Superconductivity Notes PDF

# 4. Superconductivity - Electrical resistance of metal increases linearly with increasing temperature. - Resistivity of semiconductor decreases with increasing temperature. - Metal - **PTC** of resistivity - Semiconductor - **NTC** of resistivity ## Superconductors - Materials whose resistivi...

# 4. Superconductivity - Electrical resistance of metal increases linearly with increasing temperature. - Resistivity of semiconductor decreases with increasing temperature. - Metal - **PTC** of resistivity - Semiconductor - **NTC** of resistivity ## Superconductors - Materials whose resistivity suddenly drops to zero at a particular temperature known as critical temperature (Tc) and it remains zero below critical temperature. Above Tc it behaves as a normal conductor. ## Properties of Superconductors - **Meissner effect:** When a specimen is placed in a weak magnetic field and cooled below the critical temperature, the magnetic flux originally present in the specimen is expelled/ejected from the specimen. This effect is known as the Meissner effect. - This effect is reversible and the specimen returns to its normal state when its temperature is raised above its critical temperature. - **Superconductor acts as perfect diamagnets with zero magnetic induction (B=0) in the interior when placed in a weak magnetic field.** - $B = μ_0(H+M)$ - when the temperature T of the specimen is lowered below its critical temperature (Tc), $B=0$ - $μ_0(H+M) = 0$ - $H+M = 0$ - $H=-M$ - $M = -1$ - $χ = -1$ - **As relative permeability**, $μ_r=1+χ$. - $μ_r = 1-1 = 0$ - $μ_r=0$ - This indicates perfect diamagnetism. - **Critical field (Hc):** - Superconductivity is destroyed by sufficiently strong magnetic field. the minimum value of applied magnetic field required to destroy superconductivity is called critical field (Hc) - **Above Tc, HC=0** - $Hc = Ho [1-(T/TC)²]$ - $Ho$ - critical field at absolute zero. - **Isotope effect:** It is observed that the critical temperature of superconductors varies with isotopic mass. The critical temperature is smaller for larger isotopic mass. This is called as isotopic effect. - $Tc. M^α = constant$ - $α = 1/2$ - $Tc. M^{1/2} = constant$ - $Tc1 / Tc2 = (M_1/M_2)^{1/2}$ - **Critical current:** - The maximum current that a superconductor can carry without reverting back to its normal state i.e. conducting, is known as critical current. - Every current carrying conductor produces a magnetic field around it. When current flows through superconducting wire, magnetic field is produced around it. If the current in the superconducting wire is increased, the magnetic field intensity just outside it will increase & reach the critical field Hc. If the current is increased beyond this value, the wire will be subjected to magnetic field exceeding the critical field due to which, the superconducting -cting state is destroyed and then it will revert to its normal state. - The magnetic induction due to wire of radius r just outside it is, $B=μ_0I/2πr$. $B= μ_0H$ $H=B/μ_0$ - $H= χI/2πr$ - If current is critical i.e. Ic and field is Hc. - $Hc = Icμ_0/2πr$ - $Ic = 2πrHc/μ_0$ - **Persistent current:** - When a superconducting ring is placed in a magnetic field and if the field is switched off, a current is induced in the ring. The magnitude of current remains constant, even though there is no source of e'm'f, as resistance of the superconducting ring is zero. - Such steady current flowing in the super -conductor are called persistent current. - **Zero electrical resistance (R=0):** - The electrical resistivity of superconductor is zero. A voltmeter was connected across the specimen, to measure potential difference across the specimen. - The temperature of the specimen is lowered, it is observed that below particular temperature known as the critical temperature, potential difference across the specimen is suddenly dropped to zero. - **Types of superconductors:** - **Type I:** Soft superconductors. Magnetization curve - **Type II:** Hard superconductors. Magnetization curve ## Applications of Superconductors - **Superconducting Magnets:** Solenoids made of superconducting wires can generate strong magnetic field and it produces strong magnetic field without consuming large amounts of power. As superconductors can carry much larger currents densities (persistent currents) without energy loss, the superconducting magnets will have light weight. - **SQUID (Superconducting quantum interference devices):** - To understand SQUID we must understand what is Josephson effect. - **Josephson effect:** Phenomenon occurs when two superconductors are placed in proximity with some restriction between them. It is based on quantum tunneling effect. Josephson effect produces current called as supercurrent that flows continuously. Restriction between 2 superconductors is called as Josephson junction/ weak link. - **DC Josephson effect:** In the absence of any electric or magnetic field, d.c. current flows across junction. - A direct current flows through the function without an applied voltage. A superconducting electron pair (Cooper pair) tunnel through insulating layer from one superconductor to another. A DC current is represented as $I = Icp Sin(Φ₂-Φ₁)$. ($Φ₂-Φ₁$ - phase difference) ($Φ₂-Φ₁$ - phase difference constant over time) - **AC Josephson effect:** A Radio frequency current oscillations are produced across the junction when DC voltage is applied across it weak link. - If DC voltage 'V' is applied across the junction, the current oscillates with frequency: $ν = 2eV/h$. - Phase difference varies linearly with time hence alternating current flows (AC) - **SQUID:** It is superconducting device that measure small mag, voltage field, current and voltage. - It consists of 2 Josephson junction JA and JB. - A current Iin entering in the ring is get divided in two parts IAF IB. Both current IA and IB undergoes a phase shift while crossing the junctions JA JB respectively. - In superconductors the current is caused by Cooper pair. So the interfering waves are the debroglie waves of the coopen pairs. The phase shift occurs due to applied mag field. In abscence of field, phase shift as well as phase difference is zero. - Iout is the current which oscillates betwn maxima and minima. Also voltage oscillates with changing magnetic field. Because of these extreme sensitivity to mag. field SQUID are used to for brain imaging because human brain generates the magnetic filed. - **Magnetic levitations/Maglev Trains:** - When magnet is brought near a superconducting coil. Current is induced in the superconductor, this current will produce magnetic field, which will repel the magnet. Thus magnet can be made to float in air (ie. levitate) on superconducting coil. This is called as magnetic levitation. - Thus magnetic levitations are used for development of Maglev train (Magnetic levitation trains). This trains can attain a speed upto hundred kilometers as there is no friction between the rails and wheels. - **Superconducting transmission cables:** - As superconducting cables have very low transmission loses, power can be transmitted at low voltage. Power transmission through these cables is very economical - **Bearing:** Superconducting bearing can operate without frictional loss.