Related Experiment Video
Updated: Sep 2, 2025
05:39
Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
Published on: August 2, 2019
9.7K
The BCS Energy Gap at High Density
Joscha Henheik1, Asbjørn Bækgaard Lauritsen1
1IST Austria, Am Campus 1, 3400 Klosterneuburg, Austria.
Journal of Statistical Physics
|August 3, 2022
Summary
We derived a formula for the BCS energy gap in high-density systems. This finding, combined with critical temperature research, proves the universal ratio between the energy gap and critical temperature.
Area of Science:
- Condensed Matter Physics
- Quantum Mechanics
- Statistical Mechanics
Background:
- The Bardeen-Cooper-Schrieffer (BCS) theory describes superconductivity.
- Understanding the energy gap and critical temperature in high-density systems is crucial.
Purpose of the Study:
- Derive an asymptotic formula for the BCS energy gap at high densities.
- Investigate the dependence of the energy gap on the interaction potential strength.
- Prove the universality of the ratio between the energy gap and critical temperature.
Main Methods:
- Asymptotic analysis of the BCS energy gap equation.
- Utilizing a previously derived formula for the critical temperature at high densities.
Main Results:
- An asymptotic formula for the BCS energy gap was derived.
- The formula shows a strong dependence on the interaction potential strength at the Fermi surface.
- The universality of the energy gap to critical temperature ratio is proven.
Conclusions:
- The derived formula provides new insights into superconductivity at high densities.
- The universality of the gap-to-temperature ratio holds true in this regime.
- This work unifies understanding of fundamental superconducting properties.
More Related Videos
Related Concept Videos
01:21Energy Associated With a Charge Distribution
1.6K
The work done to bring a charge through a distance r is given by the potential difference between the initial and the final position. To assemble a collection of point charges, the total work done can be expressed in terms of the product of each pair of charges divided by their separation distance, defined with respect to a suitable origin. Solving this expression gives the energy stored in a point charge distribution.
1.6K
01:01Energy Bands in Solids
1.2K
Isolated atoms have discrete energy levels that are well described by the Bohr model. And, it quantifies the energy of an electron in a hydrogen atom as En. Higher quantum numbers 'n' yield less negative, closer electron energy levels.
Band Formation:
When atoms are brought close together, as in a solid, these discrete energy levels begin to split due to the overlap of electron orbitals from adjacent atoms. This split occurs because of the Pauli exclusion principle, which states...
Band Formation:
When atoms are brought close together, as in a solid, these discrete energy levels begin to split due to the overlap of electron orbitals from adjacent atoms. This split occurs because of the Pauli exclusion principle, which states...
1.2K
03:21The Energies of Atomic Orbitals
24.3K
In an atom, the negatively charged electrons are attracted to the positively charged nucleus. In a multielectron atom, electron-electron repulsions are also observed. The attractive and repulsive forces are dependent on the distance between the particles, as well as the sign and magnitude of the charges on the individual particles. When the charges on the particles are opposite, they attract each other. If both particles have the same charge, they repel each other.
24.3K
01:22Energy Carried By Electromagnetic Waves
3.2K
Anyone who has used a microwave oven knows there is energy in electromagnetic waves. Sometimes, this energy is obvious, such as in the summer sun's warmth. At other times, it is subtle, such as the unfelt energy of gamma rays, which can destroy living cells. Electromagnetic waves bring energy into a system through their electric and magnetic fields. These fields can exert forces and move charges in the system and, thus, do work on them. However, there is energy in an electromagnetic wave,...
3.2K
01:20Strain-Energy Density
523
Understanding the strain energy density in materials under axial load is crucial for evaluating their mechanical behavior and durability. When a rod is subjected to such a load, it elongates and stores energy, known as strain energy, as potential energy within the material. This energy is measured in terms of energy per unit volume.
In the elastic region of a material, the relationship between the stress and the strain is linear and follows Hooke's Law. The strain energy density in this...
In the elastic region of a material, the relationship between the stress and the strain is linear and follows Hooke's Law. The strain energy density in this...
523
01:22Semiconductors
861
There is variation in the electrical conductivity of materials - metals, semiconductors, and insulators that are showcased with the help of the energy band diagrams.
Metals such as copper (Cu), zinc (Zn), or lead (Pb) have low resistivity and feature conduction bands that are either not fully occupied or overlap with the valence band, making a bandgap non-existent. This allows electrons in the highest energy levels of the valence band to easily transition to the conduction band upon gaining...
Metals such as copper (Cu), zinc (Zn), or lead (Pb) have low resistivity and feature conduction bands that are either not fully occupied or overlap with the valence band, making a bandgap non-existent. This allows electrons in the highest energy levels of the valence band to easily transition to the conduction band upon gaining...
861