Ubiquitous suppression of the nodal coherent spectral weight in Bi-based cuprates

High-temperature superconducting cuprates exhibit an intriguing phenomenology for the low-energy elementary excitations. In particular, an unconventional temperature dependence of the coherent spectral weight (CSW) has been observed in the superconducting phase by angle-resolved photoemission spectroscopy (ARPES), both at the antinode where the $d$-wave paring gap is maximum, as well as along the gapless nodal direction. Here, we combine equilibrium and time-resolved ARPES to track the temperature-dependent meltdown of the nodal CSW in Bi-based cuprates with unprecedented sensitivity. We find the nodal suppression of CSW upon increasing temperature to be ubiquitous across single- and bi-layer Bi cuprates, and uncorrelated to superconducting and pseudogap onset temperatures. We quantitatively model both the lineshape of the nodal spectral features and the anomalous suppression of CSW within the Fermi-liquid framework, establishing the key role played by the normal state electrodynamics in the description of nodal quasiparticles in superconducting cuprates.

Figure 1

(a) Energy distribution curves (EDCs) at the Fermi momentum ${\mathbf{k}}_{\mathrm{F}}$ along the nodal direction of Bi2212-OP91 for 30 K and 90 K, as measured by TR-ARPES ($h\nu =6.2$ eV) and equilibrium ARPES ($h\nu =27$ eV). (b) Nodal EDCs at ${\mathbf{k}}_{\mathrm{F}}$ for Bi2201-OD24 acquired by TR-ARPES. Inset: Comparison between the same experimental data (solid lines) and the EDC obtained from the 30 K data via the thermal broadening of the Fermi-Dirac distribution at 90 K (dashed line). All EDCs have been deconvoluted from the energy resolution broadening via the Lucy-Richardson algorithm [15, 20, 21] [TR-ARPES energy resolution is 11 meV and 18 meV for panels (a) and (b), respectively; equilibrium ARPES energy resolution is 5.3 meV].

Figure 2

(a) Momentum-integrated EDCs along the nodal direction before ($-0.5$ ps) and after ($+0.33$ ps) the pump excitation for Bi2201-OD24. Fermi-Dirac distribution fits are shown as solid black lines; temperature values are defined by a $99\%$-confidence-interval. (b) Transient electronic temperature $T_{\mathrm{e}}$ obtained by fitting the Fermi edge width along the nodal direction of Bi2201-OD24, for two different pump fluences ($12\mu \mathrm{J}$/${\mathrm{cm}}^2$, LF; $90\mu \mathrm{J}$/${\mathrm{cm}}^2$, HF). The solid lines represent (single-) double-exponential decay fit to (LF) HF data. Error bars in panel (b) reflect the systematic errors associated with the experiment and the number of averaging cycles acquired for each fluence. All data acquired via TR-ARPES at 6.2 eV.

Figure 3

(a) Relative variation of the nodal coherent spectral weight $\mathrm{\Delta }\mathrm{CSW}$ as a function of the electronic temperature $T_{\mathrm{e}}$ tracked via TR-ARPES, for three different doping levels of Bi2212. The inset illustrates the difference in the integrated area of the symmetrized EDCs in the $[-0.08,0.08]\mathrm{eV}$ range, which defines $\mathrm{\Delta }\mathrm{CSW}$. (b) Same as in (a), but for three doping levels of Bi2201. (a) Colored and (b) gray vertical bars mark the range of $T_c$ for the different compounds. The estimated temperatures at negative pump-probe-delays are listed in Appendix pp1 for each sample.

