Ch-5 Superconductivity_KB

L. J. Institute of Engineering and Technology Subject: Physics (Group-1) Subject code: 3110011 F.Y. - B.E. Kamaldeep Bhatia

Superconductivity SUPERCONDUCTOR A superconductor is a material that loses all its resistance to the flow of electric current when it is cooled below a certain temperature called the critical temperatureTc. Ex. Mercury (Hg), Zinc (Zn), Tin (Sn) The temperature at which a material’s electrical resistivity drops to absolute zero is called the critical temperatureTc. PROPERTIES OF SUPERCONDUCTOR i) Electrical Resistance:- The electrical resistivity of a superconducting material is very low & is of the order 10−7Ωm. ii) Effect of impurities:- When impurities are added to superconducting materials, the superconducting property is not lost but the Tc is lowered. iii) Effect of pressure & stress:- Some materials are found to exhibit the superconducting phenomena on increasing the pressure over them. For eg. Cesium is found to exhibit superconducting phenomena at Tc = 1.5 K on applying pressure of 110kbar. In superconductors, the increase in stress results in increase of the Tc value. iv) Isotope effects:- The critical temperature Tc value of a superconductor is found to vary with its isotopic mass. This variation between Tc & its isotopic mass is given by, Tc ∝ 1 M = isotopic mass √M v) Magnetic field effect:- 2

If sufficiently strong magnetic field is applied to a superconductor at any temperature below its critical temperature Tc, the superconductor is found to undergo a transition from the superconducting state to normal state. This minimum magnetic field required to destroy the superconducting state is called the critical magnetic field Hc. T2 Hc = Ho [1 − (Tc) ] Ho- critical field at T=0 K vi) Critical Current density ������������ & Critical current ������������:- The critical current density can be defined as the maximum current that can be permitted in a superconducting material without destroying its superconductivity state. The relation between critical current Ic & critical magnetic field Hc is, Ic = 2πrHc r-radius of super conducting wire. The relation between critical current density Jc & critical current Ic is, Ic Jc = A A-Area of superconducting material. vii) Persistent current:- The steady flow of current in a superconducting wire without any potential deriving it is called the persistent current. 3

viii) Meissner effect (Diamagnetic property) The complete expulsion of all the magnetic field by a superconducting material is called the ‘Meissner effect’. This process occurs due to the development of surface current, which develops the magnetization M within the superconducting material. Hence, as the developed magnetisation & the applied field are equal in magnitude but opposite in direction, they cancel each other everywhere inside the material. Thus, below Tc a superconductor is a perfectly diamagnetic substance (Xm = −1) (Prove Xm = −1 for superconductors or superconductors exhibits perfect diamagnetism.) B = μ0(M + H) μ0-permeability of free space M- intensity of magnetisation H- applied magnetic field. Therefore, 0 = μ0(M + H) But, μ0 ≠ 0 M+H=0 4

M=−H M M H = −1 (Xm = H) Hence, Xm = −1, where Xm is magnetic susceptibility For a superconductor the susceptibility is negative. THREE IMPORTANT FACTORS TO DEFINE A SUPERCONDUCTING STATE i) Critical temperature Tc ii) Critical current density Jc iii) Critical magnetic field Hc The relationship between������������, ������������ & ������������ is shown in the phase diagram. Each of these parameters is very dependent on the other two properties present. To sustain superconducting state in a material, it is required to have the both current density and magnetic field as well as the temperature, to remain below their critical values. The highest Values for Hc and Jc occur at 0K, while the highest value for Tc occurs when H and J are zero. TYPES OF SUPERCONDUCTORS 5

