Doping Dependence of the Coupling of Electrons to Bosonic Modes in the Single-Layer High-Temperature ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CuO}}_6$ Superconductor

A recent highlight in the study of high-$T_c$ superconductors is the observation of band renormalization or self-energy effects on the quasiparticles. This is seen in the form of kinks in the quasiparticle dispersions as measured by photoemission and interpreted as signatures of collective bosonic modes coupling to the electrons. Here we compare for the first time the self-energies in an optimally doped and strongly overdoped, nonsuperconducting single-layer Bi-cuprate (${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CuO}}_6$). In addition to the appearance of a strong overall weakening, we also find that the weight of the self-energy in the overdoped system shifts to higher energies. We present evidence that this is related to a change in the coupling to $c$-axis phonons due to the rapid change of the $c$-axis screening in this doping range.

Figure 1

(a) ARPES spectrum of OD sample, nonsuperconducting (non-SC) along (0, 0) to $(\pi ,\pi )$ at $T=8\mathrm{K}$. (b) is the fit of MDC at $E_F$. (c) Peak position, MDC width, and approximated bare dispersion for extracting $\mathrm{Re}(\Sigma )$; inset is the comparison of peak position taken at 8 and 45 K.

Figure 2

(a) Comparison of $\mathrm{Re}(\Sigma )$ for OD and OP samples, showing doping dependence in overall coupling strength and relative strength in mode energies. Note that SSRL and HeLM mean, measured with the 23.7 eV synchrotron light and the He I light and the blue and red areas show the dominated feature in OD and additional feature in OP, respectively. (b) and (c) are, respectively, symmetrized schematic Fermi surface maps of OD and OP samples.

Figure 3

(a) Eliashberg function and self-energy for OP (top row) and OD (bottom row) samples calculated by MEM analysis. (b) Comparison of measured $\mathrm{Re}(\Sigma )$ with a simulation using the original (for OP) and “screened” (for OD) loss-function spectrum. Note that shaded areas show the similar sizes in area of the main features in the two analyses.