Myriad phases of the Checkerboard Hubbard Model

The zero temperature phase diagram of the checkerboard Hubbard model is obtained in the solvable limit in which it consists of weakly coupled square plaquettes. As a function of the on-site Coulomb repulsion U and the density of holes per site, x, we demonstrate the existence of at least 16 distinct phases. For instance, at zero doping, the ground state is a novel d-wave Mott insulator (d-Mott), which is not adiabatically continuable to a band insulator; by doping the d-Mott state with holes, depending on the magnitude of U, it gives way to a d-wave superconducting state, a two-flavor spin-1/2 Fermi liquid (FL), or a spin-3/2 FL.Comment: 4 pages, 2 figures, minor revisions, published in Phys. Rev. B as a Rapid Communicatio

Quasiparticle scattering in two dimensional helical liquid

We study the quasiparticle interference (QPI) patterns caused by scattering off nonmagnetic, magnetic point impurities, and edge impurities, separately, in a two dimensional helical liquid, which describes the surface states of a topological insulator. The unique features associated with hexagonal warping effects are identified in the QPI patterns of charge density with nonmagnetic impurities and spin density with magnetic impurities. The symmetry properties of the QPI patterns can be used to determine the symmetry of microscopic models. The Friedel oscillation is calculated for edge impurities and the decay of the oscillation is not universal, strongly depending on Fermi energy. Some discrepancies between our theoretical results and current experimental observations are discussed.Comment: 12 pages, appendices added. Accepted for publication in Physical Review B (submitted, October 2009

Superconductivity in Inhomogeneous Hubbard Models

We present a controlled perturbative approach to the low temperature phase diagram of highly inhomogeneous Hubbard models in the limit of small coupling, $t'$, between clusters. We apply this to the dimerized and checkerboard models. The dimerized model is found to behave like a doped semiconductor, with a Fermi-liquid groundstate with parameters ({\it e.g.} the effective mass) which are smooth functions of the Hubbard interaction, $U$. By contrast, the checkerboard model has a nodeless d-wave superconducting state (preformed pair condensate, $d$-BEC) for $0 < U < U_c$, which smoothly crosses over to an intermediate BCS-like superconducting phase ($d$-BCS), also with no nodal quasi-particles, for $|U - U_c| < {\cal O}(t^\prime)$, which gives way to a Fermi liquid phase at large $U > U_c = 4.58$.Comment: 7 pages, a sign error in Eq.(3) has been corrected and its consequence has been discussed with updated figure

Modulation of the slow/common gating of CLC channels by intracellular cadmium.

Members of the CLC family of Cl(-) channels and transporters are homodimeric integral membrane proteins. Two gating mechanisms control the opening and closing of Cl(-) channels in this family: fast gating, which regulates opening and closing of the individual pores in each subunit, and slow (or common) gating, which simultaneously controls gating of both subunits. Here, we found that intracellularly applied Cd(2+) reduces the current of CLC-0 because of its inhibition on the slow gating. We identified CLC-0 residues C229 and H231, located at the intracellular end of the transmembrane domain near the dimer interface, as the Cd(2+)-coordinating residues. The inhibition of the current of CLC-0 by Cd(2+) was greatly enhanced by mutation of I225W and V490W at the dimer interface. Biochemical experiments revealed that formation of a disulfide bond within this Cd(2+)-binding site is also affected by mutation of I225W and V490W, indicating that these two mutations alter the structure of the Cd(2+)-binding site. Kinetic studies showed that Cd(2+) inhibition appears to be state dependent, suggesting that structural rearrangements may occur in the CLC dimer interface during Cd(2+) modulation. Mutations of I290 and I556 of CLC-1, which correspond to I225 and V490 of CLC-0, respectively, have been shown previously to cause malfunction of CLC-1 Cl(-) channel by altering the common gating. Our experimental results suggest that mutations of the corresponding residues in CLC-0 change the subunit interaction and alter the slow gating of CLC-0. The effect of these mutations on modulations of slow gating of CLC channels by intracellular Cd(2+) likely depends on their alteration of subunit interactions