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arXiv:1907.06799 · Physical review. B./Physical review. B

Ultrafast nonequilibrium evolution of excitonic modes in semiconductors

Yuta Murakami, Michael Schüler, Shintaro Takayoshi, Philipp Werner

Published Jan 28, 2020• 42 citations

Abstract

We study the time evolution of excitonic states after photoexcitation in the one-dimensional spinless extended Falicov-Kimball model. Several numerical methods are employed and benchmarked against each other: time-dependent mean-field simulations, the second-Born approximation (2BA) within the Kadanoff-Baym formalism, the generalized Kadanoff-Baym ansatz (GKBA) implemented with the 2BA, and the infinite time-evolving block decimation (iTEBD) method. It is found that the GKBA gives the best agreement with iTEBD and captures the relevant physics. Excitations to the particle-hole continuum and resonant excitations of the equilibrium exciton result in a qualitatively different dynamics. In the former case, the exciton binding energy remains positive and the frequency of the corresponding coherent oscillations is smaller than the band gap. On the other hand, resonant excitations trigger a collective mode whose frequency is larger than the band gap. We discuss the origin of these different behaviors by evaluating the nonequilibrium susceptibility using the nonthermal distribution and a random phase approximation. The peculiar mode with frequency larger than the band gap is associated with a partial population inversion with a sharp energy cutoff. We also discuss the effects of the cooling by a phonon bath. We demonstrate the real-time development of coherence in the polarization, which indicates excitonic condensation out of equilibrium.

DOI: 10.1103/physrevb.101.035203

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To study excitonic effects on high-harmonic generation (HHG) in Mott insulators, we investigate pumped nonequilibrium dynamics in the one-dimensional extended Hubbard model. By employing time-dependent calculations based on the exact diagonalization and infinite time-evolving block decimation methods, we find the strong enhancement of the HHG intensity around the exciton energy. The subcycle analysis in the sub-Mott-gap regime shows that the intensity region of the time-resolved spectrum around the exciton energy splits into two levels and oscillates following the driving electric field. This excitonic dynamics is qualitatively different from the dynamics of free doublon and holon but favorably contributes to HHG in the Mott insulator.

We present an analytical and numerical study of the coherent exciton polarization including exciton-exciton correlation. The time evolution after excitation with ultrashort optical pulses can be divided into a slowly varying polarization component and novel ultrafast collective modes. The frequency and damping of the collective modes are determined by the high-frequency properties of the retarded two-exciton correlation function, which includes Coulomb effects beyond the mean-field approximation. The overall time evolution depends on the low-frequency spectral behavior. The collective mode, well separated from the slower coherent density evolution, manifests itself in the coherent emission of a resonantly excited excitonic system, as demonstrated numerically.

Low-energy excitations of the excitonic states in the semimetal and semiconducting materials described by the extended Falicov-Kimball model with phonon correlation are investigated. In the framework of the unrestricted Hartree-Fock approximation, we derive a set of self-consistent equations to find the quasiparticle energies and excitonic condensate order parameters. The real part of the optical conductivity and then the dynamical excitonic susceptibility function are analytically evaluated by means of the linear response theory. Numerical results reveal the significant expansion of the excitonic condensation window in the temperature--Coulomb interaction plane by lowering the mass imbalance. Under the influence of the mass imbalance and thermal fluctuations, the BCS-BEC crossover of the excitonic condensation states has been also addressed in the collective mode signatures of the optical conductivity. Out of the condensation state, the collective excitation of the excitonic bound state is examined by analyzing the imaginary part of the dynamical excitonic susceptibility function. At large mass imbalance and low thermal fluctuations, we find an extremely sharp peak with high intensity at low frequency in the imaginary part of the dynamical excitonic susceptibility spectrum, specifying the long-lifetime exciton existence before it becomes condensed.

We consider the excitonic insulator state (often associated with electronic ferroelectricity), which arises on the phase diagram of an extended spinless Falicov-Kimball model (FKM) at half-filling. Within the Hartree--Fock approach, we calculate the spectrum of low-energy collective excitations in this state up to second order in the narrow-band hopping and/or hybridization. This allows to probe the mean-field stability of the excitonic insulator. The latter is found to be unstable when the case of the pure FKM (no hybridization with a fully localized band) is approached. The instability is due to the presence of another, lower-lying ground state and not to the degeneracy of the excitonic phase in the pure FKM. The excitonic phase, however, may be stabilized further away from the pure FKM limit. In this case, the low-energy excitation spectrum contains important information about the properties of the excitonic condensate (including the strongly suppressed critical temperature).