Dynamical Particle-Hole Asymmetry in High-Temperature Cuprate Superconductors

Motivated by the form of recent theoretical results, a quantitative test for an important dynamical particle-hole asymmetry of the electron spectral function at low energies and long wavelengths is proposed. The test requires the decomposition of the angle resolved photo emission intensity, after a specific Fermi symmetrization, into odd and even parts to obtain its ratio $\mathcal{R}$. A large magnitude $\mathcal{R}$ is implied in recent theoretical fits at optimal doping around the chemical potential, and I propose that this large asymmetry needs to be checked more directly and thoroughly. This processing requires a slightly higher precision determination of the Fermi momentum relative to current availability.

Figure 1

Top inset shows the large predicted asymmetry ${\mathcal{R}}_{{\mathcal{G}}_{\mathrm{SECFL}}}^{\mathrm{a}\mathrm{\text{−}}\mathrm{s}}$ versus $\xi$ in the small energy range of 150 meV. Similar magnitudes are found as functions of $\omega$ at various $\xi$. The figure shows ${\mathcal{S}}_{{\mathcal{G}}_{\mathrm{SECFL}}}^{\mathrm{a}\mathrm{\text{−}}\mathrm{s}}$ from Eq. (9) versus $\xi$ (main), $\omega$ (inset) in electron volt at various $\omega$ (main), $\xi$ (inset). Arrows indicate the direction of increasing energies. We used $n=0.85$, $\eta =0.05\mathrm{eV}$, and ${\Delta }_0=0.0796\mathrm{eV}$ here.

Figure 2

(I) The predicted AIP spectrum showing a shallow minimum at $\omega \sim -0.2\mathrm{eV}$, and a rise as the binding energy $|\omega |$ increases. The rise is greater as the particle density $n$ increases (bottom to top). Inset (II) reveals the role of elastic scattering width $\eta$ (top to bottom). Inset (III) shows the local DOS relevant to the tunneling conductance, for the same parameters as in (II) with a remarkable rising piece near zero bias.

Figure 3

Symmetry extraction illustrated for the simplified ECFL model. Here $n=0.85$, $\eta =0.05$, and ${\Delta }_0=0.0796$ with $\omega$ (ordinate) and $\xi$ (abscts antisymmetricissa) in electron volt. (A) Shows the spectral function ${\rho }_{\mathcal{G}}$, (B) ${\rho }_{\mathcal{G}}{f}_{\omega }$, (C) ${\rho }_{\mathcal{G}}{f}_{\omega }{\overline{f}}_{\omega }$, (D) the symmetrized object ${\mathcal{S}}_{\mathcal{G}}^{\mathrm{s}}$, (E) the antisymmetrized object ${\mathcal{S}}_{\mathcal{G}}^{\mathrm{a}\mathrm{\text{−}}\mathrm{s}}$ showing a peak and a trough, and (F) the asymmetry ratio ${\mathcal{R}}_{\mathcal{G}}$ from Eq. (3).