2 research outputs found
Massive Dirac fermions and the zero field quantum Hall effect
Through an explicit calculation for a Lagrangian in quantum electrodynamics
in (2+1)-space--time dimensions (QED), making use of the relativistic Kubo
formula, we demonstrate that the filling factor accompanying the quantized
electrical conductivity for massive Dirac fermions of a single species in two
spatial dimensions is a half (in natural units) when time reversal and parity
symmetries of the Lagrangian are explicitly broken by the fermion mass term. We
then discuss the most general form of the QED Lagrangian, both for
irreducible and reducible representations of the Dirac matrices in the plane,
with emphasis on the appearance of a Chern-Simons term. We also identify the
value of the filling factor with a zero field quantum Hall effect (QHE).Comment: 15 pages. Accepted in Jour. Phys.