Dielectric screening of surface states in a topological insulator

Hexagonal warping provides an anisotropy to the dispersion curves of the helical Dirac fermions that exist at the surface of a topological insulator. A sub-dominant quadratic in momentum term leads to an asymmetry between conduction and valence band. A gap can also be opened through magnetic doping. We show how these various modifications to the Dirac spectrum change the polarization function of the surface states and employ our results to discuss their effect on the plasmons. In the long wavelength limit, the plasmon dispersion retains its square root dependence on its momentum, $\boldsymbol{q}$, but its slope is modified and it can acquire a weak dependence on the direction of $\boldsymbol{q}$. Further, we find the existence of several plasmon branches, one which is damped for all values of $\boldsymbol{q}$, and extract the plasmon scattering rate for a representative case.Comment: 11 pages, 8 figure

Equation of State of the Fermionic 2D Hubbard Model

We present results for the equation of state of the two-dimensional Hubbard model on an isotropic square lattice as obtained from a controlled and numerically exact large-cluster dynamical mean field simulation. Our results are obtained for large but finite systems and are extrapolated to infinite system size using a known finite size scaling relation. We present the energy, entropy, double occupancy and nearest-neighbour spin correlations extrapolated to the thermodynamic limit and discuss the implications of these calculations on pseudogap physics of the 2D-Hubbard model away from half filling. We find a strong behavioural shift in energy below a temperature $T^*$ which becomes more pronounced for larger clusters. Finally, we provide reference calculations and tables for the equation of state for values of doping away from half filling which are of interest to cold atom experiments.Comment: 8 pages 6 figures - See Source for Supplementary Material File

Impact of Electron-Phonon Coupling on Near-Field Optical Spectra

The finite momentum transfer ($\boldsymbol{q}$) longitudinal optical response $\sigma^L(\boldsymbol{q},\omega)$ of graphene has a peak at an energy $\omega=\hbar v_F q$. This corresponds directly to a quasiparticle peak in the spectral density at momentum relative to the Fermi momentum $k_F -q$. Inclusion of coupling to a phonon mode at $\omega_E$ results, for $\omega<|\omega_E|$, in a constant electron-phonon renormalization of the bare bands by a mass enhancement factor $(1+\lambda)$ and this is followed by a phonon kink at $\omega_E$ where additional broadening begins. Here we study the corresponding changes in the optical quasiparticle peaks which we find to continue to directly track the renormalized quasiparticle energies until $q$ is large enough that the optical transitions begin to sample the phonon kink region of the dispersion curves where linearity in momentum is lost in the renormalized Dirac Fermion dispersion curves and the correspondence to a single quasiparticle energy is lost. Nevertheless there remains in $\sigma^L(\boldsymbol{q},\omega)$ features analogous to the phonon kinks of the dispersion curves which are observable through variation of $q$ and $\omega$.Comment: 6 pages, 5 figure

Signatures of Fermi surface reconstruction in Raman spectra of underdoped cuprates

We have calculated the Raman B$_{1g}$ and B$_{2g}$ spectra as a function of temperature, as well as doping, for the underdoped cuprates, using a model based on the resonating valence-bond spin-liquid. We discuss changes in intensity and peak position brought about by the presence of a pseudogap and the implied Fermi surface reconstruction, which are elements of this model. Signatures of Fermi surface reconstruction are evident as a sharp rise in the doping dependence of the antinodal to nodal peak ratio which occurs below the quantum critical point. The temperature dependence of the B$_{1g}$ polarization can be used to determine if the superconducting gap is limited to the Fermi pocket, as seen in angle resolved photoemission spectroscopy, or extends beyond. We find that the slope of the linear low energy B$_{2g}$ spectrum maintains its usual d-wave form, but with an effective gap which reflects the gap amplitude projected on the Fermi pocket. Our calculations capture the main qualitative features revealed in the extensive data set available on the HgBa$_2$CuO$_{4+\delta}$ (Hg-1201) cuprate.Comment: 13 pages, 14 figure