Time- and momentum-resolved gap dynamics in ${\text{Bi}}_2$${\text{Sr}}_2$${\text{CaCu}}_2$${\text{O}}_{8+\delta }$

We use time- and angle-resolved photoemission spectroscopy to characterize the dynamics of the energy gap in superconducting ${\text{Bi}}_2$${\text{Sr}}_2$${\text{CaCu}}_2$${\text{O}}_{8+\delta }$ (Bi2212). Photoexcitation drives the system into a nonequilibrium pseudogap state: Near the Brillouin zone diagonal (inside the normal-state Fermi arc), the gap completely closes for a pump fluence beyond $F\approx 15$ $\mu$J/cm${}^2$; toward the Brillouin zone face (outside the Fermi arc), it remains open to at least 24 $\mu$J/cm${}^2$. This strongly anisotropic gap response may indicate multiple competing ordering tendencies in Bi2212. Despite these contrasts, the gap recovers with relatively momentum-independent dynamics at all probed momenta, which shows the persistent influence of superconductivity both inside and outside the Fermi arc.

Figure 1

Nodal quasiparticle relaxation dynamics, characterized using a $T_e$ and ${\mu }_e$ model. (a)–(d) Nodal time-resolved ARPES spectra at selected delay times. (e) Momentum-integrated EDCs [obtained by horizontally integrating the intensity for the spectra displayed in (a)–(d)] along with Fermi function fits at selected delay times. Solid curves are the result of fitting to Eq. (2). (f) Same data as in (e), but with the linear background above $E_F$ subtracted off, and displayed on a logarithmic scale to clarify the dynamics of quasiparticles far above the Fermi energy.

Figure 2

Near-nodal superconducting gap response to photoexcitation at a fluence of 23 $\mu$J/cm${}^2$ and an equilibrium temperature $T\ll T_c$. (a)–(f) Direct time-resolved ARPES intensity maps. (g)–(l) Intensity maps after applying a deconvolution procedure to remove the effect of the experimental resolution [31, 32], and dividing by an effective Fermi function. (m) EDCs at $k_F$ extracted from panels (g) and (j).

Figure 3

Far-off-nodal superconducting gap response to photoexcitation at a fluence of 24 $\mu$J/cm${}^2$ and an equilibrium temperature $T\ll T_c$. As in Figs. 2–(l), the data have been subjected to a deconvolution procedure [31, 32] and divided by an effective Fermi function. (a) Equilibrium spectrum. The magnitude of the energy gap is about 27 meV. Bilayer bonding bands (BB) and antibonding bands (AB) are visible. (b), (c) Transient spectra. (d) EDCs from panels (a) and (c) at the AB Fermi wave vector ($k_F$).

Figure 4

Momentum dependence of the transient superconducting gap for a pump fluence of 24 $\mu$J/cm${}^2$ and $T\ll T_c$, as analyzed using symmetrized EDCs. (a) Measurements are characterized based on EDCs at the AB Fermi wave vector ($k_F$), which are then symmetrized about the Fermi level to remove the effect of the electronic occupation function [22, 42]. (b)–(f) False-color intensity plots of symmetrized EDC spectral weight versus energy and delay time. (g)–(h) EDCs at selected times for a representative near-nodal (g) and far-off-nodal (h) momentum cut. The black and cyan arrows highlight respective peak positions at $t=-1.2$ ps and $t=0.6$ ps.

Figure 5

Fluence dependence of nonequilibrium gap dynamics inside the Fermi arc. (a)–(d) Symmetrized EDCs at $k_F$ and fit curves based on Eq. (3), for a gapped $k$-space cut at $\varphi ={30}^{\circ }$ and $T=18$ K ($T\ll T_c$). Bold curves correspond to $t=0$ ps. (e) Normalized gap magnitude versus pump-probe delay. (f) Gap recovery rates ${\gamma }_{\Delta }$, extracted by fitting the data in (e) to Eq. (4) between 2–4 ps, 4–6 ps, and 6–10 ps.

Figure 6

Momentum dependence of the nonequilibrium gap with a pump fluence of 24 $\mu$J/cm${}^2$. (a) Normalized gap magnitude vs delay, and fits using Eq. (4), where fits are extracted between 2.5 and 4 ps. (b) Data and fits from (a), shown on a logarithmic scale to highlight recovery rates. (c) Amplitudes ($A_0$) and (d) recovery rates (${\gamma }_{\Delta }$) corresponding to the gap magnitude shifts characterized in (a) and (b). $A_0$ is extracted at $t_{\mathrm{ref}}\equiv 2.5$ ps.

Figure 7

Fluence-dependent gap recovery rates for a representative cut inside ($\varphi ={30}^{\circ }$) and outside ($\varphi ={21}^{\circ }$) the normal-state Fermi arc. Fits are extracted between 2 and 4 ps.

Figure 8

Cartoon illustration of a possible mechanism for the relatively invariant gap recovery rate. If the component of the gap magnitude corresponding to superconductivity responds more strongly to photoexcitation than the component corresponding to the pseudogap, signatures of the latter signal may be washed out by the former signal.