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Register a new userSpectral and transport properties of the two-dimensional Lieb lattice
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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.
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We study the condensation of exciton-polaritons in a two-dimensional Lieb lattice of micropillars. We show selective polariton condensation into the flatbands formed by S and P$_{x;y}$ orbital modes of the micropillars under non-resonant laser excitation. The real space mode patterns of these condensates are accurately reproduced by the calculation of related Bloch modes of S- and P-flatbands. Our work emphasizes the potential of exciton-polariton lattices to emulate Hamiltonians of advanced potential landscapes. Furthermore, the obtained results provide a deeper inside into the physics of flatbands known mostly within the tight-binding limit.
We study exciton-polaritons in a two-dimensional Lieb lattice of micropillars. The energy spectrum of the system features two flat bands formed from $S$ and $P_{x,y}$ photonic orbitals, into which we trigger bosonic condensation under high power excitation. The symmetry of the orbital wave functions combined with photonic spin-orbit coupling gives rise to emission patterns with pseudospin texture in the flat band condensates. Our work shows the potential of polariton lattices for emulating flat band Hamiltonians with spin-orbit coupling, orbital degrees of freedom and interactions.
We study the localization properties of the two-dimensional Lieb lattice and its extensions in the presence of disorder using transfer matrix method and finite-size scaling. We find that all states in the Lieb lattice and its extensions are localized for $W geq 1$. Clear differences in the localization properties between disordered flat band and disordered dispersive bands are identified. Our results complement previous experimental studies of clean photonic Lieb lattices and provide information about their stability with respect to disorder.
We have studied the energy spectrum of a one-dimensional Kondo lattice, where the localized magnetic moments have SU(N) symmetry and two channels of conduction electrons are present. At half filling, the system is shown to exist in two phases: one dominated by RKKY-exchange interaction effects, and the other by Kondo screening. A quantum phase transition point separates these two regimes at temperature $T = 0$. The Kondo-dominated phase is shown to possess soft modes, with spectral gaps much smaller than the Kondo temperature.
In recent years, novel two-dimensional materials such as graphene, bismuthene and transition-metal dichalcogenides have attracted considerable interest due to their unique physical properties. A range of physical effects can be transferred to the realms of photonics by creating artificial photonic lattices emulating these two-dimensional materials. Here, exciton-polaritons in semiconductor microcavities offer an exciting opportunity to study a part-light, part-matter quantum fluid of light in a complex lattice potential. In this paper, we study exciton-polaritons in a two-dimensional Lieb lattice of buried optical traps. The $S$ and $P_{xy}$ photonic orbitals of such a Lieb lattice give rise to the formation of two flatbands which are of greatest interest for the distortion-free storage of compact localized states. By using a well controlled etch-and-overgrowth technique, we manage to control the trapping as well as the site couplings with great precision. This allows us to spectroscopically monitor the flatness of the flatbands across the full Brillouin zone. Furthermore, we demonstrate experimentally that these flatbands can be directly populated by condensation under non-resonant laser excitation. Finally, using this advanced device approach we demonstrate resonant and deterministic excitation of flatband modes in transmission geometry. Our findings establish the exciton-polariton systems as a highly controllable, optical many-body system to study flatband effects and for distortion-free storage of compact localized states.
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