Continuous doping of a cuprate surface: Insights from in situ angle-resolved photoemission

We report a technique of a continuously doped surface of ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+x}$ through ozone/vacuum annealing and a systematic measurement over the nearly whole superconducting dome on the same sample surface by in situ angle-resolved photoemission spectroscopy. We find that the quasiparticle weight on the antinode is proportional to the doped carrier concentration $x$ within the entire superconducting dome, while the nodal quasiparticle weight changes more mildly. More significantly, we discover that a $d$-wave pairing energy gap extracted from the nodal region scales well with the onset temperature of the Nernst signal. These findings suggest that the emergence of superconducting pairing is concomitant with the onset of free vortices.

Figure 1

(a) Crystal structure of Bi2212, and the schematic of ozone annealing (red arrows) and vacuum annealing (blue arrows) surface treatments. (b) The schematic FS of Bi2212 after ozone (red) and vacuum annealing (blue). (c) The FS of the OD one with considerations of superlattice FS (red dashed line) and shadow FS (gray dashed line). The bold black and red lines are the fitting results corresponding to the antibonding and bonding FS, respectively. Those FSs are acquired at 30 K by integrating ±10 meV around $E_F$. (d) The FS evolution with surface treatment sequences: Ozone annealing (panel 1), and a series of vacuum annealing (panels 2–8). (e) Image plot of the integrated intensity in the vicinity of $E_F$ along the Γ-$Y$ direction for each panel in (d), showing two main bands (MB, MB′), two first superlattice bands (SB1, SB1′), and second superlattice bands (SB2). (f) The extracted doping level of each sequence. (g) The phase diagram of Bi2212: The red line is $T_c$ calculated with an empirical formula [35], the blue line is $T^{*}$ extracted from the antinodal gap closed temperature, the gray bars are the doping level for each sequence obtained in (f), and the inset picture is the one taken on the cleaved surface of this sample.

Figure 2

(a) Antinodal energy distribution curves (EDCs) at $k_F$ evolution with doping. (b) Nodal EDCs at $k_F$ evolution with doping measured on the same sample at 10 K. (c) The extracting quasiparticle weight of the node and the antinode. The $T_c$ line is plotted with the violet color.

Figure 3

(a)–(f) The upper panels display the symmetrized EDCs along the FS of six different doping levels. All data are measured on a same sample and a same temperature of $\sim 10$ K. The corresponding momentum positions are indicated in a schematic diagram of FS in the inset of the lower panel of (a). The lower panels display the spectral gap along the FS (plotted against $0.5|cos{k}_x-cos{k}_y|$) for different doping levels. The blue marked one is the total spectral gap, which is determined from the peak position of symmetrized EDCs, the red line is the corresponding $d$-wave gap function (for details, see the Supplemental Material [14]) for each doping, and the gray marked one is the pseudogap obtained as describe in the text.

Figure 4

(a) Doping dependence of the antinode gap ${\mathrm{\Delta }}_{\mathrm{AN}}$ and $d$-wave gap slope ${\mathrm{\Delta }}_0$. The red symbols are ${\mathrm{\Delta }}_0$, the blue ones ${\mathrm{\Delta }}_{\mathrm{AN}}$, and the gray ones the $T_c$-scaled gap, with three different symbols (solid square, triangle, and spaced rhombus) for three independent samples. (b) Doping dependence of $2\mathrm{\Delta }/k_B{T}_c$. The blue symbols are $2{\mathrm{\Delta }}_{\mathrm{AN}}/k_B{T}_c$, the red ones $2{\mathrm{\Delta }}_0/k_B{T}_c$, and the black ones $2{\mathrm{\Delta }}_0/k_B{T}_{\upsilon }$. The inset is a zoom-in plot to highlight the constant ratio of $2{\mathrm{\Delta }}_0/k_B{T}_{\upsilon }$. The Nernst temperatures of the doping levels that are not included in Ref. [3] are estimated from a polynomial fitting to the data in Ref. [3]. (c) A phase diagram of Bi2212. The red symbols are the pairing temperatures obtained from the constant ratio with ${\mathrm{\Delta }}_0$, the black dots the onset temperatures of the Nernst signal from Ref. [3], and the black square ones the superconducting transition temperatures.