In the previous posts in this series, we explored the fascinating history behind the various superconductors. While high-temperature superconductors remain somewhat mysterious to researchers, the simpler ones can be described by the BCS model, named after its creators: John Bardeen [1], Leon Cooper [2] and John Robert Schrieffer [3]. This description earned these scientists the 1972 Nobel Prize in Physics.
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Electrons carry a negative charge, and repel each other due to their identical charge. However, below a certain temperature, the BCS model assumes that an attractive interaction can form between pairs of electrons, overcoming their mutual repulsion [4]. This assumption raises two important questions: first, how does this attractive interaction arise, and second, what is produced by these electron pairs?
The answer to the first question is that the attraction between electron pairs is caused by the vibrations of the crystal they are in. When an electron moves through the lattice, it can interact with the positively charged atomic nuclei. This interaction enables the electron to transfer energy to the lattice, generating vibrations known as phonons. Phonons are particles representing the lattice vibrations. Thus, electrons can not only create phonons, but can also be affected by them. This means that phonons can act as mediators between different electrons. When the temperature is low enough, below a “critical temperature”, the phonon-mediated interaction becomes strong enough to overcome the electrons’ natural repulsion and creates an attraction between the negative electrons.
How do we know that phonons are actually responsible for this interaction? We can picture lattice vibrations as a system of masses, representing the atomic nuclei, connected by springs representing the attraction between the nuclei. Because the mass of the nuclei affects the vibration frequency, we can link phonons to how electrons attract each other, if we show that changing the masses will also change the critical temperature. In order to examine the phenomenon in a specific superconducting material, we need to change the atomic mass without altering the composition of the material. This can be done by using different isotopes of the same element. Isotopes have the same chemical properties but slightly different masses due to an added or missing neutron. The isotope effect [5] was predicted by BCS theory, and later confirmed. It is considered as one of the model’s greatest successes.
What is produced as a result of the attraction between electrons? Because electrons are spin-½ fermions (quantum particles!), the bound state of two electrons forms a composite boson, a particle with integer spin. Although they are made of two fermions, the composite has a total spin of 0 or 1 (in simple superconductors the composite boson has a spin of 0). These electron pairs are called Cooper pairs, named after Leon Cooper.
Bosons are known as “friendly particles” because, unlike fermions, many bosons can occupy the same energy level. In contrast, no two fermions can be found at exactly the same energy state.
In a material with unpaired electrons, the electrons occupy many different energy states. Because the paired electrons form bosons, all existing Cooper pairs may occupy the lowest energy state, a phenomenon called Bose–Einstein condensation [6]. In this situation, all the energy states formerly occupied by the electrons now merge into the lowest-energy ground state. This leaves a large gap between the ground state and the next available state. The cooper pairs can only be excited if the excitation is strong enough to cross this gap. Below a certain temperature, thermal excitations are too weak to excite electrons into this gap, preventing electron scattering. Electron scattering causes electrical resistance, so preventing electron scattering ensures perfect conduction. Therefore, at low temperatures, materials which host cooper pairs can conduct electricity resistance-free: they are superconductors.
In summary, we have presented a relatively simple outline of the BCS model, which explains the simplest kind of low-temperature superconductivity. This model does not fully explain high-temperature superconductivity, which remains an active topic of research.
English editing: Gloria Volohonsky
Guest editor: Michael Ben Shem
References:
- More about John Bardeen
- More about Leon Cooper
- More about Robert Schrieffer
- See Michael Tinkham, "Introduction to Superconductivity, 2nd edition"
- More about the isotope effect and superconductivity
- Bose-Einstein Condensation
