The quasiparticle interference of the spectroscopic imaging scanning tunneling microscopy has been investigated for the surface states of the large gap topological insulator Bi 2 Te 3 through the T-matrix formalism. Both the scalar-potential scattering and the spin-orbit scattering on the warped hexagonal isoenergy contour are considered. While backscatterings are forbidden by time-reversal symmetry, other scatterings are allowed and exhibit strong dependence on the spin configurations of the eigenfunctions at k ជ points over the isoenergy contour. The characteristic scattering wave vectors found in our analysis agree well with recent experiment results.

We investigate the competition between the extended s+/--wave and dx2-y2-wave pairing order parameters in the iron-based superconductors. Because of the frustrating pairing interactions among the electron and the hole Fermi pockets, a time-reversal symmetry breaking s+id pairing state could be favored. We analyze this pairing state within the Ginzburg-Landau theory and explore the experimental consequences. In such a state, spatial inhomogeneity induces a supercurrent near a nonmagnetic impurity and the corners of a square sample. The resonance mode between the s+/-- and dx2-y2-wave order parameters can be detected through the B1g Raman spectroscopy.

We study the Fermi liquid properties of the cold atomic dipolar Fermi gases with the explicit dipolar anisotropy using perturbative approaches. Due to the explicit dipolar anisotropy, Fermi surfaces exhibit distortions of the d r 2 −3z 2 type in three dimensions and of the d x 2 −y 2 type in two dimensions. The fermion self-energy, effective mass, and Fermi velocity develop the same anisotropy at the Hartree-Fock level proportional to the interaction strength. The Landau interaction parameters in the isotropic Fermi liquids become the tridiagonal Landau interaction matrices in the dipolar Fermi liquids which renormalize thermodynamic susceptibilities. With large dipolar interaction strength, the Fermi surface collapses along directions perpendicular to the dipole orientation. The dynamic collective zero sound modes exhibit an anisotropic dispersion with the largest sound velocity propagating along the polar directions. Similarly, the longitudinal p-wave channel spin mode becomes a propagating mode with an anisotropic dispersion in multicomponent dipolar systems.

Quasiparticle interference ͑QPI͒ in spectroscopic imaging scanning tunneling microscopy provides a powerful method to detect orbital band structures and orbital ordering patterns in transition-metal oxides. We use the T-matrix formalism to calculate the QPI spectra for the unconventional metamagnetic system of Sr 3 Ru 2 O 7 with a t 2g -orbital band structure. A detailed tight-binding model is constructed accounting for features such as spin-orbit coupling, bilayer splitting, and the staggered rotation of the RuO octahedra. The band parameters are chosen by fitting the calculated Fermi surfaces with those measured in the angular-resolved photoemission spectroscopy experiment. The calculated quasiparticle interference at zero magnetic field exhibits a hollow squarelike feature arising from the nesting of the quasi-one-dimensional d xz and d yz orbital bands, in agreement with recent measurements by Lee et al. ͓Nat. Phys. 5, 800 ͑2009͔͒. Rotational symmetry breaking in the nematic metamagnetic state also manifests in the quasiparticle interference spectra.

We extend the study of the Fermi surface instability of the Pomeranchuk type into systems with orbital band structures, which are common features in transition metal oxides. Band hybridization significantly shifts the spectral weight of the Landau interactions from the conventional s-wave channel to unconventional non-s-wave channels, which results in anisotropic ͑nematic͒ Fermi surface distortions even with ordinary interactions in solids. The Ginzburg-Landau free energy is constructed by coupling the charge-nematic, spinnematic, and ferromagnetic order parameters together, which shows that nematic electron states can be induced by metamagnetism. The connection between this mechanism and the anisotropic metamagnetc states observed in Sr 3 Ru 2 O 7 at high magnetic fields is studied in a multiband Hubbard model with the hybridized quasi-onedimensional d xz and d yz bands.