Topological invariants built from the periodic Bloch functions characterize new phases of matter, such as topological insulators and superconductors. The most important invariant is Chern number that explains quantized conductance quantum Hall effect. Here, we provide a general result for superfluid weight $D_{\rm s}$ multiband superconductor applicable to topologically nontrivial bands with nonzero $C$. We find integral over Brillouin zone metric, an calculated functions, gives in flat...

Metal nanoparticle arrays that support surface lattice resonances have emerged as an exciting platform for manipulating light–matter interactions at the nanoscale and enabling a diverse range of applications. Their recent prominence can be attributed to combination desirable photonic plasmonic attributes: high electromagnetic field enhancements extended over large volumes with long-lived lifetimes. This Review will describe design rules achieving high-quality optical responses from metal...

We show strong coupling involving three different types of resonances in plasmonic nanoarrays: surface lattice (SLRs), localized plasmon on single nanoparticles, and excitations organic dye molecules. The measured transmission spectra splittings that depend the molecule concentration. results are analyzed using finite-difference time-domain simulations, a coupled-dipole approximation, coupled-modes models, Fano theory. delocalized nature collective SLR modes suggests regime molecules near...

We report on strong coupling between surface-plasmon polaritons (SPP) and Rhodamine 6G (R6G) molecules, with double vacuum Rabi splitting energies up to 230 110 meV. In addition, we demonstrate the emission of all three energy branches strongly coupled SPP-exciton hybrid system, revealing features system dynamics that are not visible in conventional reflectometry. Finally, analogy tunable-Q microcavities, show can be controlled by adjusting interaction time waveguided SPPs R6G deposited top...

DNA origami structures can be programmed into arbitrary shapes with nanometer scale precision, which opens up numerous attractive opportunities to engineer novel functional materials. One intriguing possibility is use origamis for fully tunable, targeted, and triggered drug delivery. In this work, we demonstrate the coating of nanostructures virus capsid proteins enhancing cellular Our approach utilizes purified cowpea chlorotic mottle that bind self-assemble on surface through electrostatic...

Abstract Lasing at the nanometre scale promises strong light-matter interactions and ultrafast operation. Plasmonic resonances supported by metallic nanoparticles have extremely small mode volumes high field enhancements, making them an ideal platform for studying nanoscale lasing. At visible frequencies, however, applicability of plasmon is limited due to ohmic radiative losses. Intriguingly, plasmonic nanoparticle arrays support non-radiative dark modes that offer longer life-times but are...

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

We present a theory of the superfluid weight in multiband attractive Hubbard models within Bardeen-Cooper-Schrieffer (BCS) mean field framework. show how to separate geometric contribution from conventional one, and that is associated with interband matrix elements current operator. Our can be applied systems or without time reversal symmetry. In both cases related quantum metric corresponding noninteracting systems. This leads lower bound on given by absolute value Berry curvature. apply...

We study superconductivity of twisted bilayer graphene with local and non-local attractive interactions. obtain the superfluid weight Berezinskii-Kosterlitz-Thouless (BKT) transition temperature for microscopic tight-binding low-energy continuum models. predict qualitative differences between interaction schemes which could be distinguished experimentally. In flat band limit where pair potential exceeds width we show that BKT are determined by multiband processes quantum geometry band.

Flat band systems such as twisted bilayer graphene superconduct thanks to nontrivial wave functions. The work here relates the superfluid weight and Cooper pair mass in isolated flat bands new concept of minimal quantum metric, solving an underappreciated, yet crucial issue previous work. Moreover, authors demonstrate that do not need be energetically maximize critical temperature, showing many more materials are candidates for superconductivity at elevated temperatures.

Quantum geometry defines the phase and amplitude distances between quantum states. The distance is characterized by Berry curvature thus relates to topological phenomena. significance of full geometry, including metric, has started receive attention in last few years. Various transport interaction phenomena have been found be critically influenced geometry. For example, allows counterintuitive flow supercurrent a flat band where single electrons are immobile. In this Essay, I will discuss my...

