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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
Introduction to superconductivity 3
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
Introduction to superconductivity 4
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
Introduction to superconductivity 5
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,
Introduction to superconductivity 6
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).
Introduction to superconductivity 7
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].
Introduction to superconductivity 8
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
Introduction to superconductivity 9
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
Introduction to superconductivity 10
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
Introduction to superconductivity 11
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
Introduction to superconductivity 12
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
Introduction to superconductivity 13
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
Introduction to superconductivity 14
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
Introduction to superconductivity 15
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
Introduction to superconductivity 16
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.
Introduction to superconductivity 17
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