No. Type – I Type – II 1) These superconductors are These conductors are called as Hard called as soft superconductors. superconductors. 2) Only one critical field exists Two critical fields Hc1 & Hc2 exist for for these superconductors. these superconductors. 3) The critical field value is very The critical field value is very high. low. 4) These superconductors These superconductors do not exhibit a exhibit perfect & complete perfect & complete Meissner effect. Meissner effect. 5) They have limited They have wides applications because of applications because of very very high field strength value. low field strength value. 6) E.g. Pb, Hg, Zn Nb3Ge, Nb3Sn, YBCO. Low temperature Superconductor:- Superconductors that require liquid helium as coolant are called low temperature superconductors (LTS or Low-Tc). Liquid helium temperature is 4.2K above absolute zero. High-Temperature Superconductors:- Superconductors having their Tc values above the temperature of liquid nitrogen (77K or -1960C) are called the high temperature superconductors (HTS or high Tc). 6

MECHANISM OF SUPERCONDUCTIVITY (BCS Theory) Through invention of Superconductivity was done in 1911 by Onnes, well-define mechanism explaining the superconductivity was developed by three scientists namely Bardeen, Cooper and Schrieffer in 1957 after research of number of years. This theory is named as BCS theory based on first letter of their names. To understand this theory, first of all behaviour of electron in normal condition is required to be understand as explained below: At normal condition (room temperature) in an ordinary conductor, as per the basis of quantum mechanics, electrons with same energy having same energy level will have opposite momenta, i.e., one electron is moving towards left then other electron moves towards right. Therefore, when no electrical current is flowing, the energy levels are filled bottom upwards with the pair of electrons of opposite momentum in each energy level. Also, the crystal lattice is in (almost) stationary condition. When electrical field is applied, the crystal lattice starts to vibrate and electrons also move from one position to other. During this motion of electrons, they collide with crystal lattice continuously and exchange of energy takes place between them which develops heat. Due to this collision, electrons are facing resistance to their motion which is termed as electrical resistance. As the temperature increases (due to collision) the electrical resistance also increase. Now, when the temperature of material is reduced below to its critical temperature, crystal lattice vibrates very slowly in comparison to normal temperature. Assume an electron which is passing through a crystal lattice as shown in fig. 7

Since an electron carries negative charge, whereas ions have positive charge, all ions are attracted towards negatively charged electrons and hence the crystal lattice gets distorted as shown in fig. Due to this distorted lattice, a cloud of positive charge is being developed around the electron which is known as phonon and due to this phonon electron interaction, negatively charged electron now carries a positive charge with it. When this positively charged electron moves ahead, it attracts the other negatively charged electron and interacts with each other and form a weak bonding due to presence of phonon. . This indicates that for superconducting materials, the interaction of electrons and phonons is modified by the fact that the electrons may 8

no longer be independent, but may be bound together in pairs, known as Cooper pairs, which drifts in the lattice when current flows. Cooper pair is the new particle made up of two electrons having same momentum but opposite spin. It has twice the mass and twice the charge of an electron. Motion of such cooper pairs is only responsible for electrical current flow in the superconductor. Now, if any of the electron is to be scattered by a collision in the direction of current flow, the phonon must provide sufficient energy to break the cooper pair bonding in addition to the ordinary criteria pertaining to allowed energy and momentum before collision. But at temperature below critical temperature, the number of phonons having sufficient energy to break the cooper pair bonding is very few, and hence such pairs may pass through the lattice without breaking of the bonds and hence they experience zero resistance. If the temperature is raised above critical temperature, the energy of breaking the cooper pairs increases and hence above its critical temperature, the superconductivity ends. This theory critically postulates the mechanism of current flow in the superconductivity state. PENETRATION DEPTH OF MAGNETIC FIELD After discovery of Meissner effect, in 1935, London brothers, carried out research on depth of penetration of applied magnetic field into superconducting material. The 9

characteristic length (������) associated with the decay of the magnetic field at the surface of a superconductor is known as the penetration depth. In superconducting state, based on the research it was concluded that applied magnetic field is not zero at the surface of the superconductor but decreases exponentially as given by the equation below: H=H0������ −������������ where, H is the intensity of magnetic field at a depth x from the surface Ho is the intensity of magnetic field at the surface ������ is called London penetration depth. This expression for depth of penetration (λ) of applied magnetic field into superconducting material from the surface was achieved by adding two effects to the Maxwell's electromagnetic equations: 1) Meissner effect i.e., the magnetic induction (B) inside a superconducting material is equal to zero (B = 0) and 2) Zero resistivity i.e., the intensity of electric field (E) in a superconductor in superconducting state is equal to zero (E = 0). 10

