Resonant Franz-Keldysh exciton effect in the narrow biased quantum wire subject to a strong magnetic field

Abstract

We present an analytical investigation of quasi-one-dimensional excitons in thin uniform ͑single͒ and double nanoscaled cylindrical quantum wires ͑UQWR and DQWR͒ surrounded by a barrier of infinite height and exposed to external electric and strong magnetic fields. The DQWR is formed by inserting an impenetrable longitudinal barrier in a single-quantum wire. Both external fields are directed parallel to the quantum wire ͑QWR͒ axis. The radius of the QWRs and the magnetic length are taken to be much less than the exciton Bohr radius. For the dependencies of the positions and widths of the complex quasidiscrete energy levels of the indirect exciton in the DQWR, in which the carriers are separated by the insertion on the confinement, electric field strength and width of the interwire barrier are derived. The confinement ͑insertion͒ leads to an increase ͑decrease͒ of the exciton binding energy. The impact of the electric field ionization of the exciton is less pronounced for strongly confined and weakly separated carriers. The coefficient of the exciton absorption in the UQWR as a function of the confinement and electric field is calculated in an explicit form. The effect of the confinement and electric field on the exciton peak closely resembles that on the quasidiscrete level of the indirect exciton in the DQWR. Electron-hole attraction increases remarkably the optical Franz-Keldysh electroabsorption in the frequency region below the edge and distant from the exciton peaks. The coefficient of absorption reflecting the electric field ionization and autoionization caused by the coupling between the discrete and continuous exciton states adjacent to the different size-quantized or Landau levels is obtained analytically. A comparison of our analytical results with numerical data is performed. Estimates of the expected experimental values for the parameters of GaAs/GaAlAs QWR show that the autoionized exciton magnetostates in thin biased QWRs are sufficiently stable to be observed.

Exciton absorption spectra in narrow armchair graphene nanoribbons in an electric field

“…It follows from eq. (13) that in the narrow ribbon with small width d the diagonal potentials V N N dominate the off-diagonal ones in the set of equations (11). This allows us to set V N N = V N δ N N , omit the Σ N from eqs.…”

“…This allows us to set V N N = V N δ N N , omit the Σ N from eqs. (11) and arrive at the equations for the functions χ N (y) governed by the diagonal Coulomb contribution…”

“…The second reason is that quasi-1D structures, namely DE [10], QWR [11] and AGNR [12] are favorable for the formation of not only strictly discrete but also metastable Fano resonances [13] like exciton states adjacent to the excited size-quantized energy levels. The nature of the Fano resonances lies in the inter-subband coupling between the discrete and low-lying continuous Rydberg states.…”

“…For the semiconductor structures the Rydberg constant does not depend on the confinement parameters, i.e. on the radius [11] and magnetic field [14] for the QWR and DE, respectively. For the AGNR with width d we have Ry ∼ d −1 [15].…”

Confined Franz–Keldysh effect in ZnO quantum dots

“…The Franz-Keldysh effect in semiconducting cylindrical nanowires has been studied using the semiconductor Bloch equations [21,22]. Monozon and Schmelcher [23] studied the resonant Franz-Keldysh exciton effect in a narrow biased quantum wire subject to a strong magnetic field. More recently, the Franz-Keldysh effect in the interband optical absorption of a directgap semiconducting nanostructure has also been calculated [24].…”