Raman and ARPES combined study on the connection between the existence of the pseudogap and the topology of the Fermi surface in ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$

We study the behavior of the pseudogap in overdoped ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ by electronic Raman scattering (ERS) and angle-resolved photoemission spectroscopy (ARPES) on the same single crystals. Using both techniques we find that, unlike the superconducting gap, the pseudogap related to the antibonding band vanishes above the critical doping $p_c=0.22$. Concomitantly, we show from ARPES measurements that the Fermi surface of the antibonding band is holelike below $p_c$ and becomes electronlike above $p_c$. This reveals that the existence of the pseudogap depends on the Fermi surface topology in ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$, and more generally, puts strong constraint on theories of the pseudogap phase.

Figure 1

First row: ERS and ARPES spectra of a Bi-2212 overdoped (OD 47 K) crystal above $p_c=0.22$: (a) $B_{1g}$(antinodal) Raman response, (b) antinodal EDCs of the antibonding band below and above $T_{\mathrm{c}}$, and (c) antinodal and nodal EDCs of the antibonding band below $T_{\mathrm{c}}$. Note that the EDCs have been selected to emphasize momentum and temperature dependence, respectively. The antinodal EDC from (c) is a little broader than the one in (b) and this caused a slightly higher binding energy of the peak. For the gap determination this difference plays no role since it is relative changes of the line shape which are important. Second row: ERS and ARPES spectra of Bi-2212 overdoped (OD 77 K) crystal below $p_c$: (d) antinodal Raman response, (e) antinodal EDCs of the antibonding band below and above $T_{\mathrm{c}}$, and (f) antinodal and nodal EDCs of the antibonding band below $T_{\mathrm{c}}$. The peak at 35 and weak reminiscent peaks at 50 and 75 meV observed both in (a) and (d) are phonon lines [41, 42]. Zero binding energy corresponds to the Fermi level.

Figure 2

Antibonding band energy distribution curves at the nodes and antinodes of the overdoped Bi-2212. (a) OD 47 K and (b) OD 77 K compound in the normal state. The inset in (b) displayed (up) the electronic Raman background measured just above $T_{\mathrm{c}}$ (75 K) and at $T^{*}$ (150 K) for the OD 77 K compound; (bottom) the electronic background at 75 K subtracted from the one at 150 K. The energy size of the depletion is approximately 40 meV corresponding (after division par 2) to ${\mathrm{\Delta }}_{\text{PG}}\approx 20$ meV. The peak around 35 meV is a phonon line.

Figure 3

Fermi surface maps of (a) OD 47 K and (b) OD 77 K compound taken at 8 K using 26 eV photons. Intensity is integrated within a 20 meV window centered at the Fermi level to minimize the influence of the superconducting gap. Results of the tight-binding fit to the experimental data from (c) OD 47 K and (d) OD 77 K samples. Dotted contours in (c) and (d) delimit the Fermi surface area mapped by the ARPES data displayed in (a) and (b). Diffraction replicas are not shown. $t_{0,0}=0.416, t_{0,1}=t_{1,0}=-0.653$, and $t_{1,1}=0.542$ for bonding bands. $t_{0,0}=0.451$ for antibonding bands. $t_{1,1}=0.450, t_{0,1}=t_{1,0}=-0.630$, and $t_{1,1}=0.463, t_{0,1}=t_{1,0}=-0.653$ for OD 47 K and OD 77 K antibonding bands, respectively.