Photoemission Signatures of Photoinduced Carriers and Excitons in One-Dimensional Mott Insulators

Abstract

We theoretically study photoemission spectra for photodoped one-dimensional Mott insulators that can host excitons, and show that their spectral characteristics differ qualitatively from those of photodoped semiconductors. In conventional semiconductors, photoemission spectra are well understood; free charge carriers generate spectral weight near the bottom of the conduction band, while the formation of excitons leads to replica features of the valence band appearing inside the band gap. In one-dimensional Mott insulators, on the other hand, strong correlations give rise to fractionalized elementary excitations-spinons, holons, and doublons-which fundamentally modify the photoemission response. We find that when photodoped carriers, i.e., doublons and holons, remain unbound, the photoemission spectrum directly reflects the dispersion of spinons, i.e., magnetic elementary excitations. In contrast, when a doublon and a holon form an excitonic bound state, replica structures of the lower Hubbard band emerge inside the Mott gap, carrying contributions from both spinon and holon excitations. Importantly, the distribution of the in-gap signal depends sensitively on the degree of doublon-holon binding. The origin of these spectral features is clarified through a combination of exact diagonalization and the slave-particle approach. These results indicate that photoemission from photoinduced carriers and excitons in strongly correlated electron systems can provide information on magnetic properties and carrier-binding properties.

Figures (14)

• Figure 1: (a) Schematic picture of the photoemission spectroscopy for photodoped Mott insulators, which are induced by a pump pulse, creating doublons (doubly occupied sites) and holons (empty sites). If the interaction between doublons and holons is strong enough, they form bound states called Mott-Hubbard excitons. One can measure the momentum-resolved photoemission spectrum by applying a probe pulse, where electrons are emitted from the photodoped Mott insulator. (b) Photoemission process for semiconductor excitons, where photons emit electrons and holes remain in the system. (c) Photoemission process for Mott-Hubbard excitons, where photons emit electrons from doublons, and holons and spin excitations (spinons) remain in the system. (d) Schematic picture of photoemission spectrum of photodoped semiconductors. In the case that electrons and holes are unbound, their photoemission signal appears at the bottom of the conduction band (CB). When electrons and holes are bound, replica structures of the valence band (VB) appear below the CB. (e) Schematic picture of photoemission spectrum of photodoped Mott insulators. In the case that doublons and holons are unbound, a dispersive band signal appears just below the upper Hubbard band (UHB). When doublons and holons are bound, replica structures of the lower Hubbard band (LHB) appear below the UHB.
• Figure 2: (a) Single-particle spectral function $A(k,\omega) = A^{>}(k,\omega)+A^{<}(k,\omega)$ for equilibrium Mott insulators ($N_d=N_h=0$). The unoccupied spectrum $A^{>}(k,\omega)$ (red color scale) corresponds to the UHB, while the occupied spectrum $A^{<}(k,\omega)$ (blue) corresponds to the LHB. The black dashed line shows the band edge of the UHB. (b-d) Occupied spectrum $A^{<}(k,\omega) = A^{<}_{\mathrm{D\to S}}(k,\omega) + A^{<}_{\mathrm{S\to H}}(k,\omega)$ for photodoped Mott insulators ($N_d=N_h=1$) with (b) $V=0$, (c) $V=3$, and (d) $V=5$. $A^{<}_{\mathrm{D\to S}}(k,\omega)$ has the intensity for $\omega>0$, and $A^{<}_{\mathrm{S\to H}}(k,\omega)$ has the intensity for $\omega<0$. The calculations are performed by the exact diagonalization method. Here we use $U=20$, $\eta=0.15$, and $L=14$.
• Figure 3: Doublon-holon correlation function $\chi_{\mathrm{dh}}(r)$ of photodoped Mott insulators ($N_d=N_h=1$) for (a) $V=0$, (b) $V=3$, and (c) $V=5$. The doublon and the holon are not bound for $V=0$, while they are bound for $V=3$ and $V=5$ (the binding becomes tighter as $V$ increases). The calculations are performed by the exact diagonalization method. Here we use $U=20$, and $L=14$.
• Figure 4: (a), (d) Schematic picture of the doublon annihilation process when (a) no exciton is formed and (d) an exciton is formed. When no exciton is formed, the photoemission only creates the spinon (purple circle), and the holon remains at the same position since the holon is far away from the spinon. When an exciton is formed, the photoemission process triggers both holon and spinon dynamics. (b), (e) Time evolution of the holon number $n^{\mathrm{holon}}(r,t)$ for (b) $V=0$ and (e) $V=5$, respectively. (c), (f) Time evolution of the spinon number $n^{\mathrm{spinon}}(r,t)$ for (c) $V=0$ and (f) $V=5$, respectively. The initial state is the one with a doublon annihilated at site $L/2$. The calculations are performed by the time-dependent Lanczos method. Here the parameters are $U=20$ and $L=14$.
• Figure 5: (a) Schematic picture of the singlon annihilation process in the presence of an exciton. There are three cases: (i) photoemission far from the exciton creating a holon and a spinon, (ii) photoemission near the exciton creating a holon-doublon-holon (hdh) trion, and (iii) photoemission near the exciton creating a holon-holon-doublon (hhd) trion. (b), (c), (d), (f) Time evolution of (b) the holon number $n^{\mathrm{holon}}(r,t)$, (c) the spinon number $n^{\mathrm{spinon}}(r,t)$, (d) the hdh trion number $n^{\mathrm{hdh}}(r,t)$, and (f) the hhd trion number $n^{\mathrm{hhd}}(r,t)$. The initial state is the one obtained after singlon annihilation at site $L/2$. The calculations are performed by the time-dependent Lanczos method. The parameters are $U=20$, $V=5$, and $L=14$.