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The high-spectral-resolution spectroscopic studies of the energy gap evolution, supplemented with electronic, magnetic and structural characterization, show that the modification of the GaAs valence band caused by Mn incorporation occurs already for a very low Mn content, much lower than that required to support ferromagnetic spin - spin coupling in (Ga,Mn)As. Only for n-type (Ga,Mn)As with the Mn content below about 0.3% the Mn-related extended states are visible as a feature detached from the valence-band edge and partly occupied with electrons. The combined magnetic and low-temperature photoreflectance studies presented here indicate that the paramagnetic - ferromagnetic transformation in p-type (Ga,Mn)As takes place without imposing changes of the unitary character of the valence band with the Fermi level located therein. The whole process is rooted in the nanoscale fluctuations of the local (hole) density of states and the formation of a superparamagnetic-like state. The Fermi level in (Ga,Mn)As is coarsened by the carrier concentration of the itinerant valence band holes and further fine-tuned by the many-body interactions.

The diluted (Ga,Mn)As became a model ferromagnetic semiconductor, however there is still a disagreement on the source of its magnetism. The divergences arise from the results indicating that the holes mediated ferromagnetism reside in the valence band or the impurity band. Full understanding of character of the Mn states in GaAs can bring the increase of (Ga,Mn)As Curie temperature. In this paper we verify the ellipsometric results and compare with more precise photoreflectance method which gives a new insight into the interactions of Mn impurity states with GaAs valence band. Indeed, $E_{1}$ and $E_{1}$+${\Delta}_{1}$ inter-band transition energies for highly doped and annealed (Ga,Mn)As epitaxial layers have not confirmed the interaction between detached Mn impurity band and the valence band. Thus, the description with merged Mn states and GaAs valence band is in agreement with our results. Our findings are supported by the high resolution transmission microscopy and magnetization measurements.

The effect of outdiffusion of Mn interstitials from (Ga,Mn)As epitaxial layers, caused by post-growth low-temperature annealing, on their electronic- and band-structure properties has been investigated by modulation photoreflectance (PR) spectroscopy. The annealing-induced changes in structural and magnetic properties of the layers were examined with high-resolution X-ray diffractometry and SQUID magnetometery, respectively. They confirmed an outdiffusion of Mn interstitials from the layers and an enhancement in their hole concentration, which were more efficient for the layer covered with a Sb cap acting as a sink for diffusing Mn interstitials. The PR results revealing a decrease in the band-gap-transition energy in the as-grown (Ga,Mn)As layers, with respect to that in the reference GaAs one, are interpreted by assuming a merging of the Mn-related impurity band with the host GaAs valence band. On the other hand, an increase in the band-gap-transition energy in the annealed (Ga,Mn)As layers is interpreted as a result of the Moss-Burstein shift of the absorption edge due to the Fermi level location within the valence band, determined by the enhanced free-hole concentration. The experimental results are consistent with the valence-band origin of mobile holes mediating ferromagnetic ordering in (Ga,Mn)As, in agreement with the Zener model for ferromagnetic semiconductors., Comment: 17 pages, 4 figures. arXiv admin note: substantial text overlap with arXiv:1305.4056

Modulation photoreflectance spectroscopy and Raman spectroscopy have been applied to study the electronic- and band-structure evolution in (Ga,Mn)As epitaxial layers with increasing Mn doping in the range of low Mn content, up to 1.2%. Structural and magnetic properties of the layers were characterized with high-resolution X-ray diffractometry and SQUID magnetometery, respectively. The revealed results of decrease in the band-gap transition energy with increasing Mn content in very low-doped (Ga,Mn)As layers with n-type conductivity are interpreted as a result of merging the Mn-related impurity band with the host GaAs valence band. On the other hand, an increase in the band-gap-transition energy with increasing Mn content in (Ga,Mn)As layers with higher Mn content and p-type conductivity indicates the Moss-Burstein shift of the absorption edge due to the Fermi level location within the valence band, determined by the free-hole concentration. The experimental results are consistent with the valence-band origin of mobile holes mediated ferromagnetic ordering in the (Ga,Mn)As diluted ferromagnetic semiconductor., Comment: 20 pages, 5 figures. arXiv admin note: text overlap with arXiv:1012.4760

Fundamental optical properties of thin films of (Ga,Mn)As diluted ferromagnetic semiconductor with a low (1%) and high (6%) Mn content and of a reference GaAs film, grown by low-temperature molecular-beam epitaxy, have been investigated by photoreflectance (PR) spectroscopy. In addition, the films were subjected to complementary characterization by means of superconducting quantum interference device (SQUID) magnetometry, Raman spectroscopy, and high resolution X-ray diffractometry. Thorough full-line-shape analysis of the PR spectra, which enabled determination of the E0 electronic transition in (Ga,Mn)As, revealed significant differences between the energy band structures in vicinity of the {\Gamma} point of the Brillouin zone for the two (Ga,Mn)As films. In view of the obtained experimental results the evolution of the valence band structure in (Ga,Mn)As with increasing Mn content is discussed, pointing to a merging the Mn-related impurity band with the host GaAs valence band for high Mn content., Comment: 21 pages, 6 figures

We study the ensemble-averaged conductance as a function of applied magnetic field for ballistic electron transport across few-channel microstructures constructed in the shape of classically chaotic billiards. We analyse the results of recent experiments, which show suppression of weak localization due to magnetic field, in the framework of random-matrix theory. By analysing a random-matrix Hamiltonian for the billiard-lead system with the aid of Landauer's formula and Efetov's supersymmetry technique, we derive a universal expression for the weak-localization contribution to the mean conductance that depends only on the number of channels and the magnetic flux. We consequently gain a theoretical understanding of the continuous crossover from orthogonal symmetry to unitary symmetry arising from the violation of time-reversal invariance for generic chaotic systems., Comment: 49 pages, latex, 9 figures as tar-compressed uuencoded file