Excitons and carriers in transient absorption and time-resolved ARPES spectroscopy: An ab initio approach

D. Sangalli

Phys. Rev. Materials 5, 083803 – Published 20 August 2021

Abstract

I present a fully ab initio scheme to model transient spectroscopy signals in the presence of strongly bound excitons. Using LiF as a prototype material, I show that the scheme is able to capture the exciton signature both in time-resolved angle-resolved photoemission spectroscopy and transient absorption experiments. The approach is completely general and can become the reference scheme for modeling pump and probe experiment in a wide range of materials.

Received 4 June 2021
Accepted 5 August 2021

DOI:https://doi.org/10.1103/PhysRevMaterials.5.083803

Physics Subject Headings (PhySH)

Excitons First-principles calculations Ultrafast optics

Nonequilibrium systems

Many-body techniques Nonequilibrium Green's function Pump-probe spectroscopy Time & angle resolved photoemission spectroscopy Transient absorption spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

D. Sangalli ^*

Istituto di Struttura della Materia of the National Research Council, Via Salaria Km 29.3, I-00016 Montelibretti, Italy and European Theoretical Spectroscopy Facilities (ETSF)

^*davide.sangalli@ism.cnr.it

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Issue

Vol. 5, Iss. 8 — August 2021

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Images

Figure 1
Overview of the four nonequilibrium states considered in the present work. They are divided into free carriers and bound exciton states (left to right), and in coherent pure states and noncoherent statistical mixtures (top to bottom). $N_{c}$ is the excited density in the conduction band. The equations used to reconstruct the TR-ARPES spectral function $I (k, ω)$ and the response function $χ (ω)$ are sketched in the top. In the bottom the approximation used in the literature and holding for the noncoherent case are also reported. The graphical representation of the states is realized via their TR-ARPES signal.
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Figure 2
The optical absorption of LiF. Vertical lines mark the position of the bright eigenvalues of the BSE equation weighted by the associated oscillator strength in the positive $y$ axis. The full BSE spectrum is represented in the negative $y$ axis. The vertical dashed lines represent the position of the electron-hole continuum, i.e., the GW band gap. All the BSE eigenvalues at lower energy are part of the Rydberg exciton series.
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Figure 3
Time-dependent plot of the total carrier density $N_{c}$ per unit cell (blue and red lines) and laser pulse intensity profile of the pump (black line) are shown in the main frames. Coherent carriers (a) and noncoherent carriers (c.a) are shown in the upper panel. Coherent exciton (b) and noncoherent carriers distribution obtained dephasing the excitonic state (c.b) in the lower panel. This corresponds to four states introduced in Fig. 1. A zoom of the carrier density $N_{c}$ is shown in the uppermost inset for the excitonic case. All other insets show the associated time-dependent polarization in different time ranges.
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Figure 4
TR-ARPES spectral function, and corresponding $k$ -integrated photoemission (PE) signal of LiF. Left panel: Signal from carriers generated with a laser pulse with $ω_{P} = 14.8$ eV; coherent (a) and noncoherent (c.a) carriers give exactly the same signal. Center panel: Signal from coherent excitons (b) generated with a laser pulse with $ω_{P} = 12.5$ eV. Right panel: Signal from the carriers distribution reached, starting from the coherent exciton state, after sending to zero the off-diagonal elements of the density matrix (c.b). A replica of the valence band at energy $ε_{v k} + ω_{P}$ is shown in white. The numbers reported in the PE and ARPES panels represent the magnification factor needed for the signal in the conduction band region to reach similar intensity as the signal from the valence band (see also Supplemental Material [48]).
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Figure 5
Transient absorption $Δ ɛ_{2}^{(i)} (ω) = ɛ_{2}^{(i)} (ω) - ɛ_{2}^{(e q)} (ω)$ for LiF shown for the four states introduced in Fig 1: coherent carriers (a) and noncoherent carriers (c.a), and coherent exciton (b) and noncoherent carriers distribution obtained dephasing the excitonic state (c.b). The probe-induced polarization $P^{(i)} (t) = P_{P p} (t) - P_{P} (t)$ is shown in the inset. The blue shaded line marks the laser pump frequency, and the black dashed line the position of the quasiparticle gap. The two extra insets in the lower panel show a zoom of $ɛ_{2}^{(e q)} (ω)$ (black line) and $ɛ_{2}^{(i)} (ω)$ around the two main excitonic peaks.
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