First-principles calculations are used to establish that the electronic structure of graphene ribbons with zigzag edges is unstable with respect to magnetic polarization of the edge states. The magnetic interaction between edge states is found to be remarkably long ranged and intimately connected to the electronic structure of the ribbon. Various treatments of electronic exchange and correlation are used to examine the sensitivity of this result to details of the electron-electron interactions, and the qualitative features are found to be independent of the details of the approximation. The possibility of other stablization mechanisms, such as charge ordering and a Peierls distortion, are explicitly considered and found to be unfavorable for ribbons of reasonable width. These results have direct implications for the control of the spin-dependent conductance in graphitic nanoribbons using suitably modulated magnetic fields.

We consider the BCS-BEC (Bose-Einstein-condensate) crossover for a system of trapped Fermi atoms at finite temperature, both below and above the superfluid critical temperature, by including fluctuations beyond mean field. We determine the superfluid critical temperature and the pair-breaking temperature as functions of the attractive interaction between Fermi atoms, from the weak- to the strong-coupling limit (where bosonic molecules form as bound-fermion pairs). Density profiles in the trap are also obtained for all temperatures and couplings.

The BCS-BEC crossover is studied in a systematic way in the broken-symmetry phase between zero temperature and the critical temperature. This study bridges two regimes where quantum and thermal fluctuations are, respectively, important. The theory is implemented on physical grounds, by adopting a fermionic self-energy in the broken-symmetry phase that represents fermions coupled to superconducting fluctuations in weak coupling and to bosons described by the Bogoliubov theory in strong coupling. This extension of the theory beyond mean field proves important at finite temperature, to connect with the results in the normal phase. The order parameter, the chemical potential, and the single-particle spectral function are calculated numerically for a wide range of coupling and temperature. This enables us to assess the quantitative importance of superconducting fluctuations in the broken-symmetry phase over the whole BCS-BEC crossover. Our results are relevant to the possible realizations of this crossover with high-temperature cuprate superconductors and with ultracold fermionic atoms in a trap.

Theoretical calculations, based on hybrid exchange density functional theory, are used to show that in graphene a periodic array of defects generates a ferromagnetic ground state at room temperature for unexpectedly large defect separations. This is demonstrated for defects that consist of a carbon vacancy in which two of the dangling bonds are saturated with H atoms. The magnetic coupling mechanism is analysed and found to be due to an instability in the π electron system with respect to a long-range spin polarisation characterised by alternation in the spin direction between adjacent carbon atoms. The disruption of the π-bonding opens a semiconducting gap at the Fermi edge. The size of the energy gap and the magnetic coupling strength are strong functions of the defect separation and can thus be controlled by varying the defect concentration. The position of the semiconducting energy gap and the electron effective mass are strongly spin-dependent and this is expected to result in a spin asymmetry in the transport properties of the system. A defective graphene sheet is therefore a very promising material with an in-built mechanism for tailoring the properties of the spintronic devices of the future.

We have studied the electronic structure of the spin-1/2 quantum magnet TiOCl by polarizationdependent momentum-resolved photoelectron spectroscopy. From that, we confirm the quasi-onedimensional nature of the electronic structure along the crystallographic b-axis and find no evidence for sizable phonon-induced orbital fluctuations as origin for the non-canonical phenomenology of the spin-Peierls transition in this compound. A comparison of the experimental data to our own LDA+U and Hubbard model calculations reveals a striking lack of understanding regarding the quasi-one-dimensional electron dispersions in the normal state of this compound.