Module 3 (CS)- Electrical Conductivity in Metals & Superconductors (6)

Conducting materials

Materials that allow electric current to flow through them due to the presence of free electrons available for conduction when an electric potential difference is applied.

Classical free electron theory

A macroscopic theory proposed by Paul Drude in 1900 that describes electrical conductivity in metals by modeling the conduction electrons as a gas of free particles that collide with fixed ions in the lattice.

Quantum free electron theory

A microscopic theory developed by Sommerfeld in 1928 that incorporates quantum mechanics to explain the behavior and movement of free electrons in metals, introducing the concept of energy bands and the Fermi-Dirac distribution.

Drift velocity (Vd)

The average velocity ( V_d = rac{J}{nq} ) acquired by conduction electrons in a conductor when subjected to an electric field, moving in a direction opposite to the field due to collisions with the lattice.

Fermi energy (EF)

The energy level at absolute zero temperature, where the highest occupied electronic state exists. It serves as a reference energy for the conduction band and is crucial for understanding electron distribution in metals.

Fermi velocity (vF)

The velocity of electrons at the Fermi energy level, given by the formula v_F = rac{p}{m} , where 'p' is momentum and 'm' is the mass of the electron.

Superconductivity

A phenomenon observed in certain materials where they exhibit absolutely zero electrical resistance and expel magnetic fields, occurring below a critical temperature (Tc).

Critical temperature (Tc)

The temperature below which a material undergoes a phase transition to a superconducting state, losing all electrical resistance.

Meissner effect

The effect by which a superconducting material expels magnetic field lines from its interior upon transitioning below its critical temperature, thus demonstrating perfect diamagnetism.

Type I superconductors

Superconductors that transition abruptly to a normal conductive state when the applied magnetic field exceeds a critical value; characterized by a clear threshold for superconductivity.

Type II superconductors

Superconductors that allow magnetic fields to partially penetrate through them in quantized units, losing their superconductivity gradually rather than abruptly.

BCS theory

The theory of superconductivity derived by John Bardeen, Leon N. Cooper, and John R. Schrieffer proposing that at low temperatures, electrons form pairs (Cooper pairs) that move without resistance through a lattice.

Cooper pairs

Bound pairs of electrons that arise from attractive interactions via phonons in superconductors, allowing them to behave collectively as a single quantum entity at low temperatures.

Quantum tunneling

A phenomenon in quantum mechanics allowing particles (e.g., electrons) to pass through potential energy barriers that they would not normally be able to cross classically, explained by the wave-particle duality.

SQUID

Superconducting Quantum Interference Device, an extremely sensitive instrument used for measuring weak magnetic fields, based on quantum interference effects of Cooper pairs.

Electrical resistivity

A material property (ρ) that quantifies its resistance to electrical flow; mathematically expressed as ρ = rac{E}{J} , where 'E' is the electric field and 'J' is the current density.

Electrical conductivity (σ)

The ability of a material to conduct electric current, represented as the reciprocal of resistivity ( σ = rac{1}{ρ} ) and quantified in siemens per meter (S/m).

Relaxation time (τ)

The average time interval between successive collisions of conduction electrons in a material, impacting the resistivity and overall conductivity.

Fermi factor (f(E))

The statistical function describing the probability of occupancy of an electron energy state at thermal equilibrium, defined as f(E) = rac{1}{e^{(E - E_F)/(k_BT)} + 1} , where 'E_F' is the Fermi energy and 'k_B' is the Boltzmann constant.

Critical magnetic field (Hc)

The maximum magnetic field strength that a superconductor can withstand before it ceases to exhibit superconductivity and reverts to a normal conducting state.

Matthiessen’s Rule

A principle stating that the total resistivity (

ho_{total} = ho_{lattice} + ho_{impurities} ) of a metal is the sum of the resistivities due to scattering from lattice vibrations and impurities.