Circuit theory for noise in incoherent normal-superconducting structures

Virtanen, Pauli; Heikkilä, Tero T.

doi:10.1088/1367-2630/8/4/050

New J. Phys.

2006

DOI: 10.1088/1367-2630/8/4/050

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Circuit theory for noise in incoherent normal-superconducting structures

Pauli Virtanen¹,

Tero T. Heikkilä²

Abstract: We consider the current fluctuations in a mesoscopic circuit consisting of nodes connected by arbitrary connectors, in a setup with multiple normal or superconducting terminals. In the limit of weak superconducting proximity effect, simplified equations for the second-order cross-correlators can be derived from the general counting field theory, and the result coincides with the semiclassical principle of minimal correlations. We discuss the derivation of this result in a multi-dot case.

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Cited by 3 publications

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“…9, 10 Multiterminal structures have been discussed in the incoherent regime, 11,12,13,14 and in the presence of a supercurrent, in a short junction, 15 and for specific values of a phase difference in a three-terminal setup. The latter was described by a method based on a direct discretization of the equations governing the full counting statistics [see Eq.…”

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confidence: 99%

“…4,5,6,7 In the context of a normal-superconducting (NS) two-terminal setup, the theoretical endeavours have recently covered, e.g., the voltage dependence of the shot noise 8,9 and certain lowbias anomalies. 9,10 Multiterminal structures have been discussed in the incoherent regime, 11,12,13,14 and in the presence of a supercurrent, in a short junction, 15 and for specific values of a phase difference in a three-terminal setup. The latter was described by a method based on a direct discretization of the equations governing the full counting statistics [see Eq.…”

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confidence: 99%

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Phase-dependent noise correlations in normal-superconducting structures

Stenberg

Virtanen²,

Heikkilä³

2007

Phys. Rev. B

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We study nonequilibrium noise correlations in diffusive normal-superconducting structures in the presence of a supercurrent. We present a parametrization for the quasiclassical Green's function in the first order of the counting field χ. This we employ to obtain the voltage and phase dependence of cross and autocorrelations and to describe the role played by the setup geometry. We find that the low-voltage behavior of the effective charge q eff describing shot noise is a result of a competition between anticorrelation of Andreev pairs due to proximity effect and the depression of the local density of states. Furthermore, we show that the noise correlations are independent of the sign of the supercurrent.6 PACS numbers: 74.40.+k, 42.50.Lc, The charge transmitted through a disordered conductor in unit time varies due to the quantum nature of the transport process. This variation is characterized by the current distribution, whose width at low temperatures is directly related to the shot noise.1 In metallic conductors, the corrections induced by the quantum coherence on the current and conductance distributions are small, 2,3 but in a metal in contact to a superconductor, more pronounced effects may be observed, e.g., in the out-of-equilibrium noise experiments. 4,5,6,7 In the context of a normal-superconducting (NS) two-terminal setup, the theoretical endeavours have recently covered, e.g., the voltage dependence of the shot noise 8,9 and certain lowbias anomalies.9,10 Multiterminal structures have been discussed in the incoherent regime, 11,12,13,14 and in the presence of a supercurrent, in a short junction, 15 and for specific values of a phase difference in a three-terminal setup. The latter was described by a method based on a direct discretization of the equations governing the full counting statistics [see Eq. (1)]. 4In the presence of the superconducting proximity effect and at voltages of the order of E T /e, the effective charge q eff characterizing the magnitude of shot noise is lower than 2e, the value corresponding to a Cooper pair. 4,8,9Here E T = D/L 2 is the Thouless energy, with D the diffusion constant and L the wire length. Applying a supercurrent in a three-terminal structure (Fig. 1) allows one to study the nature of this proximity-induced change in q eff . For example, with this approach, we directly show that the lowering of q eff is due to a competition of anticorrelation effects induced by the superconducting proximity effect 4 and the depression of the local density of states.16 In principle, the effect of an extra current in the system would be twofold: to tune the coherent effects and to induce its own correlations. Here we show that within our noninteracting model supercurrent does only the previous as all the correlations in the system are independent of the supercurrent sign.The full counting statistics 17,18,19 has recently become the method of choice to calculate shot noise in diffusive mesoscopic conductors but, to our knowledge, the cross correlations in the presence of supercurre...

