Rm. Cavalcanti et Caa. Decarvalho, 2-DIMENSIONAL ELECTRON-GAS IN A UNIFORM MAGNETIC-FIELD IN THE PRESENCE OF A DELTA-IMPURITY, Journal of physics. A, mathematical and general, 31(10), 1998, pp. 2391-2399
The density of states and the Hall conductivity of a two-dimensional e
lectron gas in a uniform magnetic field and in the presence of a delta
-impurity are exactly calculated using elementary field theoretic tech
niques. The impurity creates one localized state per Landau level, but
the Hall conductivity is unaffected. Our treatment is explicitly gaug
e invariant, and can be easily adapted to other problems involving zer
o-range potentials.