I have recently been asked by a journalist to comment my work on Brown-Zak fermions (see my previous blog here ). As part of the discussion, I was asked to introduce the concept of a quasiparticle.

In condensed matter physics, simple equations are usually used to describe complex behaviours. For example, it is very simple to consider the equations of an electron not interacting with its surroundings, because the number of atoms or any other particle is usually in the order of $N_A \approx 10^{23}$, which would make analytical resolutions impossible to solve. When one tries to make the model a tad more realistic, in semiconductors for example, it is possible to treat the effect of surrounding electrons as “perturbations” on the free electron. By adding a different mass to that free electron, its behaviour will be different, slowed down or accelerated (basic understanding with newton’s law: $\Sigma F = ma$). That way, electrons in semiconductors, for example, can be modelled as a “quasiparticle”, that is, move like a heavy or light free particle.

The idea for first proposed by the Russian physicist Lev Landau in the early 1950s. He was studying the properties of liquid helium, a superfluid that can flow without any friction. He found that the behaviour of liquid helium could be explained by treating it as if it were made up of not He atoms, but of a different kind of particles that were not actually present in the liquids. These particles, which he called quasiparticles, were excitations of the underlying quantum system that could be described by their own equations of motion. This was a major breakthrough in our understanding of condensed matter physics. It has been used to explain the behaviour of a wide variety of materials, including superconductors, semiconductors, insulators. Quasiparticles are now an essential part of the theoretical framework for understanding condensed matter physics.   Let us give important examples of how the idea of quasiparticles has been used to explain the behaviour of materials:

• Superconductors. In a superconductor, the electrons are able to move without any resistance. This is because they are paired up into what are called Cooper pairs. These Cooper pairs can be thought of as quasiparticles that are different from the electrons that make up the normal state of the material.
• Semiconductors and metals. In semiconductors and metals electrons can move through the ideal crystal without any resistivity, and in real crystals all the resistivity appears due to scattering of electrons on defects, and due to the oscillations of the crystal lattice (when the position of atoms is deflected from their equilibrium).

In this picture, electrons just ignore the atoms of the crystal, while one would think that those atoms also should be an obstacle for electrons. This is happening because electrons in solid state conductors are not the same electrons which we usually discuss in vacuum. Electrons in crystals are quasiparticles, which have a very different mass from the mass of the free electron, and in some exotic cases the even have a different charge (e.g. fractional quantum Hall effect).

The idea of quasiparticles is a powerful tool that has helped us to understand a wide variety of phenomena in condensed matter physics. It is likely to continue to play a major role in our understanding of this fascinating field of science.