Dynamics of incoherent exciton formation inCu2O: Time- and angle-resolved photoemission spectroscopy

Abstract

We study dynamics of incoherent exciton formation under interband photoexcitation in Cu 2 O using time-and angle-resolved photoemission spectroscopy at 90 K. Hot electrons injected by allowed optical transitions with 3.40-eV photons show ultrafast relaxation to the conduction-band minimum (CBM), surviving up to 500 fs after excitation. While hot-electron states with high excess energy show a rapid population decay of ~25 fs, an abrupt increase to 130 fs is observed for states with excess energies of 0.15 eV. This latter is interpreted in terms of phonon bottleneck dynamics characteristic of LO-phonon mediated energy relaxation. Excitons, having a small binding energy of 60 meV, are formed below the CBM quasi-instantaneously and subsequently relax to the 1S-exciton state of the yellow series within 1.5 ps. We find that, together with possible plasma screening for electron-hole interaction, the cooling of exciton center-of-mass motion plays an important role in the exciton relaxation dynamics. The characteristic features of exciton photoionization process are critically discussed based on the detailed analysis of angle-resolved photoemission results for the 1S excitons formed 1.5 ps after excitation.Using time-and angle-resolved photoemission spectroscopy, transient changes of photoinjected hot-electron populations in energy and momentum spaces have been studied with fs-temporal resolution, providing a direct view on hot electron relaxation processes [10][11][12]. The method has been applied to several semiconductors, and ultrafast relaxation processes of hot carriers in bulk electronic states have been revealed directly [13][14][15][16][17][18][19][20][21][22][23]. Because of the renewed interest in Cu 2 O with respect to solar-cell applications and as a promising p-type transparent conductive oxide [24], understanding of the hot carrier dynamics in this material is of great importance as an indispensable basis to improve efficiencies in optoelectronic device applications. In addition to this, photoemission spectroscopy for excitonic states provides a unique capability to obtain a detailed insight into the wavefunctions of excitons [25][26][27].Recent experiments showing that the yellow-series excitons could be followed up to a high principal quantum number of n = 25 [28] boosted the renewed interest in excitons in Cu 2 O.Observations like this, together with the ongoing research related to excitonic Bose-Einstein condensation [29], sparked extensive theoretical and experimental investigations on excitons in Cu 2 O in order to gain a deeper insight into spectroscopic features beyond a simple hydrogen-like model [30][31][32][33][34]. In these studies, the precise knowledge of wavefunctions of excitons, or the IQP Bloch states of which the excitonic state is composed, is of great importance. However, the correlation between an excitonic state and the IQP Bloch states responsible for the excitonic state, which links directly the excitonic picture and IQP band structures, has so far not been obtained experimentally. T...

Detecting photoelectrons from spontaneously formed excitons

“…Based on the discussion of the excitonic interaction in this material, we naturally check how a direct photoemission feature from excitons looks like. An excitonic feature in photoemission spectra was recently observed and characterized in detail with the pump-and-probe photoemission method as an excited state above the Fermi level and below the bottom of the conduction band 38,[53][54][55] . We adopt this analysis established for pump-excited excitons while we are dealing with a spectroscopic feature below the Fermi level for a spontaneously formed steady-state object.…”

“…Another interesting observation is the significant broadening of the excitonic photoemission peak. The possible contributions for the broadening include (i) the intrinsic scattering of excitons, (ii) the broadening along kz arising from the finite extent of the excitonic wave function in the zdirection 53 and (iii) the finite experimental resolution. Since the experimental resolution is set to ~40 meV and the kz-broadening is also a few tens of meV, limited by the dispersion width in the valence band in the Γ-Υ direction (see Fig.…”

What do the two times in two-time correlation functions mean for interpreting tr-ARPES?

“…For example, experiments on a topological insulator Bi 2 Se 3 showed that while electrons rapidly disappear from the bulk conduction band, the dynamics of the topological surface state are much slower [18]. More detailed analysis may reveal intricate details of the population dynamics, which has been applied to a wide variety of systems [3,[19][20][21][22][23] A question arose from this work: what do the obtained dynamics (typically decaying exponentials) correspond to? This particular point is where the connection to equilibrium breaks down; the decay rate along t rel , which is related to the equilibrium self-energy via Eq.…”

“…Several theoretical efforts have begun in this direction, showing that the resulting spectra are a complex mixture of the valence and conduction bands [32][33][34][35][36][37]. Experimentally, in the two-dimensional di-chalcogenide materials, where the exciton binding energy is high, a direct excitation into the exciton yields a clear signature in trARPES [23,[38][39][40][41].…”

Coherence and de-coherence in the Time-Resolved ARPES of realistic materials: an ab-initio perspective

“…As the title of this review highlights we want to discuss the role played by coherence in the TR-ARPES phenomenology [146,147,148,149,150,151]. As it was introduced in the Section 2 by using simple arguments, the excitation with an external laser pulse transfers coherence in the system.…”