It is shown that, for the t-J model, dilute holes in an antiferromagnet are unstable against phase separation into a hole-rich and a no-hole phase. %'hen the spin-exchange interaction J exceeds a critical value J"the hole-rich phase has no electrons. It is proposed that for I slightly less than I, the hole-rich phase is a low-density superfluid of electron pairs. A brief discussion of phase separation in other related models is given.

The surface-plasmon properties of Au bipyramids are investigated using the finite-difference time-domain method. It is found that both the extinction cross sections and local electric-field enhancements of Au bipyramids are larger than those of Au nanorods that have longitudinal surface plasmon (LSP) wavelengths close to those of Au bipyramids. Following this result the growth of Au bipyramids using cationic surfactants of variously sized headgroups as stabilizing agents is carried out. It is found that the growth using cetyltributylammonium bromide (CTBAB) produces Au bipyramids with tunable LSP wavelengths in high yields. The oxidation behaviour of Au bipyramids using hydrogen peroxide as the oxidizing agent is fully explored and the oxidation is found to occur preferentially at highly curved surface sites. It is further demonstrated that the oxidation rate can be controlled by varying the amounts of hydrogen peroxide and hydrochloric acid. This oxidation approach can be used in conjunction with the seed-mediated growth in CTBAB solutions to produce Au bipyramids, the LSP wavelengths of which are finely tunable from 650 to 1300 nm.

The plasmon coupling in the dimers of Au nanorods linked together at their ends with dithiol molecules has been studied. The plasmon coupling in the dimers composed of similarly sized nanorods gives antibonding and bonding plasmon modes. The plasmon wavelengths of the two modes have been found to remain approximately unchanged, with the scattering intensity ratio between the antibonding and bonding modes decaying rapidly as the angle between the nanorods is increased. This plasmon coupling behavior agrees with that obtained from both electrodynamic calculations and modeling on the basis of the dipole-dipole interaction. The electric field in the gap region is largely enhanced for the bonding mode, while that for the antibonding mode is even smaller than the far field, highlighting the importance of selecting appropriate plasmon modes for plasmon-enhanced spectroscopies. An anti-crossing-like behavior in the plasmon coupling energy diagram has further been revealed for linearly end-to-end assembled dimers composed of differently sized nanorods. This result will be useful for plasmonic applications where the plasmon wavelength is required to be controllable but without sacrificing the electric field enhancement.

We investigate first-and second-order quantum phase transitions of the anisotropic quantum Rabi model, in which the rotating-and counter-rotating terms are allowed to have different coupling strength. The model interpolates between two known limits with distinct universal properties. Through a combination of analytic and numerical approaches we extract the phase diagram, scaling functions, and critical exponents, which allows us to establish that the universality class at finite anisotropy is the same as the isotropic limit. We also reveal other interesting features, including a superradiance-induced freezing of the effective mass and discontinuous scaling functions in the Jaynes-Cummings limit. Our findings are relevant in a variety of systems able to realize strong coupling between light and matter, such as circuit QED setups where a finite anisotropy appears quite naturally.