The half-filled Landau level: The case for Dirac composite fermions

Abstract

All is well with particle-hole symmetry 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). A recent conjecture, in contrast, predicted a liquid consisting of massless Dirac particles that respects the symmetry between particles and holes. Geraedts et al. used sophisticated numerical methods to provide strong evidence for this conjecture. Science , this issue p. 197