# The Half-Filled Landau Level: The Case for Dirac Composite Fermions

**"All is well with particle-hole symmetry".** Roger Mong and colleagues accross the United States provided strong evidence for a recent conjecture that contrasts with the predictions of standard theory and predicts a liquid consisting of massless Dirac particles that respects the symmetry between particles and holes

In an external magnetic field, the energy of an electron in a two-dimensional system takes discrete values, called Landau levels. At high enough fields, all electrons in a solid can fit in the lowest Landau level. If exactly half of that level is filled with electrons, standard theory predicts that a special fermion liquid phase will form that makes a distinction between the filled and empty states (particles and holes). However, a recent conjecture, in contrast, predicted a liquid consisting of massless Dirac particles that respects the symmetry between particles and holes, for which the authors of this paper provided strong evidence.

__Abstract__: In a two-dimensional electron gas under a strong magnetic field, correlations generate emergent excitations distinct from electrons. It has been predicted that “composite fermions”—bound states of an electron with two magnetic flux quanta—can experience zero net magnetic field and form a Fermi sea. Using infinite-cylinder density matrix renormalization group numerical simulations, we verify the existence of this exotic Fermi sea, but find that the phase exhibits particle-hole symmetry. This is self-consistent only if composite fermions are massless Dirac particles, similar to the surface of a topological insulator. Exploiting this analogy, we observe the suppression of 2kF backscattering, a characteristic of Dirac particles. Thus, the phenomenology of Dirac fermions is also relevant to two-dimensional electron gases in the quantum Hall regime.

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