Composite fermions obey the Luttinger theorem and particle-hole symmetry precisely but show deviations from the Dirac theory.

When electrons confined to two dimensions get exposed to a perpendicular magnetic field, their kinetic energy is quenched. Consequently, a set of discrete energy levels, namely Landau levels form. Since there is no kinetic energy, these levels are flat as a function of momentum. Interestingly, when the lowest of these levels become half-filled, a surprise happens. Each electron then couple with two magnetic flux quanta and form a quasiparticle called composite fermion, which, to the first order, behaves as a free electron. This is weird! How can one have a free-moving particle in a system that has no kinetic energy? However, somehow, electron-electron interaction produces this strange state. what we find in our recent study is that these composite fermions can also interact strongly with one another. All we need to do to achieve this is to tune the density of the composite fermions. In other words, when we lower the density, composite fermions become interacting.

Amazingly, we can control the interaction strength just by tuning the density: The lower the density, the stronger the interaction.

To study composite fermions, we employ a geometric resonance technique, which provides a direct measure of the Fermi wave vector of the composite fermions. The key idea is simple: Thanks to the Lorentz force, composite fermions execute a cyclotron motion when a perpendicular magnetic field is applied. Next, we create a weak, one-dimensional periodic perturbation to the 2D electron system. If the composite fermions can complete a cyclotron orbit without scattering, then they exhibit a geometric resonance when their orbit diameter equals the period of the perturbation; this gives a measure of the Fermi wave vector.

Such direct measurements allow us to probe the physics of composite fermions when they interact strongly. A well-established theorem that describes the Fermi sea in the presence of interaction is the Luttinger theorem. It states that the area of the Fermi sea remains unchanged in the presence of interaction.

As a function of interaction strength (density of composite fermions), our measurements reveal that indeed the area of the composite fermion Fermi sea remains fixed to great precision.

We also experimentally show that the particle-hole symmetry is precisely obeyed in the composite fermion Fermi sea.

Note that, the particle-hole symmetry is the equivalence of physics between electrons and holes. Importantly, we find out that the density of the composite fermions is equal to the minority carrier density in the lowest Landau level. This means that when the Landau level is less than half-filled, then the density of composite fermion is equal to the density of electrons in the lowest Landau level. Conversely, when the Landau level is more than half-filled, then the density of composite fermion is equal to the hole density in the lowest Landau level. Surprisingly, this is very similar to p- or n-doped semiconductors! We also derive a mathematical expression and show that this simple “minority-carrier model” best fits the experimental data.

Particle-hole symmetry is usually associated with Dirac fermions (fermions with linear energy vs. momentum relation). Indeed there is a theory that proposes the composite fermions to be Dirac fermions. This theory has instigated many follow-up works and debates. In our paper, we clearly show that our experimental results deviate from the predictions of the Dirac theory. This implies that the composite fermion may not be a Dirac particle after all!

Even more profound, we show that the composite fermions do not have to be Dirac particles to obey the particle-hole symmetry. The particle-hole symmetry can also be valid within the “minority-carrier model.”

Our paper has been published in Physical Review Letters and got featured on their homepage as an Editor’s suggestion. Here is the link to the article: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.125.046601

Here is the arXiv version:[arXiv]