Half-integer and integer quantum-flux periods in the magnetoresistance of one-dimensional rings

D’Amato, Jorge L.; Pastawski, Horacio M.; Weisz, J. F.

doi:10.1103/physrevb.39.3554

Cited by 101 publications

(39 citation statements)

References 25 publications

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“…We demonstrate our results using a lattice Hamiltonian similar to the one used in Ref. [33] and more recently in [34]. While we use the simplest model with this geometry, i.e.…”

Section: Modelmentioning

confidence: 99%

Mono-parametric quantum charge pumping: Interplay between spatial interference and photon-assisted tunneling

2005

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We analyze quantum charge pumping in an open ring with a dot embedded in one of its arms. We show that cyclic driving of the dot levels by a single parameter leads to a pumped current when a static magnetic flux is simultaneously applied to the ring. Based on the computation of the Floquet-Green's functions, we show that for low driving frequencies ω0, the interplay between the spatial interference through the ring plus photon-assisted tunneling gives an average direct current (dc) which is proportional to ω 2 0 . The direction of the pumped current can be reversed by changing the applied magnetic field.

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“…We demonstrate our results using a lattice Hamiltonian similar to the one used in Ref. [33] and more recently in [34]. While we use the simplest model with this geometry, i.e.…”

Section: Modelmentioning

confidence: 99%

Mono-parametric quantum charge pumping: Interplay between spatial interference and photon-assisted tunneling

2005

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“…For single rings, it has been * Email:r.roemer@warwick.ac.uk discussed that both periods can be present [2]. Among the theoretical studies on single ring systems, D'Amato et al [16], have discussed a tight-binding model of a disordered ring coupled to two external leads, and have calculated the Landauer conductance [17] as a function of φ. For strongly disordered rings and for arbitrary disorder with weakly coupled branches, they have found a dominant period φ 0 .…”

Section: Introductionmentioning

confidence: 99%

Magnetotransport in periodic and quasiperiodic arrays of mesoscopic rings

2003

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We study theoretically the transmission properties of serially connected mesoscopic rings threaded by a magnetic flux. Within a tight-binding formalism we derive exact analytical results for the transmission through periodic and quasiperiodic Fibonacci arrays of rings of two different sizes. The role played by the number of scatterers in each arm of the ring is analyzed in some detail. The behavior of the transmission coefficient at a particular value of the energy of the incident electron is studied as a function of the magnetic flux (and vice versa) for both the periodic and quasiperiodic arrays of rings having different number of atoms in the arms. We find interesting resonance properties at specific values of the flux, as well as a power-law decay in the transmission coefficient as the number of rings increases, when the magnetic field is switched off. For the quasiperiodic Fibonacci sequence we discuss various features of the transmission characteristics as functions of energy and flux, including one special case where, at a special value of the energy and in the absence of any magnetic field, the transmittivity changes periodically as a function of the system size.

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“…The second term contains a virtual exploration into the first polaronic excitation. It is noteworthy that when Γ = 0, this Green function would cancel out at an intermediate energy giving rise to an antiresonance [14,13]. This concept extends the spectroscopic Fano-resonances [15] to the problem of conductance [16].…”

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confidence: 94%

“…1). A maximal probability (T 1,0 = 1) requires equal rates of formation and decay [14]: Γ L = Γ R , which in our RTD implies:…”

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confidence: 99%

Tuning a resonance in Fock space: Optimization of phonon emission in a resonant-tunneling device

2001

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Phonon-assisted tunneling in a double barrier resonant tunneling device can be seen as a resonance in the electron-phonon Fock space which is tuned by the applied voltage. We show that the geometrical parameters can induce a symmetry condition in this space that can strongly enhance the emission of longitudinal optical phonons. For devices with thin emitter barriers this is achieved by a wider collector barrier.Progress in mesoscopic semiconductor devices [1] and molecular electronics [2] is driven by the need of miniaturization and the wealth of new physics provided by coherent quantum phenomena. A fundamental idea behind these advances was Landauer's view that conductance is transmittance [3,4]. Hence, the typical conductance peaks and valleys, observed when some control parameter is changed, are seen as fringes in an interferometer. However, the many-body electron-electron (ee) and electron-phonon (e-ph) interactions restrict the use of this picture. The e-e effects received much attention in different contexts [1]. While interest on e-ph interaction remained mainly focused on double barrier Resonant Tunneling Devices (RTD) [5], where phononassisted tunneling shows up as a satellite peak in a valley of the current-voltage (I-V) curve, recent observation of electro-mechanical effects in molecular electronics [6] requires a reconsideration of the e-ph problem. Theory evolved from a many-body Green's function in a simplified model for the polaronic states [7] to quantum and classical rate equations approach [8]. The latter uses an incoherent description of the e-ph interaction by adopting an imaginary self-energy correction to the electronic states [9,10].In this article, we analyze a quantum coherent solution of transport with e-ph interaction. We resort to a mapping of the many-body problem into a one-body scattering system where each phonon mode adds a new dimension to the electronic variable [11,12]. Transmission of electrons between incoming and outgoing channels with different number of phonons are then used in a Landauer's picture where the only incoherent processes occur inside the electrodes. This allows to develop the concept of resonance in the e-ph Fock space and the identification of the control parameters that optimize the coherent processes leading to a maximized phonon emission. It also gives a clue as to how "decoherence" arise within an exact many-body description. As an application, we consider a RTD phonon emitter where the relevant parameters are best known. There, the first polaronic excitation serves as an "intermediate" state for the phonon emission. An electron with kinetic energy ε ≤ ε F and potential energy eV in the emitter decays through tunneling into an electron with energy ε + eV−hω 0 in the collector plus a longitudinal optical (LO) phonon. The tuning parameter is the applied voltage while the optimization of phonon emission requires the tailoring of the tunneling rates.Let us consider a minimal Hamiltonian:where c + j and c j are electron creation and annihilation operators at s...

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Half-integer and integer quantum-flux periods in the magnetoresistance of one-dimensional rings

Cited by 101 publications

References 25 publications

Mono-parametric quantum charge pumping: Interplay between spatial interference and photon-assisted tunneling

Mono-parametric quantum charge pumping: Interplay between spatial interference and photon-assisted tunneling

Magnetotransport in periodic and quasiperiodic arrays of mesoscopic rings

Tuning a resonance in Fock space: Optimization of phonon emission in a resonant-tunneling device

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