The specific topology of the line centered square lattice (known also as the Lieb lattice) induces remarkable spectral properties as the macroscopically degenerated zero energy flat band, the Dirac cone in the low energy spectrum, and the peculiar Hofstadter-type spectrum in magnetic field. We study here the properties of the finite Lieb lattice with periodic and vanishing boundary conditions. We find out the behavior of the flat band induced by disorder and external magnetic and electric fields. We show that in the confined Lieb plaquette threaded by a perpendicular magnetic flux there are edge states with nontrivial behavior. The specific class of twisted edge states, which have alternating chirality, are sensitive to disorder and do not support IQHE, but contribute to the longitudinal resistance. The symmetry of the transmittance matrix in the energy range where these states are located is revealed. The diamagnetic moments of the bulk and edge states in the Dirac-Landau domain, and also of the flat states in crossed magnetic and electric fields are shown.

A detailed description of the tunneling processes within Aharonov-Bohm (AB) rings containing two-dimensional quantum dots is presented. We show that the electronic propagation through the interferometer is controlled by the spectral properties of the embedded dots and by their coupling with the ring. The transmittance of the interferometer is computed by the Landauer-Büttiker formula. Numerical results are presented for an AB interferometer containing two coupled dots. The charging diagrams for a double-dot interferometer and the Aharonov-Bohm oscillations are obtained, in agreement with the recent experimental results of Holleitner et al. [Phys. Rev. Lett. 87, 256802 (2001)] We identify conditions in which the system shows Fano line shapes. The direction of the asymetric tail depends on the capacitive coupling and on the magnetic field. We discuss our results in connection with the experiments of Kobayashi et al. [Phys. Rev. Lett. 88, 256806 (2002)] in the case of a single dot. ©2005 The American Physical Society

Spectral and transport properties of electrons in confined phosphorene systems are investigated in a five hopping parameter tight-binding model, using analytical and numerical techniques. The main emphasis is on the properties of the topological edge states accommodated by the quasi-flat band that characterizes the phosphorene energy spectrum.We show, in the particular case of phosphorene, how the breaking of the bipartite lattice structure gives rise to the electron-hole asymmetry of the energy spectrum. The properties of the topological edge states in the zig-zag nanoribbons are analyzed under different aspects: degeneracy, localization, extension in the Brillouin zone, dispersion of the quasi-flat band in magnetic field.The finite-size phosphorene plaquette exhibits a Hofstadter-type spectrum made up of two unequal butterflies separated by a gap, where a quasi-flat band composed of zig-zag edge states is located.The transport properties are investigated by simulating a four-lead Hall device (importantly, all leads are attached on the same zig-zag side), and using the Landauer-Büttiker formalism. We find out that the chiral edge states due to the magnetic field yield quantum Hall plateaus, but the topological edge states in the gap do not support the quantum Hall effect and prove a dissipative behavior. By calculating the complex eigenenergies of the non-Hermitian effective Hamiltonian that describes the open system (plaquette+leads), we prove the superradiance effect in the energy range of the quasi-flat band, with consequences for the density of states and electron transmission properties.

We calculate the orbital magnetization of single and double quantum dots coupled both by Coulomb interaction and by electron tunneling. The electronic states of the quantum dots are calculated in a tight-binding model, and the magnetization is discussed in relation to the energy spectrum and to the edge and bulk states. We identify effects of chirality of the electronic orbits and of the anticrossing of the energy levels when the magnetic field is varied. We also consider the effects of detuning the energy spectra of the quantum dots by an external gate potential. We compare our results with the recent experiments of Oosterkamp et al. ͓Phys. Rev. Lett. 80, 4951 ͑1998͔͒.

We apply the Keldysh formalism in order to derive a current formula easy to use for a system with many sites, one of which is interacting. The main technical challenge is to deal with the lesser Green function. It turns out that, in the case of the left-right symmetry, the knowledge of the lesser Green function is not necessary and an exact current formula can be expressed in terms of retarded Green functions only. The application is done for a triangular interferometer which gives a good account of the Fano-Kondo effect. It is found that the interference effects, in the context of Kondo correlations, give rise to a point in the parameters space where the conductance is temperature-independent. We include a comparison with the results from the Ng's ansatz, which are less accurate, but can be used also in the absence of the above mentioned symmetry.