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Electron–phonon dissipation in quantum nanodevices

Limitations of quantum-kinetic treatments

Abstract

Microscopic modelling of electronic-phase coherence versus energy dissipation plays a crucial role in the design and optimization of new-generation electronic quantum nanodevices, like quantum-cascade light sources and quantum logic gates; in this context, a variety of simulation strategies have been proposed and employed. The aim of this article is to discuss virtues versus intrinsic limitations of non-Markovian density-matrix approaches. More specifically, we shall show that the usual mean-field treatment employed to derive quantum-kinetic equations may lead to highly unphysical results, like negative distribution functions and non-dissipative carrier–optical phonon couplings. By means of a simple two-level model, we shall show that such limitations are expected to be particularly severe in zero-dimensional electronic systems—like quantum-dot nanostructures, potential constituents of quantum-computation devices—coupled to dispersionless phonon modes. Such a behaviour is in striking contrast with the case of Markovian treatments, where a proper combination of adiabatic limit and mean-field approximation guarantees a physically acceptable solution.

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Notes

  1. 1.

    A relevant exception is the so-called dynamics-controlled truncation introduced by Axt and Stahl (see, e.g. Ref. [8]), based on an expansion in powers of the exciting laser field.

  2. 2.

    Here the complex-conjugation symbol has no effect on the (real) single-particle energy \(\epsilon _{\alpha _1}\) but plays a crucial role when the latter is replaced by a corresponding (complex) self-energy [see Eq. (22)].

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Acknowledgments

We are grateful to David Taj for stimulating and fruitful discussions. We gratefully acknowledge funding by the Graphene@PoliTo laboratory of the Politecnico di Torino, operating within the European FET-ICT Graphene Flagship project (http://www.graphene-flagship.eu). Computational resources were provided by HPC@PoliTo, a project of Academic Computing of the Politecnico di Torino (http://www.hpc.polito.it).

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Correspondence to Rita Claudia Iotti.

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Iotti, R.C., Dolcini, F., Montorsi, A. et al. Electron–phonon dissipation in quantum nanodevices. J Comput Electron 15, 1170–1178 (2016). https://doi.org/10.1007/s10825-016-0858-6

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Keywords

  • Solid-state quantum devices
  • Electronic dissipation and decoherence
  • Density-matrix formalism