Modeling the Fermi arc in underdoped cuprates

Angle resolved photoemission data in the pseudogap phase of underdoped cuprates have revealed the presence of a truncated Fermi surface consisting of Fermi arcs. We compare a number of proposed models for the arcs and find that the one that best models the data is a $d$-wave energy gap with a lifetime broadening whose temperature dependence is suggestive of fluctuating pairs.

Figure 1

(Color online) (a) Spectral intensity at zero energy versus $k_x,k_y$, and (b) versus energy for $k_x=1$ for several $k_y$, for the $d$-density-wave model (Ref. 40). The black curve in (a) is the normal state Fermi surface. Zone dimensions for all figures are in $\pi ∕a$ units, and energies are in meV. For all figures (unless otherwise noted), ${\Delta }_0=50\mathrm{meV}$ and $\Gamma =25\mathrm{meV}$.

Figure 2

(Color online) (a) Experimental energy distribution curves (EDCs) for optimal doped ${\mathrm{Bi}}_2{\mathrm{Sr}}_2\mathrm{Ca}{\mathrm{Cu}}_2{\mathrm{O}}_8$ (Bi2212) around the underlying Fermi surface in the pseudogap phase $(T=140\mathrm{K})$ divided by a resolution broadened Fermi function. The bottom curve is at the node and the top curve at the antinode. The data set is the same as in Fig. 1(b) of Ref. 16. (b) Zero energy intensity from (a) as a function of the Fermi surface angle $\varphi$, where $\varphi =0°$ corresponds to the antinode and $\varphi =45°$ to the node. (c) Zero energy intensity versus $k_x,k_y$ (the data were reflected relative to $k_x=k_y$). For (b), the intensities were obtained by subtracting a background EDC (obtained from an unoccupied $k$), then normalizing this subtracted intensity by its energy integrated weight. This was designed to minimize the effect of the photoemission matrix elements. This was not done in (c) in order to demonstrate that the raw data show no indication for any deviation of the arc from the underlying Fermi surface (black curve).

Figure 3

(Color online) (a) Spectral intensity at zero energy versus $k_x,k_y$, and (b) versus energy and $k_y$ for $k_x=1$, for the model of Yang et al. (Ref. 44).

Figure 4

(Color online) Spectral intensity at zero energy versus $k_x,k_y$ for (a) the $2\times 2$ secular equation and (b) the $3\times 3$ secular equation approximations, for the antinodal nesting model with $q=(0.36,0)$.

Figure 5

(Color online) Spectral intensity versus energy and $k_y$ near the arc tip $(k_x=0.6)$ for (a) the $2\times 2$ secular equation and (b) the $3\times 3$ secular equation approximations, for the antinodal nesting model with $q=(0.36,0)$.

Figure 6

(Color online) Spectral intensity at (a) zero energy and (b) $-25\mathrm{meV}$ versus $k_x,k_y$ for the model of Wen and Lee with ${\mu }_{sh}=-50\mathrm{meV}$ (Ref. 34).

Figure 7

(Color online) (a) Spectral intensity at zero energy versus $k_x,k_y$ and (b) versus energy and $k_y$ for $k_x=0.6$, for the $d$-wave pair model.

Figure 8

(Color online) (a) Spectral intensity around the Fermi surface for the $d$-wave pair model. The top curve is at the node, whereas the bottom curve is at the antinode. (b) Spectral gap (half the peak to peak separation) versus the Fermi surface angle. The dashed curve corresponds to $\Gamma =0$.

Figure 9

(Color online) (a) Arc length versus $\Gamma$ for a $d$-wave gap and a $d^2$ gap (data from Ref. 16). (b) Experimental spectral intensity at zero energy versus Fermi surface angle [as in Fig. 2b] versus fits that assume either a $d$-wave gap $\left[\cos \left(2\varphi \right)\right]$ or a $d^2$ gap $\left[{\cos }^2\left(2\varphi \right)\right]$.