| In strongly correlated electron systems, charge, spin, orbital, and lattice degrees of freedom interact and compete with each other, which has been an attractive research direction so far. The macroscopic properties of these systems are determined by the collective behavior of the electrons, such as charge ordering, magnetic ordering, orbital ordering, etc. Therefore various electronic states and novel physical properties are presented in these systems. Up to now there is no theoretical frame that can universally describe the strongly correlated systems. Each system needs to be treated specifically, and compare the theoretical results with the experiments. The angle-resolved photoemission spectroscopy (ARPES) is a powerful, direct probe of momentum space, which directly gives the energy-momentum information of the valence electrons near the Fermi energy, while these electrons basically dominate the electrical, magnetic, optical, and thermal properties. The inelastic x-ray scattering (IXS) probes the correlation function of the system and gives information of the excited states, which is complementary to ARPES. This thesis introduces the ARPES studies of iron-based and nickel-based superconductors and IXS studies of low-dimensional carbon materials. Some results are concluded as follows:1. In EuFe2As2, ARPES measurements observe band folding, splitting, and shifts in the spin density wave (SDW) state, which cannot be explained by a simple folding picture of the itinerant electrons. The different properties of the Fermi surfaces at locations symmetric to M can be explained by the k-dependence of small Fermi surfaces, which agrees with the quantum oscillation measurements. Across the antiferromagnetic ordering of Eu2+ ions, no observable change is detected, thus the coupling between Eu layer and FeAs layer is weak. The systematic study of Eu1-xLaxFe2As2 shows that the band shifts intimately relate to the magnetic ordering.2. The electronic structure of BaNi2As2 is studies by ARPES, which shows distinct electronic structure from the 122 parent compounds of iron-based superconductors. The correlation in BaNi2As2 seems to be weaker than iron-based superconductors. No observed band folding proves that there is no long-range collinear magnetic ordering. Because of the intimate relation between magnetism and superconductivity, probably this is why the TC is so low in BaNi2As2. The band shifts in BaNi2As2 is accounted for by the large lattice distortion, however, the tiny lattice distortion in iron-based compounds cannot give rise to such large band shifts. The reasonable explanation left is that the band shifts in iron-based compounds are related to magnetism. 3. Fullerenes, such as C60 and carbon nanotubes, are studies by IXS. The experimental result of C60 has been compared to the theoretical calculation, which shows agreement for the peak positions. Weak dispersion is shown in the measurement of C60 single crystal. For vertically-aligned carbon nanotubes, dispersion ofπplasmon is extracted. The difference in IXS data between q(?) and q⊥modes is due to the alignment of the carbon nanotubes. |