Anomalous doping evolution of nodal dispersion revealed by in situ ARPES on continuously doped cuprates

We study the systematic doping evolution of nodal dispersions by in situ angle-resolved photoemission spectroscopy on the continuously doped surface of a high-temperature superconductor ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+x}$ and reveal that the nodal dispersion has three fundamentally different segments separated by two kinks, located at ∼10 meV and roughly 70 meV, respectively. These three segments have different band velocities and different doping dependence. In particular, in the underdoped region the velocity of the high-energy segment increases monotonically as the doping level decreases and can even surpass the bare band velocity. We propose that electron fractionalization is a possible cause for this anomalous nodal dispersion and may even play a key role in the understanding of exotic properties of cuprates.

Figure 1

(a) ARPES spectrum of ozone-annealed Bi2212 along the nodal direction (as illustrated in the inset), the doping level is estimated as 0.24. Ozone anneal means sample is annealed at ozone atmosphere. (b)–(f) Spectra acquired from the same sample surface after annealed in vacuum with different temperatures (called vacuum anneal) step by step, and the corresponding doping levels are estimated as 0.18, 0.15, 0.13, 0.10, and 0.08, respectively. These spectra are plotted in the same color scale as illustrated in the lower right side of (f). (g)–(i) The black lines are the raw MDC plots for the doping levels at 0.24, 0.15, and 0.08, respectively, and the blue lines are their Lorentzian fittings. (j) The MDCs before the kink (blue dashed lines,$E-E_F=-27\mathrm{meV}$) and after the kink (red solid lines, $E-E_F=-105\mathrm{meV}$) at different doping levels. (k) The EDCs before the kink (blue dashed lines, $k-k_f=0.017{\AA }^{-1}$) and after kink (red solid line, $k-k_f=0.043{\AA }^{-1}$) at different doping levels.

Figure 2

(a) MDC-derived band dispersion at the doping level equals 0.15: the red line is the peak of MDCs extracted by Lorentzian fitting, and the violet shadow represents the width of MDCs. The dashed line is a typical bare band as described in the text. (b),(c) The real parts of SE at each doping level are plotted against with the binding energy in (b) and with the peak's position of the corresponding MDCs in (c). The double-headed arrows indicate how we extract the energy positions $\mathrm{\Delta }E\left(x\right)$ and momentum position $\mathrm{\Delta }k\left(x\right)$ respectively. (d),(e) Same as (b) and (c) but for the MDCs width at each doping level. The shadow regions in (d) and (e) highlight the dramatic changes of the MDCs width. (f),(g) The determined $\mathrm{\Delta }k\left(x\right)$ and $\mathrm{\Delta }E\left(x\right)$ for each doping level. The black lines along with the shadow domes represent the UD side of the superconducting dome.

Figure 3

(a) Summary of MDC-derived nodal dispersions at different doping levels. The momentum is scaled to their corresponding $k_{\mathrm{F}}$. (b) The MDC-derived nodal dispersion segments at the binding energy range with 0–25 meV. (c) The MDC-derived nodal dispersion segments at 25–55 meV. (d) Three segments separated by two kinks which are marked with the black arrows: the brown one marks the segment at 0–5meV, the blue one marks the segment at 25–55 meV, the red one marks the segment at 80–125 meV. The black circles are the nodal dispersion at the doping level which equals 0.15. (e) The doping evolution of velocities of three segments plotted with the corresponding colors marked in (d). The empty markers with corresponding shapes represent an independent data set acquired from another sample. The colored shadow lines are guides for eyes. The gray shadow dome represents the superconducting phase region.