Roberto Rosati

Wigner-function formalism applied to semiconductor quantum devices: Failure of the conventional boundary condition scheme

The Wigner-function formalism is a well-known approach to model charge transport in semiconductor nanodevices. The primary goal of the present article is to point out and explain the intrinsic limitations of the conventional quantum-device modeling based on such a Wigner-function paradigm, providing a definite answer to open questions related to the application of the conventional spatial boundary condition scheme to the Wigner transport equation. Our analysis shows that (i) in the absence of energy dissipation (coherent limit) the solution of the Wigner equation equipped with given boundary conditions is not unique, and (ii) when dissipation and decoherence phenomena are taken into account via a relaxation-time approximation, the solution, although unique, is not necessarily a physical Wigner function.

Derivation of nonlinear single-particle equations via many-body Lindblad superoperators: A density-matrix approach

A recently proposed Markov approach provides Lindblad-type scattering superoperators, which ensure the physical (positive-definite) character of the many-body density matrix. We apply the mean-field approximation to such a many-body equation, in the presence of one- and two-body scattering mechanisms, and we derive a closed equation of motion for the electronic single-particle density matrix, which turns out to be nonlinear as well as non-Lindblad. We prove that, in spite of its nonlinear and non-Lindblad structure, the mean-field approximation does preserve the positive-definite character of the single-particle density matrix, an essential prerequisite of any reliable kinetic treatment of semiconductor quantum devices. This result is in striking contrast with conventional (non-Lindblad) Markov approaches, where the single-particle mean-field equations can lead to positivity violations and thus to unphysical results. Furthermore, the proposed single-particle formulation is extended to the case of quantum systems with spatial open boundaries, providing a formal derivation of a recently proposed density-matrix treatment based on a Lindblad-like system-reservoir scattering superoperator.

Scattering nonlocality in quantum charge transport: Application to semiconductor nanostructures

Our primary goal is to provide a rigorous treatment of scattering nonlocality in semiconductor nanostructures. On the one hand, starting from the conventional density-matrix formulation and employing as ideal instrument for the study of the semiclassical limit the well-known Wigner-function picture, we shall perform a fully quantum-mechanical derivation of the space-dependent Boltzmann equation. On the other hand, we shall examine the validity limits of such semiclassical framework, pointing out, in particular, regimes where scattering-nonlocality effects may play a relevant role; to this end we shall supplement our analytical investigation with a number of simulated experiments, discussing and further expanding preliminary studies of scattering-induced quantum diffusion in GaN-based nanomaterials. As for the case of carrier-carrier relaxation in photoexcited semiconductors, our analysis will show the failure of simplified dephasing models in describing phonon-induced scattering nonlocality, pointing out that such limitation is particularly severe for the case of quasielastic dissipation processes

Microscopic modeling of scattering quantum non-locality in semiconductor nanostructures

In spite of their intrinsic validity limits, a number of Boltzmann-like simulation schemes are extensively employed in the investigation of semiconductor nanomaterials and nanodevices. Such modeling strategies, based on the neglect of carrier phase coherence, are definitely unable to describe space-dependent ultrafast phenomena. In this letter, we shall propose a quantum-mechanical modeling strategy able to properly account for scattering-induced spatial non-locality. Its power and flexibility will be demonstrated via a few simulated experiments.

Lindblad approach to spatiotemporal quantum dynamics of phonon-induced carrier capture processes

In view of the ultrashort spatial and temporal scales involved, carrier capture processes in nanostructures are genuine quantum phenomena. To describe such processes, methods with different levels of approximations have been developed. By properly tailoring the Lindblad-based nonlinear single-particle density matrix equation provided by an alternative Markov approach, in this work we present a Lindblad superoperator to describe how the phonon-induced carrier capture affects the spatio-temporal quantum dynamics of a flying wave packet impinging on a quantum dot. We compare the results with non-Markovian quantum kinetics calculations and discuss the advantages and drawbacks of the two approaches.

Electron-phonon coupling in metallic carbon nanotubes: Dispersionless electron propagation despite dissipation

A recent study [Rosati, Dolcini, and Rossi, Appl. Phys. Lett. 106, 243101 (2015)] has predicted that, while in semiconducting single-walled carbon nanotubes (SWNTs) an electronic wave packet experiences the typical spatial diffusion of conventional materials, in metallic SWNTs, its shape remains essentially unaltered up to micrometer distances at room temperature, even in the presence of the electron-phonon coupling. Here, by utilizing a Lindblad-based density-matrix approach enabling us to account for both dissipation and decoherence effects, we test such a prediction by analyzing various aspects that were so far unexplored. In particular, accounting for initial nonequilibrium excitations, characterized by an excess energy E0, and including both intra- and interband phonon scattering, we show that for realistically high values of E0 the electronic diffusion is extremely small and nearly independent of its energetic distribution, in spite of a significant energy-dissipation and decoherence dynamics. Furthermore, we demonstrate that the effect is robust with respect to the variation of the chemical potential. Our results thus suggest that metallic SWNTs are a promising platform to realize quantum channels for the nondispersive transmission of electronic wave packets

Dispersionless propagation of electron wavepackets in single-walled carbon nanotubes

We investigate the propagation of electron wavepackets in single-walled carbon nanotubes via a Lindblad-based density-matrix approach that enables us to account for both dissipation and decoherence effects induced by various phonon modes. We show that, while in semiconducting nanotubes the wavepacket experiences the typical dispersion of conventional materials, in metallic nanotubes its shape remains essentially unaltered, even in the presence of the electron-phonon coupling, up to micron distances at room temperature.

Quantum diffusion due to scattering non-locality in nanoscale semiconductors

In view of its local character, the semiclassical or Boltzmann theory is intrinsically unable to describe transport phenomena on ultrashort space and time scales, and to this purpose genuine quantum-transport approaches are imperative. By employing a density-matrix simulation strategy recently proposed, we shall demonstrate its power and flexibility in describing quantum-diffusion phenomena in nanoscale semiconductors. In particular, as for the case of carrier-carrier relaxation in photoexcited semiconductors, our analysis will show the failure of simplified dephasing models in describing phonon-induced scattering non-locality, pointing out that such limitation is particularly severe for the case of quasielastic dissipation processes.

Microscopic modeling of quantum devices at high carrier densities via Lindblad-type scattering superoperators

We derive a local equation of motion for the electronic single-particle density matrix in the presence of one- as well as two-body scattering processes. This is done by applying the mean-field approximation to the many-electron dynamics obtained via a recently proposed Markov limit, able to furnish many-body Lindblad-type scattering superoperators. The resulting time evolution at finite/high carrier densities turns out to be non-linear (and therefore non-Lindblad), and to recover a Lindblad form in the low-density limit.

Microscopic treatment of energy dissipation and decoherence via many-body Lindblad superoperators

Starting from a recent reformulation of the Markov limit, we apply the mean- field approximation to the resulting Lindblad-type many-electron dynamics, and derive a closed equation of motion for the electronic single-particle density matrix in the presence of one- and two-body scattering mechanisms. The proposed formulation preserves the positive- definite character of the single-particle density matrix. This result is in striking contrast with conventional Markov approaches, where the single-particle mean-field equations can lead to positivity violations and therefore to unphysical results.