\Pi }_{{\it 1}}C_{5}=-{\it \Pi }_{{\it 0}}\left( C_{6}+eC_{7}\right) 
\eqnum{3.24}$$

Eq. (3.24) has an important meaning, it establishes a connection between the coefficients of the long-range modes of the zero components of the gauge potentials $(C_{6}+eC_{7})$ and the coefficient of the long-range mode of the magnetic field $C_{5}$. Note that if the induced Chern-Simons coefficient ${\it \Pi }_{{\it 1}}$, or the Debye screening coefficient ${\it %
\Pi }_{{\it 0}}$ were zero, there would be no link between $C_{5}$ and $%
(C_{6}+eC_{7})$. This relation between the long-range modes of $B$, $A_{0}$ and $a_{0}$ can be interpreted as a sort of Aharonov-Bohm effect, which occurs in this system at finite temperature. At $T=0$, we have ${\it \Pi }_{%
{\it 0}}=0$, and the effect disappears.

Up to this point no boundary has been taken into account. Therefore, it is easy to understand that the magnetic long-range mode associated with the coefficient $C_{5}$, must be identified with the one found in ref. [@8] for the infinite bulk using a different approach. However, as it is shown below, when a constant and uniform magnetic field is perpendicularly applied at the boundaries of a two-dimensional sample, this mode cannot propagate (i.e. $C_{5}\equiv 0$) within the sample. This result 