ZERO-MODE LANDAU LEVEL OF 2D MASSLESS DIRAC FERMIONS

The investigation of quasiparticles in condensed matter has yielded remarkable insights into the behavior of massless Dirac fermions in two-dimensional systems. These fermions exhibit intriguing properties, including the existence of zero-mode Landau levels and the half-integer quantum Hall effect, which can be explained through the relativistic Dirac Hamiltonian. In contrast to Dirac fermions in a vacuum, the fermions in these systems possess spins that are inherent to the system. The Dirac Hamiltonian is dependent on the symmetries present in the system, with both spin and particle-hole symmetries resulting in half-filled ground states. Although the effective Hamiltonian for massless Dirac fermions is unbound at large momenta, its eigenstates are chiral, which results in an effective presence in d-dimensional space. In two-dimensional lattices without interaction and with spin-orbit coupling, Dirac points can be present, leading to a Dirac Hamiltonian based on two spinors. The graphene system serves as a prime example of such a system.