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We investigate the role of electron correlation and disorder on theelectronic structure of layered nickelate (La$_{0.5}$Sr$_{0.5}$)$_2$NiO$_4$using core level and valence band photoemission spectroscopy in conjunctionwith density functional theory (DFT) and dynamical mean field theory (DMFT)calculations. Sr 3$d$ and La 4$d$ core level spectra exhibit multiple featuresassociated with photoemission final state effects. An increase of unscreenedfeatures in the Sr 3$d$ and La 4$d$ core level spectra with loweringtemperature suggests the reduction in density of states (DOS) at the Fermilevel, $E_F$. Valence band spectra collected using different photon energiesreveal finite intensity at $E_F$ and overall spectra are well captured byDFT+DMFT. Strong renormalization of partially filled $e_g$ bands in DFT+DMFTresult indicates strong correlation in this system. Mass enhancement factor,$m^*/m_{\text{DFT}} \sim$ 3, agrees well with values obtained from specificheat measurements. High resolution spectra in the vicinity of $E_F$ showmonotonically decreasing spectral intensity with lowering temperature, whichevolves to exhibit a Fermi cut-off at low temperatures indicating metalliccharacter in contrast to insulating transport, suggesting Anderson insulatingstate. $|E-E_F|^{1/2}$ dependence of the spectral DOS and square roottemperature dependence of spectral DOS at $E_F$ evidences the role of disorderin the electronic structure of (La$_{0.5}$Sr$_{0.5}$)$_2$NiO$_4$.

Role of electron correlation and disorder on the electronic structure of layered nickelate (La$_{0.5}$Sr$_{0.5}$)$_2$NiO$_4$