London penetration depth is defined as the distance from the surface of the superconductor to a point inside the material at which H the intensity of magnetic Ho field is equal to the magnetic Ho field at the surface (i.e.������0 ) ������ The variation of intensity of magnetic field with distance from the surface in to the material for tin is shown in Fig. The magnetic field penetrates to a depth of 10 to 100 nm from the surface of a superconductor. If the superconducting film or filament is thinner than this value, then its properties are significantly different from that of the bulk material. APPLICATIONS Magnetic levitation (Maglev) Magnetic levitation or maglev is the process by which an object is suspended above another object with no other support but magnetic fields. The magnetic levitation is brought about by enormous repulsion between two highly powerful magnetic fields. The levitation of the magnet as maglev demonstrates two critical properties of S.C. i) Zero resistance & ii) Meissner effect. Maglev Train The levitation is based on two techniques: i) Electromagnetic suspension (EMS) & ii) Electrodynamic suspension (EDS) In attractive EMS the electromagnets installed on the train bogies attract the iron rails (guideways). The vehicle magnet wraps around the iron guideways & the attractive upward force lifts the train. In EDS levitation is achieved by creating a repulsive force between the train & guideways. The basic idea of maglev train is to levitate it with magnetic fields so that there is no physical contact between the train & the rails (guideways). Consequently the maglev train can travel at very high speed. These trains travel at a speed of about 500 km/hr. Maglev Space Propulsion 11

A similar magnetic propulsion system is being used to launch the satellite into orbits directly from the earth without the use of rockets. Maglev systems could dramatically reduce the cost of getting into space because they are powered by electricity, an inexpensive energy source that stays on the ground- unlike rocket fuel that adds weight and cost to a launch vehicle. Josephson Effect & Its Application Josephson junction: - Two superconductors separated by a very thin strip of an insulator forms a Josephson junction. The wave nature of moving particles makes the electrons to tunnel through the barriers (insulator) i.e. the electrons can tunnel from one superconductor to the other. As a result of the tunnelling of electrons (cooper pairs) across the junction. This is called as d.c. Josephson effect. When a potential difference V is applied between the two sides of the junction, there will be an oscillation of the tunnelling current with angular frequency ν = 2ehV. This is called the a.c. Josephson effect. Application of Josephson Junction (SQUID) SQUID :- Superconducting Quantum Interference Device. A SQUID is formed by connecting two Josephson junction in parallel. 12

When current is passed through this arrangement it splits into two opposite arc. This current have a periodicity which is very sensitive to the magnetic flux passing normally through the closed circuit. Due to this, extremely small magnetic flux can be defected with this device. This device can also be used to detect voltages as small as 10−15V. Magnetic field changes as small as 10−21T can be detected. Weak magnetic fields produced by biological currents such as those in the brain can also be detected using SQUID. Cryotron It is a switch made of superconductor whose size can be made very small these switches consume very less current. The cryotron contains two superconducting materials A & B. The material A is inside the coil of wire B, as shown in figure. The critical field of A be HCA & that of B be HCB . Also, HCA > HCB . 13

Current passing through B induces magnetic field H. if this induced field H is greater than HCA then superconductor property of A get destroyed. Hence, resistivity increases & the contact is broken. The current in A can be controlled by the current in B, this system act as a switch. OTHER APPLICATION OF SUPERCONDUCTORS  Superconductors are used to transmit electrical power over very long distances without any power loss or any voltage drop.  Superconductor generators has small size & low energy consumption.  Superconductor coils are used in N.M.R imaging instruments.  Very strong magnetic can be generated with coils made of high Tc superconductors materials.  Superconductor act as switching system in computer. 14