superconductivity and di-electrics

• Superconductivity was discovered by Kamerlingh Onnes in 1911
• Resistance of Mercury decreases with decreasing temperature up to 4.15K, at which point it drops to zero
• Superconductivity is the phenomenon where electrical resistance of certain materials drops to zero below a critical temperature
• Critical temperature (Tc) is the temperature at which a material changes from a normal conductor to a superconductor
• Critical magnetic field (Hc) is the value at which a material loses its superconducting property and becomes a normal conductor
• Meissner effect is the expulsion of magnetic flux lines from the interior of a superconductor when below its critical temperature (Tc)
• Critical current (Ic) is the threshold value of current at which the magnetic field due to the current will be equal to the critical magnetic field
• Critical current density (Jc) is the current density at which superconducting properties disappear
• Superconductors can be Type-1 or Type-2 based on their magnetization properties in an external magnetic field
• Type-1 superconductors expel magnetic field completely below a critical field (Hc) and exhibit complete Meissner effect
• Type-2 superconductors have two critical magnetic fields (Hc1 and Hc2) and exhibit a gradual transition from superconducting to normal state
• BCS theory of superconductivity explains the formation of Cooper pairs, where two electrons attract each other via exchange of virtual phonons
• Cooper pairs are pairs of electrons with opposite spins and momenta that move as a single unit in a superconductor
• Quantum tunnelling of Cooper pairs allows them to move through barriers, and Josephson junctions involve superconductors separated by an insulating layer
• Josephson device is an insulating material of thickness nearly 1 to 2 nm sandwiched between two different superconducting materials
• DC Josephson Effect:

  • Cooper pairs in superconducting material are in the same phase
  • Tunnelling of superconducting electrons from one side with higher electron density to another side with lower electron density across the junction creates a dc voltage
  • Insulating layer introduces a phase difference (𝜙) between wave function of cooper pairs on either side, resulting in super current even with zero applied voltage
• • Super current (or junction current) is given by JcIsin𝜙 = IcIsin𝜙, where Ic is the maximum junction current depending on the thickness of the insulating layer (between 1μA to 1 mA)
• AC Josephson Effect:

  • Applying DC voltage across the Josephson junction introduces an additional phase difference between the Cooper pairs, generating an alternating current
  • Frequency of alternating current is directly proportional to applied voltage V and is given by ν = ଶୣ୚ ୦
  • Photon energy of emission or absorption at the junction is hν = 2eV, which translates to ν = 483.5 × 10 ଵଶ V Hz
  • For an applied voltage of 1μV, the frequency of the ac signal is ν = 483.5×10 12 V = 483.5×10 12 ×10 -6 = 483.5 M Hz
• SQUID stands for Superconducting Quantum Interference Device and is based on the principle of Josephson effect

  • SQUID is a sensitive magnetometer used to measure extremely weak magnetic fields as small as 10 -21 T
  • Two types of SQUID are DC SQUID and RF SQUID (or AC SQUID)
• DC-SQUID:

  • Consists of two Josephson junctions (P and Q) arranged in parallel to form a loop with a DC source connected across X and Y
  • Biasing current enters at X and leaves at Y
  • When a magnetic field is applied perpendicular to the arrangement, a phase difference is introduced between tunneling currents across P and Q, resulting in interference effect
  • Resultant current is given by Ic sin(𝜙), where 𝜙 is the flux linked with the SQUID and 𝜙 = (h/2e = 2.06 ×10 -15 wb/m2) called fluxoid
• RF-SQUID (or) AC-SQUID:

  • RF SQUID is a one-junction SQUID loop used as a magnetic field detector
  • Less sensitive than DC SQUID but cheaper and easier to manufacture
  • RF SQUID loop is placed near an LC circuit connected to RF AC source and immersed in a magnetic field
  • Oscillating current through LC circuit induces magnetic flux coupled with the loop, leading to changes in voltage across LC circuit to measure magnetic flux and its variation with time
• Dielectric materials are electrical insulators that can be polarized through an external electric field

  • Positive and negative charge entities are bounded together in dielectric materials
  • Behavior can be modified by an external electric field through reorienting charges within atoms or molecules
  • Polarization in dielectrics is proportional to the net electric field experienced by the dielectric
  • Types of polarization include Electronic Polarization, Ionic Polarization, Orientation Polarization, and Interfacial or Space-charge Polarization
• Charges accumulate at the interfaces of multiphase dielectric materials due to the application of an electric field
• Ions are diffused over a distance due to redistribution of charges in the dielectric medium
• Redistribution of electric dipoles/charges in a dielectric medium in an external electric field is known as space charge polarization
• Total polarization in a dielectric material is given by the sum of Pe, Pi, Po, and Ps
• The total polarizability is given by α = αe + αi + αo
• Expression for Internal field in the case of Liquids and Solids: When a dielectric material is placed in an external electric field, it is polarized creating electric dipoles
• Each dipole sets an electric field in the vicinity, resulting in a net electric field at any point within the dielectric material
• Dielectric loss is a measure of the energy lost as heat in a dielectric material when an alternating (AC) electric field is applied
• Dielectric loss is frequency-dependent and varies with the frequency of the applied electric field
• Different types of polarization processes contribute to dielectric loss at different frequency ranges
• Dielectric loss tends to be higher in materials with higher dielectric constants
• The frequency dependence of dielectric loss is often represented by a curve showing how the dielectric loss varies with frequency
• At low frequencies, the loss is primarily due to energy dissipated as electrons respond to changing electric fields
• In the intermediate frequency range, Ionic polarization becomes significant
• At higher frequencies, molecular or orientational polarization becomes prominent
• As frequency increases, the material's net polarization drops, and its dielectric constant drops
• At sufficiently high frequencies, none of the polarization mechanisms are able to switch rapidly enough to remain in step with the field, and the dielectric constant drops to 1
• Dielectric loss is utilized to heat food in a microwave oven