Basics of Superconductivity

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Questions and Answers

What phenomenon describes the tunneling of Cooper pairs across an insulating layer between two superconductors?

AC Josephson Effect

Quantum Superposition

DC Josephson Effect (correct)

Superconducting Transition

What is the expected probability of tunneling according to the Josephson predictions?

10^{-10} (correct)

10^{-5}

10^{-2}

10^{-15}

In the DC Josephson effect, what determines the super current flowing through the Josephson device?

Temperature of the superconductors

Thickness of the insulating layer

Number of Cooper pairs

Phase difference and maximum current density (correct)

What type of current is generated when DC voltage is applied across a Josephson junction?

Alternating current Signup and view all the answers

What is the thickness of the insulating material typically used in a Josephson device?

1 to 2 nm Signup and view all the answers

Why does a direct current appear across the Josephson device even when no external field is applied?

Due to tunneling of Cooper pairs Signup and view all the answers

What characteristic of Cooper pairs contributes to their ability to tunnel in a Josephson junction?

Same phase coherence Signup and view all the answers

B.D. Josephson made predictions in 1962 that contributed to understanding which of the following?

Superconductivity properties Signup and view all the answers

What is the primary function of the external voltage source in the RF SQUID circuit?

To control the entry and exit of Cooper pairs Signup and view all the answers

In a flux qubit, what does the Josephson junction contribute to the system?

It contributes inductance and capacitance Signup and view all the answers

How is the quantum mechanical behavior of the flux qubit represented?

As a particle moving in a double potential well Signup and view all the answers

What role does tunneling play in the operation of the flux qubit?

It allows the particle to transition between energy states Signup and view all the answers

Which of the following best describes a phase qubit?

A current-biased Josephson junction at zero voltage Signup and view all the answers

What effect does the applied magnetic flux have on the phase qubit?

It changes the phase difference between Cooper pairs Signup and view all the answers

The RF SQUID is linked to an LC circuit through what means?

Mutual induction Signup and view all the answers

What occurs to the energy levels in the RF SQUID circuit as Cooper pairs enter and leave the island?

They vary based on quantity of Cooper pairs Signup and view all the answers

What is the primary effect observed in type I superconductors when they are subjected to an external magnetic field?

Complete expulsion of the magnetic field Signup and view all the answers

In type II superconductors, what phenomenon occurs for magnetic flux when subjected to an external magnetic field?

Penetration in the form of quantized vortices Signup and view all the answers

What is the formula to calculate the critical current (Ic) for a superconducting wire?

$Ic = 2 ext{π}RHC$ Signup and view all the answers

At what temperature is the critical magnetic field of the superconducting wire given as $2 imes 10^3 A/m$?

5 K Signup and view all the answers

What value is calculated for the critical current in a wire of lead at 4.2 K?

134.5 A Signup and view all the answers

Which parameter is NOT required to calculate the critical current in superconductors?

Resistance of the wire Signup and view all the answers

What is the significance of the critical temperature for a type I superconductor?

It indicates the temperature below which superconductivity occurs Signup and view all the answers

What is the effect of applying a current to a superconducting wire?

It establishes a critical current that must not be exceeded Signup and view all the answers

What is the critical temperature for the metal in the given scenario?

7.08 K Signup and view all the answers

Which interaction is primarily responsible for the formation of Cooper pairs according to BCS theory?

Electron-phonon interaction Signup and view all the answers

What effect does increased temperature have on phonons in the context of superconductivity?

Increases the number of phonons Signup and view all the answers

What happens to the electron density in a region affected by phonon distortion?

Increases due to lattice distortion Signup and view all the answers

What happens to electron pairing at normal temperatures according to BCS theory?

Attractive forces are too small for pairing Signup and view all the answers

What role do phonons play in the conductance of superconductors?

They facilitate the scattering of electrons Signup and view all the answers

Which of the following correctly describes a Cooper pair?

Two electrons with opposite spins in a phonon field Signup and view all the answers

How does resistivity behave as temperature decreases in superconductors?

It decreases significantly Signup and view all the answers

What effect does a magnetic field greater than the critical field Hc have on superconductivity?

Causes the loss of superconducting property Signup and view all the answers

What is the formula used to express the temperature dependence of the critical field?

$H_c(T) = H_c(0) [1 - \frac{T^2}{T_c^2}]$ Signup and view all the answers

At what temperature does doping Pb with a magnetic field of $3.3 \times 10^4$ A/m result in the loss of superconducting property?

5 K Signup and view all the answers

If the critical field for niobium is $1 \times 10^5$ A/m at 8 K, what will be its transition temperature?

11.3 K Signup and view all the answers

What is the maximum critical field for lead during its superconductivity?

$8 \times 10^5$ A/m Signup and view all the answers

What precaution must be taken when using lead as a superconductor subjected to a magnetic field of $4 \times 10^4$ A/m?

Limit the field to below $8 \times 10^5$ A/m Signup and view all the answers

What happens to the superconducting property of a material when it reaches its critical temperature Tc?

It transitions to a normal conducting state Signup and view all the answers

What is the critical field required for a material at 0 K known as?

Hc(0) Signup and view all the answers

Study Notes

Superconductivity Basics

Meissner Effect: The expulsion of magnetic fields from the interior of a superconductor, observed in Type I superconductors. Type II superconductors exhibit a mixed state with quantized vortices allowing some penetration.
Critical Current: The maximum current a superconductor can carry before losing its superconducting properties. This is directly proportional to the critical magnetic field and the radius of the superconducting wire.
Critical Magnetic Field: The minimum value of the external magnetic field required to destroy superconductivity at a given temperature. This value decreases with increasing temperature.
Temperature Dependence of Critical Field: The critical field decreases as temperature rises, following Tuyn's Law, described by the formula: Hc(T) = Hc(0)[1 - (T/Tc)²].
Transition Temperature (Tc): The temperature below which a material exhibits superconductivity.

Types of Superconductors

Type I Superconductors: Exhibit perfect diamagnetism and a single critical temperature.
Type II Superconductors: Exhibit a mixed state with magnetic flux penetration through quantized vortices.
Hard Superconductors: These Type II superconductors can sustain high magnetic fields (10 T or higher) and are used in magnetizing coils.

BCS Theory

Cooper Pairs: At low temperatures, two electrons interact through a phonon exchange, creating an attractive force between them, forming a bound pair called a Cooper pair.
Electron-Phonon Interaction: Electrons interact with the lattice vibrations (phonons) of the material, influencing its conductivity.

Josephson Junction

Josephson Effect: A phenomenon involving the tunneling of Cooper pairs through a thin insulating layer (Josephson Junction) between two superconductors.
DC Josephson Effect: A direct current flows through the junction even with zero applied voltage, dependent on the phase difference between the Cooper pairs.
AC Josephson Effect: When a DC voltage is applied across the junction, an alternating current is generated.

Superconducting Qubits

RF SQUID (Radio Frequency Superconducting Quantum Interference Device): A loop containing two Josephson junctions, used for sensitive magnetic field detection.
Flux Qubit: A superconducting loop with a Josephson junction, acting as a two-state system due to the potential energy landscape.
Phase Qubit: A current-biased Josephson junction operating at zero voltage state, sensitive to the phase difference between Cooper pairs across the junction.

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Description

This quiz covers the essential concepts of superconductivity, including the Meissner effect, critical current, and critical magnetic field. It also explores the temperature dependence of these properties and defines types of superconductors. Test your understanding of these fundamental principles.