Superconducting Gap
Superconductivity is a state where electrical current flows with zero resistance in certain materials which are cooled below a certain temperature called the critical temperature. A superconducting gap is the gap in the energy spectrum of the material which is necessary for the electrons to become superconductive. The characters of such a gap depend on the specific material and yield further insight into the behaviour and properties of the material.
In a superconductor, electrons are bound together and form Cooper pairs, which then can travel through the material with zero resistance. The pairing of the electrons is possible because of Cooper pair exchange, which is a quantum mechanical effect which can be explained using the BCS theory. Theoretically, a zero energy gap isolates the Cooper pairs from the other electrons. In other words, the Cooper pairs need to lower their energy, and this is only possible by a superconducting gap in the energy spectrum of the material.
In order to better understand the nature of the superconducting gap, it is necessary to discuss the spectrum of a superconductor. Generally, it consists of two parts; the normal state below the critical temperature and the superconducting state above it. Below the critical temperature, the behavior of the electrons is similar to that of an ordinary conductor. Electrons have energies up to a certain energy level (called the Fermi energy), where they become degenerate and free to move throughout the system. This Fermi energy is also the upper limit of the normal state.
Above this critical temperature the material is in a completely different state. The electrons no longer interact with each other by exchanging energy and particles, but instead form Cooper pairs. This pairing changes the shape of the energy spectrum and creates a gap in the spectrum, which is the superconducting gap. The width of this gap is determined by a number of factors, such as the strength of the pairing interaction, the concentration of electrons, and the number of dimensions in the system.
The presence of a superconducting gap can also be observed using a variety of techniques. The most commonly used technique is scanning tunneling microscopy (STM), which is used to measure the electronic structure of a material by sending a current through it. When the Fermi energy of the system is fixed, a gap in the energy spectrum appears when the sample is cooled to the critical temperature. This gap can then be used to accurately determine the superconducting gap of the material.
In summary, a superconducting gap is the gap in the energy spectrum of a material which is necessary for the electrons to become superconductive. It is the fundamental parameter in superconductivity and can be measured using a variety of techniques. The width of the gap is determined by the strength of the pairing interaction, the concentration of electrons, and the number of dimensions in the system. By understanding the nature of this gap, one can gain valuable insight into the behaviour and properties of superconductors.
