Phase diagram of a DMS quantum well, using the parameters described in the text. Full and broken lines represent
first and secondorder phase transitions, respectively, between ferromagnetic (F) and paramagnetic (P) phases. In the inset we
show the carrier spin polarization for two different densities. The broken line corresponds to k_{F} = 0.2 nm^{1}, in this case there is
a firstorder transition between the x = 1 ferromagnetic phase and the paramagnetic phase. The continuous line corresponds to
k_{F} = 0.39 nm^{1}. Upon lowering the temperature we obtain a continuous transition between the P and the F phases followed by
an abrupt transition between two F phases with different values of x . As commented in the text, this last
transition is probably spurious.
(Brey and Guinea [2000]) 

Phase diagram of a DMS quantum well as a function of T and magnetic field for a hole density such that
k_{F} = 0.2 nm^{1}.
The line separating the fully polarized from the partially polarized system represents a firstorder transition.
(Brey and Guinea [2000]) 
Dispersion relation \
w versus q^{ }a for surface and bulk
magnetoplasmons due to the intra and interLandau levels (lefthand side and righthand side),
where the w_{ij+} and
w_{ij} are maximum and minimum dispersion energy of the bulk magnetoplasmon
modes, respectively, and the w_{ijS}
is the dispersion energy of the surface magnetoplasmon modes. Here i and j represent the Landau
level index, respectively.
The values of the parameters are as follows:
n = 7.7x10^{11} cm^{2}, a = 82.7 nm,
L = 30 nm, m= 0.0665 m_{0} ,
e = 13.1,
e_{0} = 1.0, and
E_{ij} = (ij)hw
(Haeng Lee et al. [2001]) 

Dispersion relation hw
versus the strength of magnetic field B for surface and bulk magnetoplasmons due to the intra and interLandau levels (lefthand side and righthand side).
The values of the parameters are as follows:
n = 7.7x10^{11} cm^{2}, a = 82.7 nm,
L = 30 nm, m= 0.0665 m_{0} ,
e = 13.1,
e_{0} = 1.0, and
E_{ij} = (ij)hw
(Haeng Lee et al. [2001]) 

Dispersion relation hw
versus the ratio of the confining
potential parameter to cyclotron resonance frequency w_{z}/w_{c}
for surface and bulk magnetoplasmons due to the intra and interLandau
levels (lefthand side and righthand side).
The values of the parameters are as follows:
n = 7.7x10^{11} cm^{2}, a = 82.7 nm,
L = 30 nm, m= 0.0665 m_{0} ,
e = 13.1,
e_{0} = 1.0, and
E_{ij} = (ij)hw
(Haeng Lee et al. [2001]) 

Raman intensities for surface and bulk magnetoplasmons
due to the interLandau levels at a specific value of qa = 3.0 and
k_{z} = 2pa/5.
The values of the parameters are as follows:
l = a2d = L, N = 40
and g = 0.02 meV.
(Haeng Lee et al. [2001]) 
The 2D average interparticle distance versus the magnetic
field for the exciton, and the singlet and triplet states of the
charged exciton in a quantum well of width 100 Å.
(Riva et al. [2001]) 

The 2D pair correlation function versus the magnetic field for the exciton and the spinsinglet and spintriplet states of a
charged exciton in a 100 Å wide quantum well.
(Riva et al. [2001]) 

Comparison between the experimental and theoretical transition energies for charged excitons and excitons in a 300 Å
wide quantum well. The open symbols are the experimental results for B > 8 T shifted by 0.5 meV.
(Riva et al. [2001]) 

Comparison between the experimental and the theoretical transition energies for charged excitons and excitons in a 100 Å
wide quantum well. For clarity, the low magnetic field region are shown.
The symbols are the experimental results.
(Riva et al. [2001]) 

Comparison between the experimental and the theoretical transition energies for charged excitons and excitons in a 100 Å
wide quantum well. For clarity, the high magnetic field region are shown.
The symbols are the experimental results.
(Riva et al. [2001]) 

The binding energy of a charged exciton in a 300 Å.
(Riva et al. [2001]) 

The binding energy of a charged exciton in a 100 Å wide quantum well calculated using the symmetric hole mass approximation
(thick curves) and the asymmetric hole mass approximation (thin curves).
(Riva et al. [2001]) 

Comparison of the difference in energy between the
upper and lower s^{ } transition lines (symbols) with our
theoretical binding energy for the negative trion singlet state (solid curve), the energy difference between our theoretical dark triplet
and singlet states (dashed curve), and the energy difference between our bright triplet and singlet states (dotted curve).
(Riva et al. [2001]) 