The ground state and transport properties of the Lieb lattice flat band in the presence of an attractive Hubbard interaction are considered. It is shown that the superfluid weight can be large even for an isolated and strictly flat band. Moreover the superfluid weight is proportional to the interaction strength and to the quantum metric, a band structure quantity derived solely from the flat-band Bloch functions. These predictions are amenable to verification with ultracold gases and may explain the anomalous behaviour of the superfluid weight of high-Tc superconductors.

Bose-Einstein condensation is a remarkable manifestation of quantum statistics and macroscopic quantum coherence. Superconductivity and superfluidity have their origin in Bose-Einstein condensation. Ultracold quantum gases have provided condensates close to the original ideas of Bose and Einstein, while condensation of polaritons and magnons have introduced novel concepts of non-equilibrium condensation. Here, we demonstrate a Bose-Einstein condensate (BEC) of surface plasmon polaritons in lattice modes of a metal nanoparticle array. Interaction of the nanoscale-confined surface plasmons with a room-temperature bath of dye molecules enables thermalization and condensation in picoseconds. The ultrafast thermalization and condensation dynamics are revealed by an experiment that exploits thermalization under propagation and the open cavity character of the system. A crossover from BEC to usual lasing is realized by tailoring the band structure. This new condensate of surface plasmon lattice excitations has promise for future technologies due to its ultrafast, room-temperature and on-chip nature.Bosonic quantum statistics imply that below a certain critical temperature or above a critical density the occupation of excited states is strictly limited, and consequently, a macroscopic population of bosons accumulates on the ground state 1 . This phenomenon is known as Bose-Einstein condensation (BEC). Superconductivity of metals and high-temperature superconducting materials are understood as BEC of Cooper pairs 2, 3 . The BEC phenomenon is central in superfluidity of helium although the condensate constitutes a small fraction of the particles 4 . Textbook Bose-Einstein condensates with large condensate fractions and weak interactions were created with ultracold alkali atoms 5-7 , and the fundamental connection between the superfluidity of Cooper pairs and the Bose-Einstein condensation was confirmed by experiments with ultracold Fermi gases 3 . While all these condensates allow essentially equilibrium description, as was the original one by Bose and Einstein, the phenomenology has expanded to non-equilibrium systems [8][9][10][11][12] . Hybrid particles of semiconductor excitons and cavity photons, called exciton-polaritons, have shown condensation and interaction effects [13][14][15][16][17][18][19] , creating coherent light output that deviates from usual laser light. Magnons, that is, spin-wave excitations in magnetic materials 20, 21 , and photons in microcavities 22, 23 form condensates as well. The most technologically groundbreaking manifestation of macroscopic population due to bosonic statistics has so far been laser light, which is a highly non-equilibrium state not thermalized to a temperature of any reservoir. As the BEC phenomenon has been observed only in a limited number of systems, new ones are needed for pushing the time, temperature and spatial scales where a BEC can exist, as well as for opening viable routes to technological applications of BEC.Here we report the observation of BEC for bosonic quasip...

We study superconductivity of twisted bilayer graphene with local and non-local attractive interactions. We obtain the superfluid weight and Berezinskii-Kosterlitz-Thouless (BKT) transition temperature for microscopic tight-binding and low-energy continuum models. We predict qualitative differences between local and non-local interaction schemes which could be distinguished experimentally. In the flat band limit where the pair potential exceeds the band width we show that the superfluid weight and BKT temperature are determined by multiband processes and quantum geometry of the band.Recent experimental discoveries of superconductivity in bilayer graphene twisted close to a "magic angle" θ * [1-3] call for a reconsideration of traditional theories of superconductivity [4, 5], in particular because the superconductivity occurs in a regime where the non-interacting electronic states form an asymptotically flat (dispersionless) band [6][7][8][9][10][11][12][13][14][15][16][17]. As the system is two-dimensional, the transition to superconductivity is bound to occur at the Berezinskii-Kosterlitz-Thouless (BKT) temperature T BKT [18][19][20] which can be determined from k B T BKT = π 8 arXiv:1906.06313v3 [cond-mat.mes-hall]

Structuring metallic and magnetic materials on subwavelength scales allows for extreme confinement and a versatile design of electromagnetic field modes. This may be used, for example, to enhance magneto-optical responses, to control plasmonic systems using a magnetic field, or to tailor magneto-optical properties of individual nanostructures. Here we show that periodic rectangular arrays of magnetic nanoparticles display surface plasmon modes in which the two directions of the lattice are coupled by the magnetic field-controllable spin–orbit coupling in the nanoparticles. When breaking the symmetry of the lattice, we find that the optical response shows Fano-type surface lattice resonances whose frequency is determined by the periodicity orthogonal to the polarization of the incident field. In striking contrast, the magneto-optical Kerr response is controlled by the period in the parallel direction. The spectral separation of the response for longitudinal and orthogonal excitations provides versatile tuning of narrow and intense magneto-optical resonances.

We study the properties of a weakly interacting Bose-Einstein condensate (BEC) in a flat band lattice system by using the multiband Bogoliubov theory and discover fundamental connections to the underlying quantum geometry. In a flat band, the speed of sound and the quantum depletion of the condensate are dictated by the quantum geometry, and a finite quantum distance between the condensed and other states guarantees stability of the BEC. Our results reveal that a suitable quantum geometry allows one to reach the strong quantum correlation regime even with weak interactions.