Light-Induced Renormalization of the Dirac Quasiparticles in the Nodal-Line Semimetal ZrSiSe

In nodal-line semimetals, linearly dispersing states form Dirac loops in the reciprocal space with a high degree of electron-hole symmetry and a reduced density of states near the Fermi level. The result is reduced electronic screening and enhanced correlations between Dirac quasiparticles. Here we investigate the electronic structure of ZrSiSe, by combining time- and angle-resolved photoelectron spectroscopy with ab initio density functional theory (DFT) complemented by an extended Hubbard model ($\mathrm{DFT}+U+V$) and by time-dependent $\mathrm{DFT}+U+V$. We show that electronic correlations are reduced on an ultrashort timescale by optical excitation of high-energy electrons-hole pairs, which transiently screen the Coulomb interaction. Our findings demonstrate an all-optical method for engineering the band structure of a quantum material.

Figure 1

(a) Sketch of the linearly dispersing Dirac states. Under intense laser light, electrons and holes are injected in the band structure far from the Dirac nodes, and can efficiently screen the Coulomb interaction. Calculated (b) and measured (c) Fermi surface of ZrSiSe. It consists of two diamond-shaped lines centered at $\overline{\mathrm{\Gamma }}$, which originate from the valence band (VB, green) and the conduction band (CB, blue). An additional surface state (SS, red) is identified around $\overline{X}$, at the boundary of the surface Brillouin zone ($\overline{\mathrm{\Gamma }}\overline{M}=1.2{\AA }^{-1}$, $\overline{\mathrm{\Gamma }}\overline{X}=0.85{\AA }^{-1}$). (d)–(f) Experimental band dispersion, measured at 143 eV photon energy, along the black lines in panel (c). The two linearly dispersing bulk state, shown along the $\overline{\mathrm{\Gamma }}-\overline{M}$ direction in (d), form the Dirac loop, with nodes above the Fermi level. Panels (e) and (f), shown as a reference for the TR-ARPES data in Fig. 2, illustrate the dispersion of the bulk (e) and surface (f) states near $E_F$.

Figure 2

(a)–(c) Band dispersion of the bulk bands, taken along the path (e) indicated in Fig. 1, for different delay times before (a), 50 fs after (b), and 300 fs after (c) the arrival of the optical excitation. Blue lines indicate the ab initio calculations for $U=1.47\mathrm{eV}$ and $V=0.33\mathrm{eV}$. (d)–(f) Similar temporal evolution of the band structure along $\overline{M}-\overline{X}-\overline{M}$ [direction (f) in Fig. 1], focusing on the dispersion of the surface state at different delay times. Red and yellow lines are the $\mathrm{DFT}+U+V$ and DFT calculations, respectively. In both the bulk and the surface states, a change in the band dispersion during optical excitation (50 fs) illustrates the light-induced renormalization of the band dispersion. The intensity at each binding energy is normalized to the same value integrated over the entire momentum window in order to increase the visibility of the signal above $E_F$.

Figure 3

(a) Simulated ARPES intensity from the ab initio calculations for $U=1.47\mathrm{eV}$ and $V=0.33\mathrm{eV}$, broadened by the experimental momentum and energy resolution. The electron occupancy is defined by a Fermi-Dirac distribution for an effective temperature $T^{*}=600\mathrm{K}$, as inferred from the experimental data at 200 fs. (b) Experimental spectral function at $t0$, during optical excitation. (c) MDCs at selected energies, indicated in (b) by dashed lines, and Lorentzian fits. (d) Peak positions as a function of energy; colors correspond to different delay times. (e) Calculated band dispersion for $\mathrm{DFT}+U+V$ (red) and DFT (yellow), respectively. (f) Change in band position, $\mathrm{\Delta }k$, obtained as the difference between the experimental and peak position calculated with $\mathrm{DFT}+U+V$. The black line indicates the theoretical $\mathrm{\Delta }k$ obtained as difference between the DFT and the $\mathrm{DFT}+U+V$ calculations.