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The normal state single particle spectral function of the high temperature superconducting cuprates, measured by the angle resolved photoelectron spectroscopy (ARPES), has been considered both anomalous and crucial to understand.
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In the sudden approximation, the ARPES intensity I ( \mathaccentV v e c 17 E k , ω ) = M ( \mathaccentV v e c 17 E k ) A ( \mathaccentV v e c 17 E k , ω ) f ( ω ) I(\mathaccentV{vec}17E{k},\omega)=M(\mathaccentV{vec}17E{k})A(\mathaccentV{vec}17E{k},\omega)f(\omega) . Here, \mathaccentV v e c 17 E k \mathaccentV{vec}17E{k} is the momentum and − ω -\omega is the energy of the final N − 1 N-1 state (as we set ℏ = 1 \hbar=1 in this Letter), where N N is the number of electrons in the initial state. A ( \mathaccentV v e c 17 E k , ω ) = ℑ m G ( \mathaccentV v e c 17 E k , ω − i 0 + ) / π A(\mathaccentV{vec}17E{k},\omega)=\Im m\ G(\mathaccentV{vec}17E{k},\omega-i0^{+})/\pi is the single particle spectral function, M ( \mathaccentV v e c 17 E k ) M(\mathaccentV{vec}17E{k}) is the dipole matrix element, constant for an EDC, and f ( ω ) f(\omega) is the Fermi-Dirac function. At the chemical potential ω ≡ 0 \omega\equiv 0
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ℜ e Φ ( ω ) = − 1 π Ω 0 e x p ( − τ 2 ω 0 2 ) [ ω 0 ω − 2 ( ω 2 + τ 2 ) D ( ω ω 0 ) ] \Re e\ \Phi(\omega)=-\frac{1}{\sqrt{\pi}\Omega_{0}}\mathop{exp}\nolimits\left(-\frac{\tau^{2}}{\omega_{0}^{2}}\right)\left[\omega_{0}\omega-2(\omega^{2}+\tau^{2})D\left(\frac{\omega}{\omega_{0}}\right)\right] where D ( x ) = π 2 e − x 2 erfi ( x ) D(x)=\frac{\sqrt{\pi}}{2}e^{-x^{2}}\mathrm{erfi}(x) is the Dawson function. C Φ = 1 / ( π Ω 0 ) C_{\Phi}=1/(\pi\Omega_{0}) and ω c = C Φ ω 0 2 \omega_{c}=C_{\Phi}\omega_{0}^{2} where C Φ C_{\Phi} and ω c \omega_{c} are parameters defined in Ref. [ 4 ]
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