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Quantum theory of terahertz conductivity of semiconductor nanostructures

In collaboration with T. Ostatnický of Charles University we participated to the development of the first theory of the quantum conductivity describing the transport in the terahertz spectral range, which does not contain internal contradictions. We have shown that the broken translation symmetry of the nanostructures induces a broadband drift-diffusion current which must be explicitly taken into account.
Usually, all the relevant charge carrier scattering processes in the studied system are not known since their independent experimental determination is difficult. The usual approach based on the Kubo formula introduces a phenomenological charge scattering rate (or relaxation time) accounting for all the scattering processes. This approximation is highly pertinent in the optical range. However, the approach fails at low frequencies in nanocrystals in the regime where the scattering rate is comparable to the probing frequency; e.g., it always yields nonzero conductivity at zero frequency (dc regime) even if the nanocrystals are mutually perfectly isolated.
We have shown [1] that the broken translation symmetry of the nanostructures induces a broadband drift-diffusion current, which is not taken into account in the analysis based on Kubo formula in the relaxation time approximation. The proper introduction of this current removes all the contradictions, fulfills the classical limit in the case of large nanocrystals and it is at the origin of significant reshaping of the conductivity spectra up to terahertz or multiterahertz spectral ranges. It is used for the interpretation of temperature dependent photoconductivity spectra in various nanocrystal systems.


Fig. 1: Comparison of quantum (solid line) and classical (dashed line) conductivity in GaAs cube-shaped nanocrystals of selected sizes at 300 K and free carrier concentration of 1016 cm-3. Note the excellent agreement of quantum calculations with the classical ones for large nanocrystals (1024 nm).

Reference:
[1] T. Ostatnický, V. Pushkarev, H. Němec, and P. Kužel, Quantum theory of terahertz conductivity of semiconductor nanostructures, Phys. Rev. B 97, 085426 (2018).