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arXiv:2301.06075 · Physical review. B./Physical review. B

Wannier-Stark ladders and Stark shifts of excitons in Mott insulators

Mina Udono, Tatsuya Kaneko, K. Sugimoto

Published Aug 25, 2023• 8 citations
arXivHTMLPDF

Abstract

External-field driven energy-level discretization, such as Landau quantization or Stark localization, is one of the most intriguing phenomena in quantum systems. We investigate the emergence of the Wannier-Stark ladder coming from the particle-hole continuum and the Stark shifts of the exciton levels in one-dimensional Mott insulators under the dc electric field. The discretized peak structure in the optical-conductivity spectra newly appears by applying the dc electric field, and the positions of these peaks can be reproduced from the energy levels of a simple effective model in the strong-coupling regime. Our results not only suggest that Mott insulators can serve as a viable platform for Stark discretization, but also pave the way for investigations of dynamical properties in correlated many-body systems under a dc electric field.

DOI
10.1103/physrevb.108.l081304

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External-field driven energy-level discretization, such as Landau quantization or Stark localization, is one of the most intriguing phenomena in quantum systems. We investigate the emergence of the Wannier-Stark ladder coming from the particle-hole continuum and the Stark shifts of the exciton levels in one-dimensional Mott insulators under the dc electric field. The discretized peak structure in the optical-conductivity spectra newly appears by applying the dc electric field, and the positions of these peaks can be reproduced from the energy levels of a simple effective model in the strong-coupling regime. Our results not only suggest that Mott insulators can serve as a viable platform for Stark discretization, but also pave the way for investigations of dynamical properties in correlated many-body systems under a dc electric field.
We theoretically investigate the single-particle excitation spectra of a one-dimensional Hubbard model at half filling using an infinite matrix-product state and elucidate the discretized energy spectra emerging under the influence of a dc electric field. In a weak electric-field regime, we observe two kinds of spectral structures in the density of states. With increasing the electric-field strength, the discretized spectra, the period of which is proportional to the strength, become dominant, and the density of states exhibits the Wannier-Stark ladder in their spectra. In addition, we also simulate time- and angle-resolved photoemission spectroscopy using an ultrashort terahertz pump pulse that approximates a dc electric field. Our results represent a significant step forward in understanding the states in strongly correlated electron systems driven by a static electric field.
A numerical calculation of the DC Stark effect for hydrogen and sodium atoms and Wannier-Mott excitons in an external uniform DC electric field is carried out within the operator perturbation theory method. New adequate model for description of the unique especialitites in the photoionization spectra of the hydrogenic atoms is proposed. It is found that the Stark shift for the n=2 state of excitons in the Cu2 O semiconductor (yellow series) at the electric field strength 600 V/cm results in — 3,1 10 -4 eV which agrees well with experimental data of Gross et al. It is indicated also that the analogous unique especialitites may possibly take a place in the Wannier-Mott excitons spectra near the threshold boundary
One-dimensional semiconductors are characterized by strongly bound excitons. Therefore, the Frenkel regime of excitons localized within a few unit cells is readily reached and traditional Wannier exciton models become inadequate. In the presence of strong electric fields, excitons are polarized and, in extreme cases, ionized. Such strong-field effects have previously been described analytically for Wannier excitons. In the present work, we show that analytical results can be extended to the more involved Frenkel case as well. Hence, by analytically solving the difference equation describing Frenkel excitons in electric fields, we derive close-form expressions for resonances providing Stark shifts and ionization rates. Moreover, closed-form results for exciton electroabsorption spectra and dynamic polarizability are obtained.
We applied a many-body Wannier functions method to theoretically calculate the excitonic optical conductivity spectrum and energy structure in a one-dimensional (1D) Mott insulator at absolute zero temperature with a large system size. Focusing on full charge fluctuations associated with holon and doublon pairs, we employ a charge model, which is interpreted as an effective model for investigating the photoexcitations of a 1D extended Hubbard model under a half-filling of the spin-charge separation. As a result, theoretical spectra with the appropriate broadenings qualitatively reproduce the recent experimental data of ET-F2TCNQ{\mathrm{F}}_{2}\mathrm{TCNQ}F2​TCNQ at 294 K with and without a modulated electric field. Regarding the excitonic energy structure, we found that the excitons, particularly for even-parity, are weakly bound by many-body effects. This is also consistent with the fitting parameters reported in a recent experiment. Thus, the theoretical method presented in this paper is useful for understanding the physical roles of the charge fluctuations in many-body excited states of a 1D Mott insulator.
Summary form only given.Fano resonances arise due to quantum mechanical coupling of a discrete state to a degenerate continuum. The line shape in optical absorption spectra is characterized by an intrinsic broadening of the line, strong asymmetry, and a reduced absorption at one side of the peak falling well below the pure continuum level. Intensive theoretical investigations predicted Fano resonances as a general feature of a large variety of low-dimensional semiconductors. We present the observation of Fano resonances in semiconductor superlattices (SL). In SL, discrete excitonic states of the Wannier-Stark ladder are in resonance with subband continua of lower ladder states. The coupling between discrete and continuous states is mediated by Coulomb interaction, which is also responsible for the formation of the discrete excitonic states. As a unique feature of Fano resonances in SL, the Fano coupling strength can be continuously changed in the experiment by tuning the applied electric field. We have also performed time-integrated four-wave-mixing experiments to investigate the influence of Fano coupling on the polarization decay of a Wannier-Stark exciton. We have been able to resolve the polarization decay of a Fano resonance in the time-integrated signal and to follow its changes with field.
We employ dynamical density-matrix renormalization-group (DDMRG) and field-theory methods to determine the frequency-dependent optical conductivity in one-dimensional extended. half-filled Hubbard models. The field-theory approach is applicable to the regime of "small" Mott gaps which is the most difficult to access by DDMRG. For very large Mott gaps the DDMRG recovers analytical results obtained previously by means of strong-coupling techniques. We focus on exciton formation at energies below the onset of the absorption continuum. As a consequence of spin-charge separation, these Mott-Hubbard excitons are bound states of spinless, charged excitations ("holon-antiholon" pairs). We also determine exciton binding energies and sizes. In contrast to simple band insulators, we observe that excitons exist in the Mott-insulating phase only for a sufficiently strong intersite Coulomb repulsion. Furthermore, our results show that the exciton binding energy and size are not related in a simple way to the strength of the Coulomb interaction.