chapter 1 introduction to...

Chapter 1

Introduction to superconductivity

From the beginning itself, superconducting phenomenon was somewhat

accidental. The road was full of twists, bends, ups and downs. The unexpected twists were

always there in definite points of the journey and still it continues. As majority of the

discoveries came from accidental inventions or intuitions, experimental part gained upper

hand in this branch of physics even if there are ingeniously built theories. The backbone of

this journey is a series of spectacular, completely unanticipated experimental discoveries.

Each of these discoveries created waves in experimental as well as theoretical physics. A lot,

including veterans in the field of theoretical physics tried to find out the reasons as it was one

of the fascinating areas with lots of challenges with limited success. This chapter discusses

the history of superconductivity briefly.

1.1 The discovery and history: A review

Kamerlingh Onnes was successful to liquefy helium on 10 th July 1908. It is a

landmark in the history of superconductivity. Even before that many other gases which have

low boiling points were liquefied. But those temperatures were not as low as to observe

superconductivity in elements. In 1911, when Kamerlingh Onnes was studying the behavior

of metals at low temperatures he first observed this fascinating phenomenon-

superconductivity. Onnes and his colleagues, found that the resistance of mercury, when

cooled below 4.2 K, dropped to practically zero [1]. He also observed that very high currents

can be passed through mercury in this superconducting state until a maximum current density

was reached. At that point, the mercury would return to the normal state [2, 3]. His success in

Introduction to superconductivity 2

the field was the fruit of a long journey that took decades, to achieve low temperatures by

liquefying light gases [4]. Onnes was fascinated in this area because of Johannes van der

Waals theoretical predictions about the behavior of gases, who successfully related the

temperature at which a gas would liquefy to the strength of the intermolecular forces. In

1910, Nobel Prize was awarded to Johannes van der Waals for this work [5]. After years of

hard work Onnes became the first man who reached 4.2 K mark by liquefying Helium, which

later led to the beginning of a new era of superconductivity [6]. In 1913, Kamerlingh Onnes

won Nobel Prize in Physics "for his investigations on the properties of matter at low

temperatures which led, inter alia, to the production of liquid helium" [7].

Superconductors are not just better than ordinary conductors of electricity,

they are absolutely different by mechanism and order. From those days, it has been a

fascinating phenomenon and an attracting subject to physicists, chemists, technologists,

material scientists, experimentalists and theoreticians due to various reasons. All these groups

of people saw a big future even if their perspectives were different. But soon everyone

understood that even if the dreams were beautiful the path is not so easy. The fascination of

physicists with superconductivity is from its exclusive properties that are intellectually

challenging and potential for a wide range of applications. Even if it has to address many

more issues we can surely say that it is one of the discoveries which changed the progress of

mankind.

After the discovery, the scientific community all-around the world was very

much eager to search for the possibilities of this phenomenon. Though the field generated

much interest in the scientific community, developments were slow due to practical

difficulties to attain such low temperatures. By 1930s, superconductivity was discovered in


many elemental superconductors such as Ga, Sn, Pb, Nb, Ta etc. Major breakthroughs in this

field can be summarized as follows:

Meissner effect is the expulsion of a magnetic field from a superconductor during

its transition from normal state to the superconducting state. German physicists

Walther Meissner and Robert Ochsenfeld observed this phenomenon for the first

time in 1933 [8].

The London equations, developed by brothers Fritz and Heinz London in 1935

provide simple but useful description of the electrodynamics of superconductivity.

These equations were able to explain meissner effect [9].

Ginzburg-Landau theory named after Vitaly Lazarevich Ginzburg and Lev

Landau is based on the theory of second-order phase transitions developed by

Landau, according to which a phase transition of second order occurs when the state

of a body changes gradually while its symmetry changes discontinuously at TC [10,

11].

Development of first superconducting magnet by George Yntema in 1954 using

Niobium wire [12].

BCS Theory put forward by Bardeen, Cooper and Schrieffer in 1957 described the

microscopic mechanism of superconductivity. BCS theory explains the

superconducting phenomena by the formation of paired electrons called Cooper

pairs [13, 14].

Josephson Effect which was a mathematical prediction of relations between current

and voltage across a weak link. Josephson in his theory, which was put forward


during 1962, predicted the tunneling of superconducting Cooper pairs through these

weak links [15].

Discovery of intermetallics and alloys such as NbTi, Nb3Sn, NbAl during 1950

which initiated practical applications of superconductivity [15].

Discovery of High Tc superconductivity by J Georg Bednorz and K Alex Muller

working at the IBM research laboratory in 1986 [16].

Discovery of Superconductivity in MgB2 by Akimitsu group in 2001 [17].

