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We experimentally study the propagation of microwaves in an artificial honeycomb lattice made of dielectric resonators. This evanescent propagation is well described by a tight-binding model, very much like the propagation of electrons in graphene. We measure the density of states, as well as the wave function associated with each eigenfrequency. By changing the distance between the resonators, it is possible to modulate the amplitude of next-(next-)nearest-neighbor hopping parameters and to study their effect on the density of states. The main effect is the density of states becoming dissymmetric and a shift of the energy of the Dirac points. We study the basic elements: an isolated resonator, a two-level system, and a square lattice. Our observations are in good agreement with analytical solutions for corresponding infinite lattice. [ABSTRACT FROM AUTHOR]

We report on the measurement of phase coherence length in a high-mobility two-dimensional electron gas patterned in two different geometries, a wire and a ring. The phase coherence length is extracted both from the weak localization correction in long wires and from the amplitude of the Aharonov-Bohm oscillations in a single ring, in a low-temperature regime when decoherence is dominated by electronic interactions. We show that these two measurements lead to different phase coherence lengths, namely LΦwire ∝ T-1/3 and LΦring ∝ T-1/2. This difference reflects the fact that the electrons winding around the ring necessarily explore the whole sample (ergodic trajectories), while in a long wire the electrons lose their phase coherence before reaching the edges of the sample (diffusive regime). [ABSTRACT FROM AUTHOR]

We develop a gauge-independent perturbation theory for the grand potential of itinerant electrons in twodimensional tight-binding models in the presence of a perpendicular magnetic field. At first order in the field, we recover the result of the so-called modern theory of orbital magnetization and, at second order, deduce a new general formula for the orbital susceptibility. In the special case of two coupled bands, we relate the susceptibility to geometrical quantities such as the Berry curvature. Our results are applied to several two-band systems-either gapless or gapped. We point out some surprising features in the orbital susceptibility-such as in-gap diamagnetism and parabolic band-edge paramagnetism-coming from interband coupling. From this we draw general conclusions on the orbital magnetism of itinerant electrons in multiband tight-binding models. [ABSTRACT FROM AUTHOR]