Dissociation of one-dimensional excitons by static electric field

TL;DR

The study addresses how a static electric field influences excitons in one-dimensional semiconductors by employing a two-band lattice model with on-site Coulomb interaction. It shows that bound excitons persist at zero field and exhibit a quadratic Stark shift under weak fields, while sufficiently strong fields induce dissociation and reveal an equally spaced Wannier-Stark ladder in the linear optical spectrum. The results connect tightly with first-principles calculations in carbon nanotubes, providing a practical spectral fingerprint for field-induced ionization in 1D systems. The framework offers a tractable approach to understanding exciton dynamics in low-dimensional materials and informs experiments probing exciton dissociation in nanowires and nanotubes.

Abstract

The quantum states of an electron-hole pair in one-dimensional semiconductors under a static electric field are theoretically analyzed using a two-band model with on-site Coulomb interaction. In the absence of static field, the electron and hole are always bound, forming an exciton regardless of the Coulomb interaction strength, in contrast to what occurs in higher-dimensional semiconductors. The static field modifies the wave function of the electron-hole pair, turning bound states into continuum states. However, at low static fields, the linear optical spectra resemble those of the unbiased semiconductor, exhibiting a quadratic redshift of the main exciton absorption line as the field increases. When the static field exceeds a critical threshold, the exciton dissociates and the linear optical spectra exhibit signatures of the Wannier-Stark ladder with squally spaced peaks, making them a valuable tool for experimentally probing exciton dissociation.

Figures (5)

• Figure 1: Absorption spectrum, in arbitrary units, in the absence of Coulomb and dipole-dipole interactions for different values of the static electric field, indicated on each curve. Spectra have been shifted upwards for clarity.
• Figure 2: Absorption spectrum in arbitrary units in the absence of static electric field ($F=0$) for different values of $U$, indicated on each curve. In this plot, the optical bandgap corresponds to $\hbar\Delta\omega/T=-2$. The inset displays the binding energy $E_\mathrm{b}=-E_0-2T$ as a function of $U$.
• Figure 3: (a) Absorption spectra as a function of energy $\hbar\Delta\omega$ and electric field $F$ for $U=T$, normalized to the maximum value of the dataset. The fan-chart of the Wannier-Stark ladder is revealed at high fields. (b) Detailed view at low field strengths, illustrating the quadratic Stark effect and the progressive attenuation of the exciton line.
• Figure 4: Stark shift of the exciton energy $\Delta E$ as a function of the electric field $F$ for $U=T$. Solid line correspond to the quadratic fitting $\Delta E=\kappa_\mathrm{s} F^2$. The inset shows the dependence of the coefficient $\kappa_\mathrm{s}$ on the interaction parameter $U$. Dashed line is a guide to the eye.
• Figure 5: Maximum of the absorption coefficient of the exciton line $\rho_\mathrm{max}(F)$, normalized to its value at $F=0$, as a function of the static electric field for $U=T$ (solid blue line). Black dashed line corresponds to the nonlinear fit given by Eq. \ref{['eq:17']}. The inset shows the dependence of dissociation field $F_\mathrm{d}$ on the interaction parameter $U$. Black solid line is a guide to the eye.