Gapless pairing and the Fermi arc in the cuprates

We argue that the Fermi arc observed in angle-resolved photoemission measurements in underdoped cuprates can be understood as a consequence of inelastic scattering in a phase-disordered $d$-wave superconductor. We analyze this phenomenon in the context of strong-coupling Eliashberg theory, deriving a “single-lifetime” model for describing the temperature evolution of the spectral gap as measured by single-particle probes such as photoemission and tunneling.

Figure 1

(Color online) (a) Im $G$ around the Fermi surface from Eq. (1) with $\Phi ={\Phi }_0\cos \left(2\varphi \right)$, where ${\Phi }_0=40\mathrm{meV}$ and $\gamma =30\mathrm{meV}$. The top curve is at the node $(\varphi =45°)$ and the bottom curve at the antinode $(\varphi =0°)$, with $\varphi$ steps of 5°. (b) Spectral gap (half the peak to peak separation) versus $\varphi$ for $\gamma$ ranging from 0 (dashed curve) to $60\mathrm{meV}$ (bottom curve) with $\gamma$ steps of $10\mathrm{meV}$.

Figure 2

(Color online) (a) Fit of $\gamma \left(T\right)$ as given by the left hand side of Eq. (8) to values extracted from ARPES.[32] A constant term of $2.3\mathrm{meV}$ has been added to account for residual/instrumental broadening at $T=0$. The fitted value of ${\Omega }_0$ is $28\mathrm{meV}$. (b) Relative arclength versus $T$ from the fit in (a) assuming $(\Phi ∕Z_0)d_k={\Phi }_0\cos \left(2\varphi \right)$ with ${\Phi }_0=40\mathrm{meV}$ and $T^{*}=300\mathrm{K}$. Solid points are the data from Ref. 3. The dashed curve assumes instead that $\gamma \propto T$ for all $T$.