We study spatial coherence properties of a system composed periodic silver nanoparticle arrays covered with fluorescent organic molecule (DiD) film. The evolution this composite structure from the weak to strong coupling regime is investigated by systematically varying strength between localized DiD excitons and collective, delocalized modes array known as surface lattice resonances. A gradual observed, features clearly visible in interference fringes. high degree demonstrated regime, even...

Abstract Structuring metallic and magnetic materials on subwavelength scales allows for extreme confinement a versatile design of electromagnetic field modes. This may be used, example, to enhance magneto-optical responses, control plasmonic systems using field, or tailor properties individual nanostructures. Here we show that periodic rectangular arrays nanoparticles display surface plasmon modes in which the two directions lattice are coupled by field-controllable spin–orbit coupling...

Plasmonic nanoarrays which support collective surface lattice resonances (SLRs) have become an exciting frontier in plasmonics. Compared with the localized plasmon resonance (LSPR) individual particles, these modes appealing advantages such as angle-dependent dispersions and much narrower linewidths. Here, we investigate systematically how geometry of affects SLRs supported by metallic nanoparticles. We present a general theoretical framework from various SLR given can be straightforwardly...

The right-handed twist along aqueous dispersed cellulose nanocrystals allows chiral plasmonics upon electrostatic binding of gold nanoparticles in dilute environment, through tuning the particle sizes and concentrations. Simulations using nanoparticle coordinates from cryo-electron tomography confirm experimental results. finding suggests generalization for other helical colloidal templates nanoscale plasmonics.

We consider two-body bound states in a flat band of multiband system. The existence pair dispersion predicts the possibility breaking degeneracy and creating order, such as superconductivity. Within separable interaction potential approximation, we find that finiteness effective mass is determined by band-structure invariant, which uniform case becomes quantum metric. results offer simple foundation to understand predict flat-band propose an experiment test interaction-induced motion.

In a partially filled flat Bloch band electrons do not have well defined Fermi surface and hence the low-energy theory is liquid. Nevertheless, under influence of an attractive interaction, superconductor described by Bardeen-Cooper-Schrieffer (BCS) wave function can arise. Here we study effective Hamiltonian generic Hubbard model with band. We obtain for physics eliminating higher-lying bands via perturbative Schrieffer-Wolff transformation. At first order in interaction energy recover...

In a flat Bloch band the kinetic energy is quenched and single particles cannot propagate since they are localized due to destructive interference. Whether this remains true in presence of interactions challenging question because dispersion usually leads highly correlated ground states. Here we compute numerically state lattice models with completely structure ring geometry. We find that as function magnetic flux threading has half-flux quantum $\Phi_0/2 = hc/(2e)$ period, indicating only...

Using dynamical mean-field theory and exact diagonalization we study the phase diagram of repulsive Haldane-Hubbard model, varying interaction strength sublattice potential difference. In addition to quantum Hall with Chern number $C=2$ band insulator $C=0$ present already in noninteracting system also exhibits a Mott insulating phase, $C=1$ phase. We explain latter by spontaneous symmetry breaking where one spin-components is state other state.

We study lasing at the high-symmetry points of Brillouin zone in a honeycomb plasmonic lattice. use symmetry arguments to define singlet and doublet modes $\Kp$-points reciprocal space. experimentally demonstrate \changed{that is based on lattice two-dimensional feedback}. By comparing polarization properties \changed{$T$-matrix} simulations, we identify mode as one singlets with an energy minimum $\Kp$-point enabling feedback. Our results offer prospects for studies topological radiatively...

Plasmonic lattices of metal nanoparticles have emerged as an effective platform for strong light-matter coupling, lasing, and Bose-Einstein condensation. However, the full potential complex unit cell structures has not been exploited. On other hand, bound states in continuum (BICs) attracted attention, they provide topologically protected optical modes with diverging quality factors. Here, we show that quadrumer nanoparticle enable lasing a quasi-BIC mode highly out-of-plane character. By...