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confidence: 99%

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Phase-dependent noise correlations in normal-superconducting structures

Stenberg

Virtanen²,

Heikkilä³

2007

Phys. Rev. B

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Quantum detectors for the third cumulant of current fluctuations

Heikkilä¹,

Ojanen²

2007

Phys. Rev. B

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We consider the measurement of the third cumulant of current fluctuations arising from a point contact, employing the transitions that they cause in a quantum detector connected to the contact. We detail two generic detectors: a quantum two-level system and a harmonic oscillator. In these systems, for an arbitrary relation between the voltage driving the point contact and the energy scales of the detectors, the results can be expressed in terms of an effective detector temperature T_eff. The third cumulant can be found from the dependence of T_eff on the sign of the driving voltage. We find that proper ordering of the fluctuation operators is relevant in the analysis of the transition rates. This is reflected in the effective Fano factor for the third cumulant measured in such setups: it depends on the ratio of the voltage and an energy scale describing the circuit where the fluctuations are produced.Comment: 12+ pages, 8 figure

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Local and non-local shot noise in multiwalled carbon nanotubes

Tsuneta¹,

Virtanen²,

Wu³

et al. 2009

Europhys. Lett.

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We have investigated shot noise in multiterminal, diffusive multiwalled carbon nanotubes (MWNTs) at 4.2 K over the frequency f = 600 − 850 MHz. Quantitative comparison of our data to semiclassical theory, based on non-equilibrium distribution functions, indicates that a major part of the noise is caused by a non-equilibrium state imposed by the contacts. Our data exhibits non-local shot noise across weakly transmitting contacts while a low-impedance contact eliminates such noise almost fully. We obtain F tube < 0.03 for the intrinsic Fano factor of our MWNTs.Multiwalled carbon nanotubes (MWNTs) are miniscule systems, their diameter being only a few nanometers. Yet, in surprisingly many cases their transport properties can be described with incoherent theories, interference effects showing up only through weak localization [1,2]. This is in contrast to single-walled tubes, where interference effects dominate, and give rise for example to Fabry-Perot resonances with distinctive features in conductance and current noise [3].When interference effects are washed out, semiclassical analysis based on non-equilibrium distribution functions is adequate, and the circuit theory of noise becomes a powerful tool in considering nanoscale objects [4,5]. This theory makes it straightforward to calculate current noise of incoherent dots and wires, and to relate the current noise to the transmission properties of the corresponding section of the mesoscopic object. Semiclassical analysis provides a way to make a distinction between sample and contact effects, and thereby it allows one to investigate contact phenomena, of which only a little is known in carbon nanotube systems.We have investigated the influence of contacts on the shot noise in multiterminal, diffusive carbon nanotubes. We have made four-lead measurements on MWNTs in which two middle probes have been employed for noise measurements. We show that quantitative information can be obtained from such measurements using semiclassical circuit theory in the analysis. We find that probes with contact resistance R C < 1 kΩ act as strongly inelastic probes, resulting in incoherent, classical addition of noise of two adjacent sections, while "bad" contacts (R C ∼ 10 kΩ) act as weakly perturbing probes which need to be analysed on the same footing as the other parts of the sample. We also find that good contacts eliminate noise that couples to the probe from a nonneighboring voltage biased section. In addition, we find from our analysis that the tubes themselves are quite noise-free, with a Fano-factor F tube < 0.03. As far as we know, our results are the first shot noise measurements addressing the contact issues in carbon nanotubes.To clarify the results of our multi-probe noise measurements, let us consider the three-terminal structure depicted schematically in Fig. 1. Assume that the aver-age current I flows between 1 and 2, and the average potential of the terminal 3 adjusts to the potential of the node. In our work, terminal 3 is disconnected from the ground at low frequenc...

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Circuit theory for noise in incoherent normal-superconducting structures

Cited by 3 publications

References 23 publications

Phase-dependent noise correlations in normal-superconducting structures

Phase-dependent noise correlations in normal-superconducting structures

Quantum detectors for the third cumulant of current fluctuations

Local and non-local shot noise in multiwalled carbon nanotubes

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