Figure 4

(a) Nodal EDCs at ${\mathbf{k}}_{\mathrm{F}}$ and MDCs at $-8$ meV for Bi2212-OP91 and Bi2201-OD24, probed by TR-ARPES at different temperatures. Black solid lines represent the results of the EDC-MDC global fitting procedure using Eq. (1), as explained in the main text. Optimal fits to the data are found with $(\alpha =0.8$, $\beta =20)$ and $(\alpha =0.6$, $\beta =21.5$) for Bi2212-OP91 and Bi2201-OD24, respectively. (b) Temperature evolution of the imaginary part of the electron self-energy extracted via fitting of MDCs at $-8$ meV (integration windows $\pm 5\mathrm{meV}$) via a Lorentzian-like function for Bi2201-OD24 and Bi2212-OP91. The solid black lines are quadratic curves defined by the $\beta$ coefficients obtained via the global fit procedure of panel (a). (c) Comparison between the experimental CSW suppression (TR-ARPES data from Fig. 3; equilibrium ARPES for Bi2212-OP91 in full green circles) and the simulated $\mathrm{\Delta }{\mathrm{CSW}}^{\mathrm{FL}}$ within the FL model via Eq. (1). The solid black line is computed for $\alpha =0.7$, $\beta =20.75$, $\mathrm{\Gamma }=0.02$, while the yellow shading accounts for the parameters' range defined by the global fit. (d) Normalized temperature evolution of the spectral function $\mathrm{\Delta }A(0,{\mathbf{k}}_{\mathrm{F}})$, for Bi2201-OD24 (TR-ARPES data) and Bi2212-OP91 (TR- and equilibrium ARPES). The integration range in momentum and energy is $0.005{\AA }^{-1}$ and $6\mathrm{meV}$, respectively. The solid lines are best fits to the experimental data by using Eq. (2) for the different models with $\mathrm{\Gamma }=0.02$: FL (black, $\beta =20.35$), MFL (red, $\lambda =0.96$), and $T^3$ (orange, $\eta =3.28\times {10}^4$). All spectra have been deconvoluted from the energy resolution before extracting EDCs and MDCs in panels (a), (b), and (d).

Figure 5

Momentum distribution curves (MDCs) at $\omega =-2$ meV (5 meV integration window) along the nodal direction $\mathrm{\Gamma }$-Y of Bi2212-OP91. Black curves have been acquired at the Elettra synchrotron, BaDElPh beamline; the blue curve has been acquired at the CLS, QMSC beamline, with 27 eV photons; the red curve has been acquired at the UBC-Moore Center for Ultrafast Quantum Matter with 6.2 eV photons. The blue and red curves represent the photon energies employed in this work. Vertical dashed lines highlight the separation between antibonding (AB) and bonding (B) states, which is approximately 0.01 ${\AA }^{-1}$.

Figure 6

(a, b) Characterization of the response of the Scienta R4000 analyzer at the QMSC beamline: count-rate under the quasiparticle peak in the analog-to-digital converter (ADC) and single-pulse-counting (PC) detection mode, respectively. The orange and light blue markers indicate the maximum count-rate employed in this work. (c) Comparison between nodal EDCs at ${\mathbf{k}}_{\mathrm{F}}$ of Bi2212-OP91 acquired at the QMSC beamline with ADC (orange line) and PC (light blue markers) mode at the maximum count-rate. Temperature 20 K and photon energy 27 eV. (d) Nodal EDCs at ${\mathbf{k}}_{\mathrm{F}}$ of Bi2212-OP91 acquired with the TR-ARPES setup at UBC using a Scienta DA30 analyzer in the two different detection modes. Temperature 10 K and photon energy 6.2 eV. All EDCs shown here have not been deconvoluted for the energy resolution broadening.

Figure 7

(a) Momentum-integrated TR-ARPES map along the nodal direction of Bi2212-OP91 as a function of the pump-probe delay (integration window [$-0.1$ ${\AA }^{-1}$, 0.1 ${\AA }^{-1}$] about ${\mathbf{k}}_{\mathrm{F}}$; high fluence data). Noncoherent/background contributions to the spectral weight have been subtracted as explained in the text. Right panel: Momentum integrated energy distribution curves for selected pump-probe delays; black lines are fits to Fermi-Dirac like functions. (b) $\omega$-integrated nodal TDOS of Bi2212-OP91 as a function of the effective electronic temperature, normalized to the lowest temperature value. The momentum and energy integration windows are [$-0.1$ Å${}^{-1}$, 0.1 Å${}^{-1}$] and [$-40$ meV, 40 meV], respectively. The orange shaded area highlights variations of $\pm 3$%.