Spatial Variation of Currents and Fields Due to Localized Scatterers in Metallic Conduction

Landauer, Rolf

doi:10.1147/rd.13.0223

Cited by 3,428 publications

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“…The pioneering works of Landauer 1 and Büttiker [2][3][4] lay the foundations for what is now known as the scattering approach to electron transport. The basic tenet is that a coherent conductor is characterized by its scattering matrix.…”

Section: Introductionmentioning

confidence: 99%

Keldysh action of a multiterminal time-dependent scatterer

Snyman

Nazarov

2008

Phys. Rev. B

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We present a derivation of the Keldysh action of a general multichannel time-dependent scatterer in the context of the Landauer-Büttiker approach. The action is a convenient building block in the theory of quantum transport. This action is shown to take a compact form that only involves the scattering matrix and reservoir Green's functions. We derive two special cases of the general result, one valid when reservoirs are characterized by well-defined filling factors, the other when the scatterer connects two reservoirs. We illustrate its use by considering full counting statistics and the Fermi-edge singularity.

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Section: Introductionmentioning

confidence: 99%

Keldysh action of a multiterminal time-dependent scatterer

Snyman

Nazarov

2008

Phys. Rev. B

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“…We shall present here the semiclassical explanation of shot noise, relating the quantum properties of chaotic cavities to the interference between contributions of mutually close classical trajectories. Similar methods have recently been used for explaining universal spectral fluctuations of chaotic quantum systems [1,2], and to calculate the universal mean conductance in [3,4].Following Landauer and Büttiker [6,7], we treat transport as scattering between two leads attached to the cavity. One lead is assumed to support N 1 ingoing channels and the second one N 2 outgoing channels.…”

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confidence: 99%

Semiclassical prediction for shot noise in chaotic cavities

Braun¹,

Heusler²,

Müller³

et al. 2006

J. Phys. A: Math. Gen.

126

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We show that in clean chaotic cavities the power of shot noise takes a universal form. Our predictions go beyond previous results from random-matrix theory, in covering the experimentally relevant case of few channels. Following a semiclassical approach we evaluate the contributions of quadruplets of classical trajectories to shot noise. Our approach can be extended to a variety of transport phenomena as illustrated for the crossover between symmetry classes in the presence of a weak magnetic field.PACS numbers: 72.20.My, 72.15.Rn, 05.45.Mt, 03.65.Sq Ballistic chaotic cavities have universal transport properties, just as do disordered conductors. The explanation of such universality cannot rely on any disorder average but must make do with chaos in an individual clean cavity. We shall present here the semiclassical explanation of shot noise, relating the quantum properties of chaotic cavities to the interference between contributions of mutually close classical trajectories. Similar methods have recently been used for explaining universal spectral fluctuations of chaotic quantum systems [1,2], and to calculate the universal mean conductance in [3,4].Following Landauer and Büttiker [6,7], we treat transport as scattering between two leads attached to the cavity. One lead is assumed to support N 1 ingoing channels and the second one N 2 outgoing channels. In contrast to the random-matrix treatment of [5,7] and work on quantum graphs in [8], our results cover all orders in the inverse number of channels, N = N 1 + N 2 , and thus apply to the experimentally relevant case of few channels [9]. Previously unknown and surprisingly simple expressions for the shot noise arise, both with and without time reversal invariance (see Eq. (11) below).The transition amplitudes between ingoing channels a 1 and outgoing channels a 2 define an N 1 × N 2 matrix t = {t a1a2 }. That matrix determines the power of shot noise as P = tr(tt † − tt † tt † ) , in units 2e 3 |V | πh depending on the voltage V ; for us, . . . denotes an average over a small energy interval. Previous work had involved averages over ensembles of matrices t and obtained [5,7] (1) here β = 1 refers to the so-called "orthogonal case" of time-reversal invariant dynamics; if a magnetic field is applied to break time-reversal invariance ("unitary case", β = 2), the second ("weak localization") term disappears. Higher orders in 1 N are as yet unknown. In the semiclassical limit, each transition amplitude t a1a2 is given by a sum over trajectories α leading from an ingoing channel a 1 to an outgoing channel a 2 , t a1a2 ∼ α(a1→a2) Aα √ TH e iSα/h [10]. It can be shown that the absolute value of the initial angle of the relevant trajectories (i.e. the angle enclosed between the initial piece and the direction of the lead) is dictated by the ingoing channel, whereas the final angle is determined by the outgoing channel. The contribution of each trajectory depends on the Heisenberg time T H = Ω (2πh) f −1 , with Ω the volume of the energy shell and f the number of free...

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“…Knowledge of the phase shifts allows us to compute the linear DC conductance through the TA at T = 0 using the Landauer-Buttiker formalism [3,16]. In the ground state, the m = 0 combination of the leads is totally decoupled, and therefore δ 0 = 0.…”

Section: Su(4) Kondomentioning

confidence: 99%

Kondo effect and spin filtering in triangular artificial atoms

Zaránd

Brataas

Goldhaber‐Gordon

2003

Solid State Communications

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We study strongly correlated states in triangular artificial atoms. Symmetry-driven orbital degeneracy of the single particle states can give rise to an SU (4) Kondo state with entangled orbital and spin degrees of freedom, and a characteristic phase shift δ = π/4. Upon application of a Zeeman field, a purely orbital Kondo state is formed with somewhat smaller Kondo temperature and a fully polarized current through the device. The Kondo temperatures are in the measurable range. The triangular atom also provides a tool to systematically study the singlet-triplet transitions observed in recent experiments [4,11].

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Spatial Variation of Currents and Fields Due to Localized Scatterers in Metallic Conduction

Cited by 3,428 publications

References 0 publications

Keldysh action of a multiterminal time-dependent scatterer

Keldysh action of a multiterminal time-dependent scatterer

Semiclassical prediction for shot noise in chaotic cavities

Kondo effect and spin filtering in triangular artificial atoms

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