High-Energy Anomaly in the Angle-Resolved Photoemission Spectra of ${\mathrm{Nd}}_{2-x}{\mathrm{Ce}}_x{\mathrm{CuO}}_4$: Evidence for a Matrix Element Effect

We use polarization-dependent angle-resolved photoemission spectroscopy (ARPES) to study the high-energy anomaly (HEA) in the dispersion of ${\mathrm{Nd}}_{2-x}{\mathrm{Ce}}_x\mathrm{Cu}{\mathrm{O}}_4$, $x=0.123$. We find that at particular photon energies the anomalous, waterfall-like dispersion gives way to a broad, continuous band. This suggests that the HEA is a matrix element effect: it arises due to a suppression of the intensity of the broadened quasiparticle band in a narrow momentum range. We confirm this interpretation experimentally, by showing that the HEA appears when the matrix element is suppressed deliberately by changing the light polarization. Calculations of the matrix element using atomic wave functions and simulation of the ARPES intensity with one-step model calculations provide further evidence for this scenario. The possibility to detect the full quasiparticle dispersion further allows us to extract the high-energy self-energy function near the center and at the edge of the Brillouin zone.

Figure 1

(a) Experimental geometry. (b) Cuts in the reciprocal space used in the present investigation. (c)–(g) Experimental ARPES intensity distribution maps recorded with parameters given in the labels. (h)–(l) calculated ARPES intensities using the parameters of (c)–(g), respectively. For both the ARPES data and the calculations linear intensity scales with arbitrary scales were used.

Figure 2

(a) Bottom of the band along the ($-\pi$, 0)–($\pi$, 0) direction between the center of the BZ and the antinodal point. Circles: ARPES data. Dashed line: tight binding (TB) fit. Solid line: present density functional theory (DFT) calculations. (b) Momentum distribution curve of the data shown in Fig. 1 at $E_B=0.5\mathrm{eV}$, symmetrized relative to $k_y=0$. The blue line shows a quadratic momentum dependence. (c) Imaginary part of the self-energy $\Im \mathrm{\Sigma }$ as a function of the binding energy near the nodal and the antinodal point. The lines are fits to the data (see text). (d) Width $\mathrm{\Gamma }$ of the spectral weight at the bottom of the band near the antinodal point [$k_{\parallel }=(\pi ,0)$] and at the cut through the nodal point [$k_{\parallel }=(3\pi /8,0)$]. Red region indicates the range of the existence of quasiparticles ($\mathrm{\Gamma }<E_B$).