POUX, A.; POUX, Armelle.
Resumen:
Condensed Matter physics is a branch of Physics which includes the laws of quantum
mechanics, electromagnetism and statistical mechanics. In this area, we consider a
two-dimensional electron gas (2DEG), which can be defined as a system of electrons
that are confined by opposing forces to a thin planar region.
Nowadays, it is more interesting to study the impact of the geometry or of some
topological defects introduced on the sample, to get closer of reality.
In the work that we have proposed to realize, we have considered a sample immersed
on a magnetic field. Or more simply, we wanted to study the Hall effect for particular
cases, on usual semiconductors. In fact, we have tried to understand how we can
influence the behavior of the Hall conductivity, with a curved surface (rather than
the flat case) and by introducing some topological defects.
In a first work, we have considered the single cone immersed into a magnetic
field. We realized that we can consider the conical tip in two different ways : with
and without a singularity at the tip. We saw that we obtained different Landau
Levels LL, which change the type of plateaus that we obtain and the shifting in the
Hall conductivity. After discussing this, we changed some parameters (the opening
angle α of the cone, the geometric potential) to see how this influenced the Hall conductivity
when we varied the magnetic field. We compared two types of geometric
models : the da Costa and the Dirac models.
In a second work, we have studied the effect of a screw dislocation on the Hall
conductivity. For that, we have changed the torsion parameter of the medium β.
We did not observe any shift of the Hall conductivity, but we noticed a change of
the size of the conduction plateaus. In order to appreciate the presence of both a
screw dislocation and a disclination, we have considered a 2DEG with a dispiration.
By changing α, which is the deficit/excess angle, we obtained, this time, a shift of
the Hall conductivity.
In summary, we tried to explain the behaviour of the Hall conductivity in the
presence of singularities and how taking into account the geometry is important.