Quantum transport of electrons in open nanostructures with the Wigner-function formalism

Bordone, Paolo; Pascoli, M.; Brunetti, Rossella; Bertoni, Alberto; Jacoboni, Carlo; Abramo, A.

doi:10.1103/physrevb.59.3060

Cited by 81 publications

(66 citation statements)

References 12 publications

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“…Let N ′ (Λ) be a subspace of N (Λ). If N ′ (Λ) is an invariant subspace of L eff , then it is an invariant subspace of the full generator of the Markovian semigroup (22), and consequently an invariant subspace of the semigroup. A statistical operator ρ 0 , initially prepared in N ′ (Λ), would remain in N ′ (Λ) at all times, and evolve unitarily according to dρ…”

Section: A Markovian Evolution By Coarse Grainingmentioning

confidence: 99%

“…For non-commuting L eff and Λ, this statement can be generalized to Theorem 1. If a subspace of N (Λ), the null-space of operator Λ, is also an invariant subspace of L eff , then it supports decoherence-free (unitary) evolution according to the map (22).…”

Section: A Markovian Evolution By Coarse Grainingmentioning

confidence: 99%

“…, the intersection of the null-spaces N (L eff ) and N (Λ), is a steady state for the evolution according to the map (22).…”

Section: Identification Of the Steady Statementioning

confidence: 99%

“…Theorem 1 gives us a straightforward, general recipe for the classification of the decoherence-free subspaces in the case of Markovian dynamics (22). What one needs to do is to construct the operator Λ according to Eq.…”

Section: A Markovian Evolution By Coarse Grainingmentioning

confidence: 99%

“…14 The purpose of this paper is to provide a simple description of the nonunitary evolution of a ballistic nanostructure's active region due to the injection of carriers from the contacts. Carrier injection from the contacts into the active region is traditionally described by either an explicit source term, such as in the single-particle density matrix, 15,16,17,18,19,20 Wigner function 2,3,21,22,23,24,25,26,27,28,29 and Pauli equation 30,31 transport formalisms, or via a special self-energy term in the ubiquitous nonequilibrium Green's function formalism. 32,33,34,35,36,37 In this work, the problem of contact-induced decoherence is treated using the open systems formalism: 38 we start with a model interaction Hamiltonian that describes the injection of carriers from the contacts, and then deduce the resulting nonunitary evolution of the active region's many-body reduced statistical operator in the Markovian approximation.…”

Section: Introductionmentioning

confidence: 99%

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Decoherence due to contacts in ballistic nanostructures

Knežević

2008

Phys. Rev. B

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The active region of a ballistic nanostructure is an open quantum-mechanical system, whose nonunitary evolution (decoherence) towards a nonequilibrium steady state is determined by carrier injection from the contacts. The purpose of this paper is to provide a simple theoretical description of the contact-induced decoherence in ballistic nanostructures, which is established within the framework of the open systems theory. The active region's evolution in the presence of contacts is generally non-Markovian. However, if the contacts' energy relaxation due to electron-electron scattering is sufficiently fast, then the contacts can be considered memoryless on timescales coarsened over their energy relaxation time, and the evolution of the current-limiting active region can be considered Markovian. Therefore, we first derive a general Markovian map in the presence of a memoryless environment, by coarse-graining the exact short-time non-Markovian dynamics of an abstract open system over the environment memory-loss time, and we give the requirements for the validity of this map. We then introduce a model contact-active region interaction that describes carrier injection from the contacts for a generic two-terminal ballistic nanostructure. Starting from this model interaction and using the Markovian dynamics derived by coarse-graining over the effective memory-loss time of the contacts, we derive the formulas for the nonequilibrium steady-state distribution functions of the forward and backward propagating states in the nanostructure's active region. On the example of a double-barrier tunneling structure, the present approach yields an I-V curve that shows all the prominent resonant features. We address the relationship between the present approach and the Landauer-Büttiker formalism, and also briefly discuss the inclusion of scattering.

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Section: A Markovian Evolution By Coarse Grainingmentioning

confidence: 99%

Section: A Markovian Evolution By Coarse Grainingmentioning

confidence: 99%

“…, the intersection of the null-spaces N (L eff ) and N (Λ), is a steady state for the evolution according to the map (22).…”

Section: Identification Of the Steady Statementioning

confidence: 99%

Section: A Markovian Evolution By Coarse Grainingmentioning

confidence: 99%