Symmetry

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

  • By Aude Marjolin
  • 13 April 2016

"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.