Virtual electron diffusion during quantum tunneling of the electric charge

Averin, D. V.; Nazarov, Yu. V.

doi:10.1103/physrevlett.65.2446

Cited by 520 publications

(499 citation statements)

References 2 publications

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“…This is the standard result [37] for the conductance in the cotunneling regime. Second, near the transmission resonances, we can neglect the terms involving the trigamma function which are smaller than the Fermi function by a factor βΓ λ .…”

Section: Weak-coupling Limitmentioning

confidence: 99%

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Phase coherent transmission through interacting mesoscopic systems

2001

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This is a review of the phase coherent transmission through interacting mesoscopic conductors. As a paradigm we study the transmission amplitude and the dephasing rate for electron transport through a quantum dot in the Coulomb blockade regime. We summarize experimental and theoretical work devoted to the phase of the transmission amplitude. It is shown that the evolution of the transmission phase may be dominated by non-universal features in the short-time dynamics of the quantum dot. The controlled dephasing in Coulomb coupled conductors is investigated. Examples comprise a single or multiple quantum dots in close vicinity to a quantum point contact. The current through the quantum point contact "measures" the state of the dots and causes dephasing. The dephasing rate is derived using widely different theoretical approaches. The Coulomb coupling between mesoscopic conductors may prove useful for future work on electron coherence and quantum computing.

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Section: Weak-coupling Limitmentioning

confidence: 99%

“…Due to the small number of levels, all contributions to the transmission amplitude can be computed explicitly. The starting point is the two-level Hamiltonian for the quantum dot, 37) where U 0 denotes the strength of the electron-electron interaction. The dot is coupled via matrix elements…”

Section: Finite Temperaturementioning

confidence: 99%

Phase coherent transmission through interacting mesoscopic systems

2001

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“…In the presence of an electric field E, the hopping conductivity in the paramagnetic state is σ ∼ exp −r/ξ − e 2 /(κrT ) + eEr/T , [25], with the inelastic co-tunneling localization length [15,21]. For sufficiently high electric fields E > T /eξ the tunneling term, exp(−r/ξ), in the conductivity is not important.…”

mentioning

confidence: 99%

“…The mechanism for electron propagation through an array of grains at low temperatures is elastic and/or inelastic co-tunneling. The corresponding probabilities in the limit of weak coupling between the grains [17] are given by [21]. Assuming that all probabilities P i (m 2 ) are approximately the same [11] for each grain, P i (m 2 ) = P(m 2 ) for all i, and expressing them in terms of the localization length ξ(m 2 ), defined by P(m 2 ) = exp[−a/ξ(m 2 )], we obtain [15]…”

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confidence: 99%

Electron Transport in Nanogranular Ferromagnets

2007

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We study electronic transport properties of ferromagnetic nanoparticle arrays and nanodomain materials near the Curie temperature in the limit of weak coupling between the grains. We calculate the conductivity in the Ohmic and non-Ohmic regimes and estimate the magnetoresistance jump in the resistivity at the transition temperature. The results are applicable for many emerging materials, including artificially self-assembled nanoparticle arrays and a certain class of manganites, where localization effects within the clusters can be neglected.PACS numbers: 73.43.Qt Arrays of ferromagnetic nanoparticles are becoming one of the mainstreams of current mesoscopic physics [1,2,3,4]. Not only ferromagnetic granules promise to serve as logical units and memory storage elements meeting elevated needs of emerging technologies, but also offer an exemplary model system for investigation of disordered magnets. At the same time the model of weakly coupled nanoscale ferromagnetic grains proved to be useful for understanding the transport properties of doped manganite systems [5,6] that have intrinsic inhomogeneities. Recent studies showed that above the Curie temperature these materials possess a nanoscale ferromagnetic cluster structure which to a large extend controls transport in these systems [7,8,9,10]. This defines an urgent quest for understanding and quantitative description of electronic transport in ferromagnetic nanodomain materials based on the model of nanogranular ferromagnets.In this paper we investigate electronic transport properties of arrays of ferromagnetic grains [11] near the ferromagnetic-paramagnetic transition, see Fig. 1. At low temperatures, T < T s c , the sample is in a so called superferromagnetic (SFM) state, see Fig. 1, set up by dipole-dipole interactions. Near the macroscopic Curie temperature, T s c , thermal fluctuations destroy the macroscopic ferromagnetic order. At intermediate temperatures T s c < T < T g c , where T g c is the Curie temperature of a single grain, the system is in a superparamagnetic (SPM) state where each grain has its own magnetic moment while the global ferromagnetic order is absent. At even higher temperatures, T > T g c , the ferromagnetic state within each grain is destroyed and the complete sample is in a paramagnetic state. We consider the model of weakly interacting grains in which the sample Curie temperature is much smaller than the Curie temperature of a single grain, T s c ≪ T g c . We first focus on the SPM state, and discuss a d−dimensional array (d = 3, 2) of ferromagnetic grains taking into account Coulomb interactions between electrons. Granularity introduces additional energy parameters apart from the two Curie temperatures, T g c and T s c : each nanoscale cluster is characterized by (i) the charging c , where T s c is the macroscopic Curie temperature of the system, the ferromagnetic grains (superspins) form a superferromagnet (SFM); for T s c < T < T g c , where T g c is the Curie temperature for a single grain, the system is in a superparamagne...