Discovery of Iron based superconductors which are iron containing chemical

compounds belonging to HTS family, in 2006 [18].

1.2 Characteristics of superconducting state

The onset of superconductivity initiates astonishing changes in different

physical properties of a superconducting material as part of the phase transition from normal

state to superconducting state.

1.2.1 Meissner effect

In 1933 German researchers Walther Meissner and Robert Ochsenfeld

discovered that a superconducting material will expel magnetic field from its interior [8].

This happens due to the development of an opposing magnetic field which is developed by a

screening current that drifts on the surface of the superconductor which nullifies the external

magnetic field in the interior of the superconductor [19]. This phenomenon is known as

Meissner effect. In other words, superconductor placed in a weak external magnetic field,

penetrates for only a short distance called the London penetration depth, after which it decays


rapidly to zero. The expulsion of magnetic field in a superconductor at temperature below TC

is shown in figure 1.1.

Figure 1.1 Meissner effect

1.2.2 Critical surface

The extreme values of temperature, electrical current and magnetic field in

superconducting state are interdependent for a superconductor. That is the superconducting

state is defined by these three factors: critical temperature (TC), critical magnetic field (HC),

and critical current density (JC). Critical temperature (TC) is the temperature below which the

material becomes a superconductor. Critical field (HC) is the maximum magnetic field which

can be held out by a material in the superconducting state and critical current density (JC) is

the maximum current that can be tolerated by a superconductor in the superconducting state.

Each of these parameters is very much dependent on the other two. Magnetic field, current

density and temperature must be below the critical values of the respective material to retain

superconductivity. That is, for a specific material, at a particular magnetic field and current,


there will be a unique value of transition temperature. The phase diagram between these three

parameters for a particular material gives a surface called as critical surface. In the regions

outside this surface, the material is in normal state. The highest values for critical field (HC)

and critical current density (JC) are exhibited when the material is close to 0 K, while the

maximum value for critical temperature (TC) materializes when magnetic field and current

values are zero [20, 21]. Figure 1.2 shows the critical surface.

Figure 1.2 Schematic diagram of the critical surface for a Type II superconductor.

1.3 Classification of superconductors

Superconductors can be classified according to several criteria such as critical

temperature, behavior in an applied field, superconducting mechanism etc.

1.3.1 Based on critical temperature

Based on critical temperature, superconductors are classified into High

Temperature Superconductors (HTS) and Low Temperature Superconductors (LTS).


1.3.1.1 High Temperature Superconductors (HTS)

The classification is not rigid or doesn’t have specific bench mark as high and

low are very much relative. Some consider superconductors as HTS when the material has a

TC above boiling point of liquid nitrogen (77 K). Many others include materials with TC

higher than 30 K in this group. Usually materials such as MgB2, iron based superconductors

etc are included in this category as these materials have higher TC compared to conventional

superconductors [21-27].

1.3.1.2 Low Temperature Superconductors (LTS)

Usually elemental superconductors, alloys and intermetallics such as NbTi,

Nb3Sn etc. having TC below 30 K are included in this group. Major share of practical

superconductors belong to this category.

1.3.2 Based on behavior in an applied field

Based on the behavior in the presence of an applied field, superconducting

materials are classified as type I and type II superconductors.

1.3.2.1 Type I superconductors

Type I superconductors not only have lower ability to withstand magnetic

field but also entirely different magnetic behavior. When magnetic field larger than a

threshold is applied to a type I superconductor, its superconducting properties will be lost at

the moment. Type I superconductors expel the external magnetic field from its core up to a

critical field (HC). For external fields above HC, the superconductor becomes normal material

and allows the external fields to infiltrate into the material. Due to the inability to withstand

magnetic field, type I superconductors are not used for magnet applications [21-27].


1.3.2.2 Type II superconductors

Figure 1.3 Penetration of flux lines through a type II superconductor

Type II superconductor’s behavior is quite different from type I category.

Alloys, intermetallics, ceramics and metal oxides belong to this group. They allow partial

penetration of magnetic field through them after a particular field called, lower critical field

HC1. Below this field, the material expels the magnetic flux lines from the core and behaves

similar to type I superconductor. At fields above HC1, the external magnetic flux lines start to

penetrate into the core of the superconductor in the form of quantized flux vortices. These

quantized flux vortices are known as fluxons. Each fluxon is a tube of radius of the London

penetration depth λ in which superconducting screening currents circulate around a small non

superconducting core of radius ξ as shown in figure 1.3. The flux carried by a single fluxon is

h/2e. As the external field increases, more and more flux vortices will be created in the

superconductor. These flux vortices arrange themselves in a regular pattern in the lattice.

