Model of Quasiparticles Coupled to a Frequency-Dependent Charge-Density-Wave Order Parameter in Cuprate Superconductors

We investigate a model where superconducting electrons are coupled to a frequency dependent charge-density wave order parameter ${\Delta }_{\mathbf{r}}(\omega )$. Our approach can reconcile the simultaneous existence of low-energy Bogoljubov quasiparticles and high energy electronic order as observed in scanning tunneling microscopy (STM) experiments. The theory accounts for the contrast reversal in the STM spectra between positive and negative bias observed above the pairing gap. An intrinsic relation between scattering rate and inhomogeneities follows naturally.

Figure 1

Density plots of the integrated spectral weight in a window of $\pm 5\mathrm{meV}$ around $E_F$. (a) static CDW with ${\Delta }_2^0-{\Delta }_1^0=0.054\mathrm{eV}$ (cf. inset to Fig. 2). (b) dynamic CDW (${\Delta }_i^0=0$); Residual parameters as given in the text.

Figure 2

LDOS for the model with (a) static CDW scattering (${\Delta }_2^0-{\Delta }_1^0=0.054\mathrm{eV}$) and (b) frequency dependent CDW scattering. The upper insets depict the modulations of ${\Delta }_{\mathbf{r}}^0$ (a) and $v_{\mathbf{r}}^2$ (b) in the unit cell. Further parameters: chemical potential $\mu =-0.23\mathrm{eV}$, (doping $x\approx 0.07$), $\Gamma =1\mathrm{meV}$, and $\Omega =1\mathrm{eV}$.

Figure 3

Fourier-transformed LDOS at the CDW scattering vector, $\mathbf{Q}=\frac{2\pi }{4}$. (a) Static CDW scattering with ${\Delta }_2^0-{\Delta }_1^0=0.054\mathrm{eV}$, (b) frequency dependent CDW scattering. The phase has been chosen such that $\mathrm{Im}{N}_{\mathbf{Q}}(\omega )=0$. Lower insets: LDOS at $\omega =+5\mathrm{meV}$ (squares) and $\omega =-5\mathrm{meV}$ (circles). Further parameters as in Fig. 2.