Momentum Distribution Sum Rule for Angle-Resolved Photoemission

Within a spectral function $A(\mathbf{k},\omega )$ interpretation of angle-resolved photoemission (ARPES), the intensity obeys the sum rule $\int d\omega f\left(\omega \right)A(\mathbf{k},\omega )=n\left(\mathbf{k}\right)$, where $f$ is the Fermi function and $n\left(\mathbf{k}\right)$ the momentum distribution. We show the usefulness of this sum rule for analyzing ARPES data. The integrated intensity in B${\mathrm{i}}_2$S${\mathrm{r}}_2$CaC${\mathrm{u}}_2$ ${\mathrm{O}}_8$ at ${\mathbf{k}}_F$ is independent of temperature even though the spectrum is strongly $T$ dependent. We also demonstrate the possibility of measuring $n\left(\mathbf{k}\right)$ using ARPES for YB${\mathrm{a}}_2$C${\mathrm{u}}_4$ ${\mathrm{O}}_8$.