This state is known as mixed state or vortex state. If the applied field is increased further, the

flux vortices fill the superconducting core and reduce the superconducting area. At a

particular high field which is characteristic of the superconducting material, called the upper

critical field HC2, the entire superconducting area is filled by vortices and the superconductor


turns into a normal material. Superconductors which follow this pattern of behavior are

known as type II superconductors which are widely used for magnetic applications [21-27].

The behavior of type I and type II superconductors in external magnetic field is shown in

figure 1.4

Figure 1.4 Behavior of type I and type II superconductors in external magnetic field

1.3.3 Based on superconducting mechanism

Figure 1.5 Formation of cooper pair in a superconducting material- BCS mechanism


Based on superconducting mechanism superconductors are classified as

conventional superconductors and unconventional superconductors. Superconductors which

fit into the BCS frame work are known as conventional superconductors. Superconductors

whose behavior cannot be explained by BSC theory are known as unconventional

superconductors. Formation of cooper pairs by electron-phonon interaction [13, 14] is

depicted in the figure 1.5.

1.4 Superconducting materials

Ever since the invention of superconductivity in 1911, researchers around the

world tried to raise the temperature at which superconductivity occurs by different methods

which produced a flurry in the field. Even though there are thousands of superconductors

known today, only a very small number of them are used for practical applications. After a

century of the discovery of this enchanting phenomenon many materials under different

categories such as metals, alloys, intermetallics, ceramics, organic molecules and fullerenes

are found to be superconducting at different conditions. Even though there are a lot of

theories which predicts superconductivity in compounds by different methods, success rate is

very limited. Such studies were not able to produce a superconductor which has practical

importance. Still the phenomenon is somewhat elusive and mysterious. Good conductors Au,

Cu, Ag etc. never show transition from normal state to superconducting state even at very

low temperatures. At the same time, materials which are highly resistive at room

temperatures show superconducting transitions at low temperatures. The phenomena always

astonished researchers with unexpected twists. As superconductors are perfectly diamagnetic

in nature, the invention of superconductivity in iron based compounds surprised researchers

since it contains the most familiar ferromagnetic element Fe. At any time a breakthrough can


happen. This makes the area very interesting even if it is challenging. List of selected

superconducting materials belonging to different classes are included in table 1.1 [19, 21-31].

Table 1.1 List of selected superconducting materials

Type Example TC (K)

Elements Al 1.2

Cd 0.5

Ga 1.1

In 3.4

La(α) 4.8

La(β) 4.9

Pb 7.2

Hg(α) 4.2

Hg(β) 4

Mo 0.9

Nb 9.3

Os 0.7

Rh 0.5

Ta 4.5

Tc 8.2

Tl 2.4

Th 1.4

Sn 3.7

Ti 0.4

W 0.01

U(α) 0.6

U(β) 1.8

V 5.3

Zn 0.9

Zr 0.8

Alloys VTi 7.0

NbTi 9.0

MoTc 16.0

Amorphous

materials

U85.7Fe14.3 1.0

Th80Co20 3.8


Type Example TC (K)

Organic materials Cs2RbC60 33

(TMTSF)2TaF6

TMTSF-tetramethyltetrathiafulvalene

1.35

C60/CHBr3 117

Cs2RbC60 33

Magnetic material ErRh4B4 10

A15 type V3Ga 14.0

V3Si 17.0

Nb3Sn 18.0

Nb3Ge 23.2

Laves phase ZrV2 9.6

Chevrel phase SnMo6S8 12.0

PbMo6S8 15.0

Heavy electron

systems

UPd2Al3 2.0

CeCu2Si3 0.6

Oxides Ba(PbBi)O3 13

Ba0.6K0.4BiO3 30

LiTi2O4 13.7

Cuprates YBa2Cu3O7 92

Bi2Sr2Ca1Cu2O8 80

Bi2Sr2Ca2Cu3O10 110

TlBa2Ca2Cu3O10 122

Hg2Sr2Ca2Cu3O10 135

Borides ZrB12 5.82

YRh4B4 11.3

MgB2 39

Borocarbides YPd2B2C 23

Oxypnictides LaFeAsO0.9F0.1 26

SmFeAsO0.85 55

1.5 Applications of superconductors

Superconducting materials can substitute the conventional materials in many

applications and with much better performance. The choice between conventional and

superconductive materials is generally related to technical and economic aspects. Even if


there are so many technical hurdles superconductors are already used in many fields such as

electrical, medical, electronics, transport, space etc. They are an inevitable part of any

accelerator system. They are widely used in research laboratories, ultrasensitive magnetic

detectors called SQUIDS, fusion reactors etc. Cooling superconductors much below room

temperature is the main hurdle which restricts their use in day to day life. Many applications

are operational in laboratories and pilot plants which will be introduced soon to the public

domain. A superconductor which can be operated at a temperature close to room temperature

is a dream of any one in this research area because of its potential to change the world.

