Change of quasiparticle dispersion in crossing $T_c$ in the underdoped cuprates

One of the most remarkable properties of the high-temperature superconductors is a pseudogap regime appearing in the underdoped cuprates above the superconducting transition temperature $T_c$. The pseudogap continously develops out of the superconducting gap. In this paper, we demonstrate by means of a detailed comparison between theory and experiment that the characteristic change of quasiparticle dispersion in crossing $T_c$ in the underdoped cuprates can be understood as being due to phase fluctuations of the superconducting order parameter. In particular, we show that within a phase fluctuation model the characteristic back-turning BCS bands disappear above $T_c$ whereas the gap remains open. Furthermore, the pseudogap rather has a U shape instead of the characteristic V shape of a $d_{x^2-y^2}$-wave pairing symmetry and starts closing from the nodal $\vec{k}=(\pi ∕2,\pi ∕2)$ directions, whereas it rather fills in at the antinodal $\vec{k}=(\pi ,0)$ regions, yielding further support to the phase fluctuation scenario.

Figure 1

Spectral weight $A(\vec{k},\omega )$ in the pseudogap state ($T=2.0T_c$, top) and in the superconducting state slightly below $T_c\left(T=0.75T_c\right)$ calculated from the phase fluctuation model. For comparison we also show the spectral weight for the phase coherent BCS limit (bottom).

Figure 2

(Color online) (a) Superconducting state. Energy distribution of the photoemission intensity along the direction shown as a red arrow on the sketch below. The BCS-like dispersion is clearly observed for the bonding band. (b) Pseudogap state. No more bending back of the dispersion is observed. Instead, spectral weight fades upon approaching the Fermi level.

Figure 3

Gap function $\Delta \left(\vec{k}\right)$ in the pseudogap state ($T=2.0T_c$, top) and in the superconducting state slightly below $T_c$ $\left(T=0.75T_c\right)$ calculated from the phase fluctuation model. For comparison we also show the BCS gap function (bottom).

Figure 4

Values of the leading edge (pseudo) gap (LEG) as a function of the Fermi surface angle within the quadrant of the Brillouin zone (see lower panel) given with respect to the binding energy of the leading edge of a nodal energy distribution curve. The curve joining the low-gap extremity of these data points would represent the $\vec{k}$ dependence of the pseudogap. For details see Ref. 8.