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We analyze the influence of phonons on the d-wave pairing instability in the Hubbard model on the two-dimensional square lattice at weak to moderate interaction U, using a functional renormalization group scheme with frequency-dependent interaction vertices. As measured by the pairing scale, the B1g buckling mode enhances the pairing, while other phonon modes decrease the pairing. When various phonon modes are included together, the net effect on the scale is small. However, in situations where d-wave superconductivity and other tendencies, e.g. antiferromagnetism, are closely competing, the combined effect of different phonons may be able to tip the balance towards pairing., Comment: 4 pages, 3 figures

Angle-resolved photoemission data on optimally- and under-doped high temperature superconductors reveal a dichotomy between the nodal and antinodal electronic excitations. In this paper we propose an explanation of this unusual phenomenon by employing the coupling between the quasiparticle and the commensurate/incommensurate magnetic excitations., Comment: 11 pages, 9 figures

We present a theory for a finite-length superconducting nanowire coupled to an environment. We show that in the absence of dissipation quantum phase slips always destroy superconductivity, even at zero temperature. Dissipation stabilizes the superconducting phase. We apply this theory to explain the "anti-proximity effect" recently seen by Tian et. al. in Zinc nanowires., Comment: 4 pages, 3 figures

We generalize the numerical renormalization group scheme to study the phonon-mediated retarded interactions in the high Tc cuprates. We find that three sets of phonon-mediated retarded quasiparticle scatterings grow under RG flow. These scatterings share the following common features: 1) the initial and final quasiparticle momenta are in the antinodal regions, and 2) the scattering amplitudes have a $x^2-y^2$ symmetry. All three sets of retarded interaction are driven to strong coupling by the magnetic fluctuations around $(\pi,\pi)$. After growing strong, these retarded interaction will trigger density wave orders with d-wave symmetry. However, due to the d-wave form factor they will leave the nodal quasiparticle unaffected. We conclude that the main effect of electron-phonon coupling in the cuprates is to promote these density wave orders., Comment: 4 pages, 3 figures, references added, added more details about others' previous studies

We present a perspective on the recent discoveries of possible charge ordering in underdoped Bi_2Sr_2CaCu_2O_{8+\delta} and Na_xCa_{2-x}CuO_2Cl_2 by high-resolution scanning tunnelling spectroscopy., Comment: 4 pages, 4 figures; Version 2 changes: 1) Abstract revised. 2) Introduction expanded to discuss additional relevant experiments. 3) Discussion added to clarify relation between condensed (hole crystal) and uncondensed charge order states. 4) Figures 1,2,3 combined to 2 figures. 5) Figure 4 revised to correct error (qualitatively unchanged). 6) References added

In this paper we perform a renormalization group analysis on the 1+1 dimensional version of an effective field theory (previously proposed by Dung-Hai Lee, cond-mat/011393) describing (quantum) fluctuating stripe and superconductor orders. We find four possible phases corresponding to stripe order/disorder combined with superconducting order/disorder., Comment: 8 pages, 3 figures, revtex