One of the most promising fields of application is generation of very high

magnetic fields which has lots of practical importance. Such high magnetic fields are

necessary in medical imagers such as MRIs, particle accelerators, nuclear fusion reactors etc.

At present majority of MRIs generate high magnetic field using LTS superconductors. NbTi

has the major share in this area. For very high magnetic fields, LTS-HTS combination is

used. Superconducting magnets are widely used in focusing and accelerating particles in

particle accelerators such as Large Hadron Collider (LHC). Particles are directed around the

accelerator loop by a strong magnetic field maintained by superconducting magnets. In LHC,

1232 dipole magnets 15 meters in length, bend the beams, and 392 quadrupole magnets, each

5–7 meters long, focus the beams. Just before collision, another type of magnet is used to

converge the particles closer together to increase the chances of collisions. Superconducting

radio frequency cavities also find applications in these kind of particle accelerators. Magnetic

field essential for plasma confinement in fusion reactors is also generated by huge

superconducting magnets. Current leads for powering magnets are also made using

superconducting materials. Current leads made of superconductors can reduce the heat input

considerably that saves precious cryogen and thereby reduces the operating cost


The Superconducting Quantum Interference Device (SQUID) based on the

Josephson effect is the most sensitive magnetometer. SQUID based technology is widely

used for mapping of extremely weak magnetic signals from living organisms. In material

science and physics research, SQUID based magnetometers are widely used for magnetic

characterization of materials. They also find application as highly sensitive voltmeters, as

ultrasensitive detectors of nuclear magnetic resonance and as transducers for gravitational

wave antennas. The Magnetic Property Measurement System (MPMS) and Physical Property

Measurement System (PPMS) are widely used for characterization of samples.

Superconducting Magnetic Energy Storage (SMES) is a cutting-edge

technology that stores electricity in the form of magnetic field of a coil made up of

superconducting wires which has near zero loss of energy. The energy is fed to the coil made

up of superconductor and coil is closed (persistent mode), the current stays forever since

there is no loss and this current produces a magnetic field. The energy stored can be

recovered in a very short interval of time. SMES loses only a little amount of electricity in

the energy storage process compared to other methods of storing energy.

Superconducting transmission lines and fault current limiters are two

important applications of superconductors in energy transmission. Power grids around the

globe are reaching their limits. In the meantime, electricity demand is growing.

Superconducting power transmission grids are very attractive because of their reduced energy

loss, relatively small size and high capacity. At present, power applications of high

temperature superconductors emphasize on use of BSCCO in wire and tape forms and YBCO

in the form of thin films. Current densities necessary for practical power applications are

already achieved using these materials. In many countries like China commercial application


of superconductors have already started in this sector. Superconducting Fault Current Limiter

(SFCL) is also a promising area for superconductors in power sector. As long as the material

is superconducting, the current will move through the superconductor devoid of any

resistance or loss. If a short circuit occurs, the high short circuit current will cause the

superconductor to lose its superconducting properties and suddenly turn into normal material

offering high resistance to the current. Immediately the current stops. The system will

automatically restart when the material cools.

Table 1.2 Important applications of superconductors

Area Applications

Energy Generation

and Storage

Magnetic levitated flywheel, SMES, Generators

Energy Distribution Cables, Transformers, Current leads, FCLs, Motors

Transportation Maglev trains, Space applications

Magnets NMR magnets, MRI magnets, Magnets for

confinement of plasma in fusion reactors, Magnets

for particle accelerators, High field magnets for

materials characterization

Biomedical Detection of extremely weak neuro magnetic fields,

Magneto Encephalo Graphy(MEG), Magneto Cardio

Graphy (MCG)

Industrial Magnets for shielding and separation, Sensors

R & D Superconducting RF cavities in particle accelerators,

Synchrotrons and High field magnets for materials

characterization


Superconductor Magnetic Levitation (SML) is another important application

of superconductors based on the perfect diamagnetism of superconductors. Superconductors

can be levitated above a magnet with stability. In type II superconductors, the magnetic flux

exclusion is partial and Abrikosov vortices will be present in the material. Magnetic flux

lines will be pinned through these vortices. This can be used to levitate trains which can

move at very high speeds.

Even after many decades of its discovery, the realm of superconductivity was

confined to highly sophisticated research laboratories. Now superconductors have started to

involve in day to day life [21, 22, 24, 25, 31-39]. Important applications of superconducting

materials in different areas are tabulated in table 1.2.


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