atoms/molecules.

Other conjugated polymers. Other conjugated polymers containing bisoli-

tons can be used instead of polythiophene. It is known that positively-charged

bisolitons exist, for example, in polyparaphenylene, polypyrrole and poly(2,5-

diheptyl-1,4-phenylene-alt-2,5-thienylene) (PDHPT) [63]. The structure of

polyparaphenylene is depicted in Fig. 10.4a. A bisoliton on a polyparapheny-

lene chain is schematically shown in Fig. 10.4b. For example, a derivative

of polyparaphenylene, p-sexiphenyl depicted in Fig. 10.4c, is widely used in

(a)

(b)

(c)

(d)

[

]

Figure 10.4. (a) Chemical structure of polyparaphenylene. (b) Schematic structural diagram

of a positively-charged bisoliton on a polyparaphenylene chain [63]. (c) Molecular structure

of p-sexiphenyl, and (d) the chemical structure of soluble poly(2,5-diheptyl-1,4-phenylene-alt-

2,5-thienylene) (PDHPT).

282 ROOM-TEMPERATURE SUPERCONDUCTIVITY

organic light-emitting diodes. Why not use it as a basic material for a room-

temperature superconductor? The structure of PDHPT is illustrated in Fig.

10.4d.

As established experimentally, the physical properties of polymers strongly

depend upon preparation conditions. For instance, the same polymer prepared

by different techniques has different conductivities [63]. Unfortunately for

experimentator, this fact adds one more degree of freedom for achieving the

goal.

Graphite. For the last thirty years, graphite is one of the most studied ma-

terials. Several books are dedicated to a description of the physical properties

of graphite (see, for example, [34]). It is also one of the most promising su-

perconducting materials. Graphite intercalation compounds (GICs) able to su-

perconduct were discussed in Chapter 3. Depending on their structure and the

preparation technique, there are stage 1 and stage 2 GICs. All superconduct-

ing GICs are alkali-doped and, therefore, magnetic due to alkali spins ordered

antiferromagnetically. In the superconducting GICs, the charge carriers are

however electrons, not holes. Graphite-sulphur (CS) composites exhibit su-

perconductivity at T

= 35 K [35]. It is assumed that, in the CS composites,

superconductivity occurs in a small fraction of the samples. The resistance in

the CS composites remains ﬁnite down to the lowest measured temperature,

indicating that superconducting clusters are isolated from each other [66].

The physical properties of graphite as well as other organic polymers de-

pend on the preparation method. In most experiments, highly oriented py-

rolytic graphite (HOPG) is used. In practice, all large-size single crystals of

graphite, including commercially available ones, never have an ideal structure:

they always have intrinsic carbon defects. The last statement is also valid for

large-size single crystals of superconducting cuprates. Both graphite and the

cuprates have the layered structure.

There exist both theoretical predictions and experimental evidence that elec-

tronic instabilities in pure graphite can lead to the occurrence of superconduc-

tivity and ferromagnetism, even at room temperature ([66, 67] and references

therein). Some experiments indeed show that the superconducting and ferro-

magnetic correlations in graphite coexist [35, 66]. In graphite, an intrinsic

origin of high-temperature superconductivity relates to a topological disorder

in graphene layers [66]. (A single layer of three-dimensional graphite is called

graphene.) This disorder enhances the density of states at the Fermi level. For

example, four hexagons in graphene (see Figs. 3.19 and 10.5) can in princi-

ple be replaced by two pentagons and two heptagons [67]. Such a defect in

graphene modiﬁes its band structure. The disorder in graphene transforms an

ideal two-dimensional layer into a network of quasi-one-dimensional channels

preferable for bisolitons. In high magnetic ﬁelds (> 20 T), the in-plane resis-

Room-temperature superconductors 283

Armchair edge

Zigzag edge

Figure 10.5. Two basic types of graphite edges [67].

tance of graphite exhibits an anomalous behavior attributed to the formation of

charge-density-wave (CDW) [66]. This means that, in a high magnetic ﬁeld,

mobile bisolitons condense into the localized CDW states.

Interestingly, themagnetization of HOPG samplesshows ferromagnetic hys-

teresis loops up to 800 K [66–68]. The details of this hysteresis depend on

the sample, sample heat treatment and the direction of the applied ﬁeld. The

ferromagnetic signal in graphite is weak; however, as shown experimentally,

ferromagnetic impurities cannot be responsible for this ferromagnetic order-

ing [68]. Most experimental results suggest that this ferromagnetism is intrin-

sic. Its origin is attributed partly to topological defects and in part to strong

electron correlations in graphite [66–68]. In practice, the graphene sheets are

always ﬁnite. Their electronic properties are drastically different from those

of bulk graphite. It is experimentally established that the electronic properties

of nanometer-scale graphite are strongly affected by the structure of its edges

[66–69]. The graphene edges induce electronic states near the Fermi level.

Any graphene edge can be presented by a linear combination of the two basic

edges: zigzag and armchair, shown in Fig. 10.5. The free energy of an arm-

chair edge is lower than that of a zigzag edge [69]. It is assumed that the zigzag

edges are partly responsible for the ferromagnetic ordering [67]. Finally, it is

worth noting that the magnitude of a ferromagnetic moment in graphite is age-

dependent. The storage of graphite samples at ambient conditions results in

a drastic decrease of the magnetization. As an example, a one-year storage

brings the samples to a diamagnetic state without noticeable changes in their

composition and lattice parameters [67].

Are graphite-based compounds able to superconduct above room tempera-

ture? Undoubtedly, yes. From experimentaldata, the bisolitons seem to exist in

graphite above T ∼ 600 K. The appearance of bisolitons at high temperatures

in graphene depends on the graphene structure: graphene sheets must be topo-