Time-resolved ARPES spectra of nonequilibrium excitonic insulators: Revealing macroscopic coherence with ultrashort pulses

The nonequilibrium (NEQ) excitonic-insulator (EI) phase is a dynamical state of matter for excited insulators or semiconductors, and it is characterized by self-sustained coherent oscillations of the excitonic condensate. In this Rapid Communication we highlight the main qualitative features of a NEQ-EI time- and angle-resolved photoemission spectroscopy (tr-ARPES) spectrum. We show that monochromatic probes yield a steady-state spectrum with excitonic structures originating from the dressing of conduction states with the coherent condensate. These structures are replicas of the NEQ valence bands but shifted upward in energy by the condensate frequency. Reducing the probe duration below the condensate period, the band structure gradually fades away and the tr-ARPES signal becomes proportional to the excitonic wave function. In addition, the signal amplitude becomes periodic in the impinging time of the probe, with the same period of the oscillating condensate.

Figure 1

Color plot of the tr-ARPES spectra $N_k\left(\epsilon \right)$ vs $\omega =\epsilon -{\omega }_p$ and $k$ for probe pulses of different duration $T_p$ impinging the system at different times $\tau$. The system is in the BEC NEQ-EI phase characterized by $\delta \mu =0.82$. Energies are measured in units of the bare gap ${\epsilon }_g$. Decreasing the duration of the probe pulse (slides from right to left) the photoemission signal loses information on the NEQ band structure and it acquires a dependence on the impinging time $\tau$ of the pulse (slides from top to bottom). Notice that for long pulses (right most slides) the valence band is only slightly distorted.

Figure 2

Color plot of the tr-ARPES spectra $N_k\left(\epsilon \right)$ vs $\omega =\epsilon -{\omega }_p$ and $k$ for probe pulses of different duration $T_p$ impinging the system at different times $\tau$. The system is in the BCS NEQ-EI phase characterized by $\delta \mu =1.05$. Energies are measured in units of the bare gap ${\epsilon }_g$. Notice that for long pulses (right most slides) the valence band is strongly distorted, its shape turning convex.

Figure 3

tr-ARPES spectrum integrated over energy for $\delta$-like probes vs the impinging time $\tau$. Left: BEC regime with $\delta \mu =0.82$ and hence $n_c=0.07$. Right: BCS regime with $\delta \mu =1.05$ and hence $n_c=0.2$. In both cases the shape around $k=0$ at $\tau =\pi /\left(2\delta \mu \right)$ resembles the shape of the excitonic structure appearing in the photoemission spectrum for long probe pulses ($T_p\to \infty$) (see the blue curves).