Fine Structure in the Tunneling Spectra of Electron-Doped Cuprates: No Coupling to the Magnetic Resonance Mode

We reanalyze high-resolution scanning tunneling spectra of the electron-doped cuprate ${\mathrm{Pr}}_{0.88}{\mathrm{LaCe}}_{0.12}{\mathrm{CuO}}_4$ ($T_c=24\mathrm{K}$). We find that the spectral fine structure below 35 meV is consistent with strong coupling to a bosonic mode at about 16 meV, in quantitative agreement with early tunneling spectra of ${\mathrm{Nd}}_{1.85}{\mathrm{Ce}}_{0.15}{\mathrm{CuO}}_4$. Since the energy of the bosonic mode is significantly higher than that (9.5–11 meV) of the magnetic resonancelike mode observed by inelastic neutron scattering, the coupling feature at about 16 meV cannot arise from strong coupling to the magnetic mode. The present work thus demonstrates that the magnetic resonancelike mode cannot be the origin of high-temperature superconductivity in electron-doped cuprates.

Figure 1

Normalized second derivative $(d^{2}I/d{V}^2{)}_S/(dI/dV{)}_N$ for the conventional superconductor Pb along with the electron-phonon spectral function ${\alpha }^2(\omega )F(\omega )$ (where $S$ represents the superconducting state and $N$ the normal state). The figure is reproduced from Ref. 27. It is apparent that the dip features in $(d^{2}I/d{V}^2{)}_S$ match precisely with the peak features in ${\alpha }^2(\omega )F(\omega )$ (see the vertical solid lines).

Figure 2

(a) Tunneling conductance $(dI/dV{)}_S$ in the superconducting state for the electron-doped ${\mathrm{Pr}}_{0.88}{\mathrm{LaCe}}_{0.12}{\mathrm{CuO}}_4$ (PLCCO) crystal (○). The data are digitized from Ref. 26. The normal-state tunneling conductance $(dI/dV{)}_N$ is approximated by a straight line, which is obtained with conservation of states. (b) Normalized conductance $\overline{g}=(dI/dV{)}_S/(dI/dV{)}_N$. The solid line is the numerically calculated curve in terms of an anisotropic $s$-wave gap symmetry and the dashed line is the numerically calculated curve in terms of $d$-wave gap symmetry.

Figure 3

(a) The second derivative spectrum $(d^{2}I/d{V}^2{)}_S$ together with the first derivative spectrum $(dI/dV{)}_S$ for the ${\mathrm{Pr}}_{0.88}{\mathrm{LaCe}}_{0.12}{\mathrm{CuO}}_4$ crystal. The figure is reproduced from Ref. 26. (b) A histogram of the occurrences of ${\Delta }_R$ and the energies $E_{p1}$ and $E_{p2}$ for a map of tunneling spectra on a $64\AA \times 64\AA$ area of the sample. The data are taken from Ref. 26.

Figure 4

Electron-boson spectral functions (top two curves) for two ${\mathrm{Nd}}_{1.85}{\mathrm{Ce}}_{0.15}{\mathrm{CuO}}_4$ samples along with $-(2{\Delta }_R)d\overline{g}/d\omega$ (bottom curve) for PLCCO (where $\omega =eV-{\Delta }_R$). The electron-boson spectral functions are reproduced from Ref. 23 and $-(2{\Delta }_R)d\overline{g}/d\omega$ is numerically calculated from Fig. 2b after the data are smoothened.