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Low-energy scales and temperature-dependent photoemission of heavy fermions

We solve the $S=1/2$ Kondo lattice model within the dynamical mean field theory. Detailed predictions are made for the dependence of the lattice Kondo resonance and the conduction electron spectral density on temperature and band filling $n_{c}$. Two low-energy scales are identified in the spectra: a renormalized hybridization pseudogap scale $T^{*}$, which correlates with the single-ion Kondo scale, and a lattice Kondo scale $T_{0} < T^{*}$, which acts as the Fermi-liquid coherence scale. The lattice Kondo resonance is split into a main branch, which is pinned at the Fermi level, and whose width is set by $T_{0}$, and an upper branch at $ω\approx T^{*}$. The weight of the upper branch decreases rapidly away from $n_{c}=1$ and vanishes for $n_{c}\lesssim 0.7$. In contrast, the pseudogap in the conduction electron spectral density persists for all $n_{c}$. On increasing temperature, the lattice Kondo resonance at the Fermi level vanishes on a temperature scale of order $10 T_{0}$, as in impurity model calculations. In contrast to impurity model spectra, however, the position of the lattice Kondo resonance depends strongly on temperature, particularly close to the Kondo insulating state. The results are used to make predictions on the temperature dependence of the low-energy photoemission and inverse photoemission spectra of metallic heavy fermions and doped Kondo insulators. We compare our results with available high-resolution measurements on YbInCu$_4$ and YbAgCu$_4$. The loss in intensity with increasing temperature, and the asymmetric lineshape of the low-energy spectra are well accounted for by our model. More detailed agreement with experiment would require including the $f$-orbital degeneracy and crystal-field excited states.