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“…The other one, δσ (2) xy , is due to elastic cotunneling (EC) [5], it involves diffusion of an electron through the grain (that is why it is suppressed at temperatures greater than the Thouless energy of the grain E Th ):…”

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confidence: 99%

Hall Resistivity of Granular Metals

Kharitonov

Efetov

2007

Phys. Rev. Lett.

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We calculate the Hall conductivity σxy and resistivity ρxy of a granular system at large tunneling conductance gT ≫ 1. We show that in the absence of Coulomb interaction the Hall resistivity depends neither on the tunneling conductance nor on the intragrain disorder and is given by the classical formula ρxy = H/(n * ec), where n * differs from the carrier density n inside the grains by a numerical coefficient determined by the shape of the grains. The Coulomb interaction gives rise to logarithmic in temperature T correction to ρxy in the range Γ T min(gT Ec, E Th ), where Γ is the tunneling escape rate, Ec is the charging energy and E Th is the Thouless energy of the grain. does not depend on the mean free path and allows one to experimentally determine the carrier concentration n. Recently, much attention from both experimental and theoretical sides has been paid to granular systems (see a review [1] and references therein). Although various physical quantities have been calculated in different regimes, the Hall transport in the granular matter has not been addressed theoretically yet. In this work we calculate the Hall conductivity(HC) of a granular system and Coulomb interaction corrections to it in the metallic regime, when the intergrain tunneling conductance G T = (2e 2 / )g T is large, g T ≫ 1 (further we set = 1).Technically, calculating HC σ xy appears to be more complicated than calculating the longitudinal conductivity(LC) σ xx . The granularity of the system is ensured by the condition that the conductance G 0 = 2e 2 g 0 of the grain is much larger than the tunneling conductance G T , g 0 /g T ≫ 1. In this limit the main contribution to σ xx comes from the tunnel barriers between the grains rather than from scattering on impurities inside the grains. In the absence of Coulomb interaction LC equalswhere a is the size of the grains and d is the dimensionality of the system. Therefore when studying longitudinal transport one can neglect electron dynamics inside the grains, which simplifies calculations significantly. On the contrary, for Hall transport one is forced to take the intragrain electron dynamics into account, since the Hall current originates from the transversal drift in crossed magnetic and electric fields inside the grains. As we find in this work the intragrain electron dynamics can be included within the diagrammatic approach by considering higher diffusion modes inside the grain. This procedures accounts for the finiteness of the ratio g T /g 0 , and allows one, in principle, to study both LC and HC of the granular system for arbitrary ratio g T /g 0 . The obtained results reproduce the solution of the classical electrodynamics problem for a granular medium (e.g. the formulacan be obtained as a series in g T /g 0 ). Quantum effects (e.g. Coulomb interaction and weak localization) may be incorporated into this scheme afterwards.We perform calculations for magnetic fields H such that ω H τ ≪ 1, where ω H = eH/mc is the Larmor frequency and τ is the electron scattering time inside the grai...

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Virtual electron diffusion during quantum tunneling of the electric charge

Cited by 520 publications

References 2 publications

Phase coherent transmission through interacting mesoscopic systems

Phase coherent transmission through interacting mesoscopic systems

Electron Transport in Nanogranular Ferromagnets

Hall Resistivity of Granular Metals

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