Particle-Hole Asymmetry in the Cuprate Pseudogap Measured with Time-Resolved Spectroscopy

One of the most puzzling features of high-temperature cuprate superconductors is the pseudogap state, which appears above the temperature at which superconductivity is destroyed. There remain fundamental questions regarding its nature and its relation to superconductivity. But to address these questions, we must first determine whether the pseudogap and superconducting states share a common property: particle-hole symmetry. We introduce a new technique to test particle-hole symmetry by using laser pulses to manipulate and measure the chemical potential on picosecond time scales. The results strongly suggest that the asymmetry in the density of states is inverted in the pseudogap state, implying a particle-hole asymmetric gap. Independent of interpretation, these results can test theoretical predictions of the density of states in cuprates.

Figure 1

(a) The momentum-energy map of ARPES intensity on overdoped Bi2212 along the $\mathrm{\Gamma }\text{−}Y$ momentum direction. (b) The ARPES intensity integrated along the momentum range indicated by the double arrows in (a) both before pumping and after pumping. $\mathrm{\Delta }{\mu }_{\mathrm{vac}}$ and $T_e$ are obtained by fitting the edge. (c) The intensity along the dotted line indicated in (a) both before and after pumping. $\mathrm{\Delta }ϵ$ is obtained from the shift in peak position. (d),(e) An illustration (not to scale) of the valence band dispersion along $\mathrm{\Gamma }\text{−}Y$ and its response to pumping.

Figure 2

(a) The density of states in a Bi2212 sample in the normal state. (b) The expected function $\mathrm{\Delta }{\mu }_{ϵ}(T_e)$ both with and without the superconducting (SC) gap. (c) $\mathrm{\Delta }{\mu }_{ϵ}$ and $T_e$ as a function of delay time $t$ after pumping an overdoped Bi2212 sample with a $34\mu \mathrm{J}/{\mathrm{cm}}^2$ pulse. (d) $\mathrm{\Delta }{\mu }_{ϵ}$ is shown as a function of $T_e$, eliminating $t$ as a variable. Data points are collected from delay times up to 10 ps, pump fluences between 3 and $34\mu \mathrm{J}/{\mathrm{cm}}^2$, and initial temperatures between 25 and 80 K. Empty circles denote the data collected between a $-0.3$ and 0.3 ps delay.

Figure 3

The function $\mathrm{\Delta }{\mu }_{ϵ}(T_e)$ is plotted for OP Bi2212 with $T_c=91\mathrm{K}$ (a), a slightly UD Bi2212 with $T_c=78\mathrm{K}$ (b), and a very UD Dy-Bi2212 with $T_c=55\mathrm{K}$ (c). Data are collected over many delay times, pump fluences, and initial temperatures. The inset of (a) shows the cuprate phase diagram, including the superconducting (SC) and pseudogap (PG) phases, with black lines indicating the four samples in this study. Empty circles denote the data taken between a $-0.3$ and 0.3 ps delay, and gray bars indicate $T_c$. (a) uses data from Ref. [29].

Figure 4

An illustration of how the YRZ model is potentially consistent with results on the chemical potential in underdoped (a),(c),(e) and very underdoped (b),(d),(f) Bi2212. (a),(b) A diagram of the pseudogap, parametrized by the Fermi surface angle $\phi$ shown in the quarter Brillouin zone in the inset of (b). The very underdoped sample has a larger pseudogap. (c),(d) The calculated density of states, with the green shaded region indicating occupied states. Arrows indicate the edges of the antinodal pseudogap. (e),(f) Qualitative predictions of the function ${\mu }_{ϵ}(T_e)$. Gray bars indicate $T_c$.