Signatures of four-particle correlations associated with exciton-carrier interactions in coherent spectroscopy on bulk GaAs

D. Webber, B. L. Wilmer, X. Liu, M. Dobrowolska, J. K. Furdyna, A. D. Bristow, and K. C. Hall

Phys. Rev. B 94, 155450 – Published 31 October 2016

Abstract

Transient four-wave mixing studies of bulk GaAs under conditions of broad bandwidth excitation of primarily interband transitions have enabled four-particle correlations tied to degenerate (exciton-exciton) and nondegenerate (exciton-carrier) interactions to be studied. Real two-dimensional Fourier-transform spectroscopy (2DFTS) spectra reveal a complex response at the heavy-hole exciton emission energy that varies with the absorption energy, ranging from dispersive on the diagonal through absorptive for low-energy interband transitions to dispersive with the opposite sign for interband transitions high above band gap. Simulations using a multilevel model augmented by many-body effects provide excellent agreement with the 2DFTS experiments and indicate that excitation-induced dephasing (EID) and excitation-induced shift (EIS) affect degenerate and nondegenerate interactions equivalently, with stronger exciton-carrier coupling relative to exciton-exciton coupling by approximately an order of magnitude. These simulations also indicate that EID effects are three times stronger than EIS in contributing to the coherent response of the semiconductor.

Received 20 May 2016

DOI:https://doi.org/10.1103/PhysRevB.94.155450

Physics Subject Headings (PhySH)

Excitons Semiconductors

Four-wave mixing Spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

D. Webber¹, B. L. Wilmer², X. Liu³, M. Dobrowolska³, J. K. Furdyna³, A. D. Bristow², and K. C. Hall¹

¹Department of Physics and Atmospheric Science, Dalhousie University, Halifax, Nova Scotia B3H 4R2 Canada
²Department of Physics and Astronomy, West Virginia University, Morgantown, West Virginia 26506-6315, USA
³Department of Physics, University of Notre Dame, Notre Dame, Indiana 46556, USA

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Vol. 94, Iss. 15 — 15 October 2016

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Images

Figure 1
(a) Linear absorption (solid curve) of the GaAs sample showing the heavy-hole exciton (HH) and light-hole exciton (LH) resonances together with the laser spectrum (dashed) used in the TFWM experiments. Inset: Laser spectrum plotted over a wider energy range. (b) TFWM results at 10 K as a function of time delay ( $τ$ ) between $\vec{E_{1}}$ and $\vec{E_{2}}$ and detection photon energy for an excited carrier density of $8.0 \times 10^{15} {cm}^{- 3}$ . (c) Same as (b) for a density of $5.4 \times 10^{16} {cm}^{- 3}$ . (d) The four-wave mixing signal as a function of density for a detection photon energy within the interband continuum at 1.53 eV. (e) Same as (d) for detection at the exciton peak. The red dashed line in (d) and (e) is a fit to a power law, showing cubic scaling for the interband continuum signal and weaker scaling for the exciton response.
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Figure 2
(a) Linear absorption (solid curve) with the laser spectrum (dashed) used in the 2DFTS experiments. (b) The strain-split heavy-hole and light-hole excitons were modeled as a three-level system with transition energies $ℏ ω_{H H}$ and $ℏ ω_{L H}$ , respectively. The interband transitions were modeled as ten independent equally-spaced two-level systems with transition energies $ℏ ω_{C}^{(1)} ... ℏ ω_{C}^{(10)}$ . (c),(d) Experimental results for the amplitude (c) and real part (d) of the 2DFTS signal. These data were taken with parallel polarizations in the two input excitation pulses. (e),(f) Simulation results for the amplitude (e) and real part (f) of the 2DFTS signal using the optimum EID and EIS parameters.
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Figure 3
Simulation results of the normalized 2DFTS signal for varying levels of EID and EIS. (a),(b) Amplitude and real part of the calculated 2DFTS signal with no EID or EIS. (c),(d) Simulated results with no EIS with EID coefficients governing exciton-exciton and exciton-continuum interactions of $γ_{EID}^{X} = 0.27 \times 10^{- 4} {cm}^{3} s^{- 1}$ and $γ_{EID}^{C} = 3.6 \times 10^{- 4} {cm}^{3} s^{- 1}$ , respectively. (e),(f) Simulated results for no EID, but including EIS with the same magnitude of coupling coefficients as in (c),(d) with a negative sign. (g),(h) Same as (e) and (f) but with positive values for the EIS coefficients.
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Figure 4
Simulation results of the normalized 2DFTS signal for varying levels of EIS with the EID coefficients held constant at the optimum values. (a) Simulated results with negative EIS coefficients three times smaller in magnitude than the EID coefficients. (b) Simulated results without EIS added. (c) Same as (a) with positive EIS coefficients. (d)–(f) Real part of 2DFTS signal shown in (a)–(c). Cross diagonal slices of the amplitude and real 2DFTS spectra are plotted along lines I, II, and III as a function of emission energy in (g), (h), and (i), respectively.
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Figure 5
Results of 2DFTS experiments for the same conditions as in Fig. 2 taken with orthogonal linear excitation pulse polarizations, showing the (a) magnitude and (b) real part of the 2DFTS spectrum. The overall magnitude of the signal strength, which is displayed here using a normalized contour scale, is reduced relative to the results in Figs. 2 and 2 by approximately six times.
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Figure 6
Normalized amplitude results of 2DFTS experiments and simulations for varying excited carrier density. (a)–(c) Results of 2DFTS experiments for excited carrier densities of $1.6 \times 10^{16} {cm}^{- 3}, 3.2 \times 10^{16} {cm}^{- 3}$ , and $8.0 \times 10^{16} {cm}^{- 3}$ , respectively. (d)–(f) Simulation results for the same excited carrier densities as (a)–(c).
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