Abstract
We consider high order current cumulants in disordered systems out of equilibrium. They are interesting and reveal information which is not easily exposed by the traditional shot noise. Despite the fact that the dynamics of the electrons is classical, the standard kinetic theory of fluctuations needs to be modified to account for those cumulants. We perform a quantummechanical calculation using the Keldysh technique and analyze its relation to the quasi classical Boltzmann-Langevin scheme. We also consider the effect of inelastic scattering. Strong electronphonon scattering renders the current fluctuations Gaussian, completely suppressing the n > 2 cumulants. Under strong electron-electron scattering the current fluctuations remain non-Gaussian.
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References
Ya. M. Blanter, M. Büttiker Physics Reports 336, 2, (2000).
A.Ya. Shulman Sh.M. Kogan Sov. Phys. JETP 29, 3 (1969).
S.V. Gantsevich, V.L. Gurevich and R. Katilius Sov. Phys. JETP 30, 276 (1970).
L.S. Levitov and G.B. Lesovik Sov. Phys. JETP Lett. 58, 230, (1993).
L.S. Levitov and M. Reznikov “Electron shot noise beyond the second moment” condmat/0111057.
M. Reznikov, private comm.
L.D. Landau and E.M. Lifshitz Statistical Mechanics, (Pergamonn Press, Oxford, 1980), Pt. 1.
L.S. Levitov, H. Lee and G.B. Lesovik Journal of Math. Phys. 37, 4845 (1996).
I. Klich “Full Counting Statistics: An elementary derivation of Levitov’s formula” condmat/0209642, to appear in these proceedings.
L.V. Keldysh JETP 20, 1018 (1965).
We note that even physical observables corresponding to the second current correlator may be associated with different current correlation functions, such as symmetrised, antisymmetrzied or combinations thereof. For discussion of this point see G.B. Lesovik and R. Loosen, Pism’ma Zh. E’ksp. Teor. Fiz. 65, 280 (1997) [JETP Lett. 65, 295, (1997)]; U. Gavish, Y. Levinson and Y. Imry Phys. Rev. B. 62, R10637 (2000).
R de-Piccioto, M. Reznikov, M. Heiblum, V. Umansky, G. Bunin and D. Mahalu Nature 389,6647 (1997).
L. Saminadayar, D. C. Glattli, Y Jin and B. Etienne Phys.Rev. Lett. 79,2526 (1997).
E.M. Lifshitz and L.P. Pitaevskii Physical Kinetics (Pergamonn Press, Oxford, 1981).
M. Lax Rev. Mod. Phys. 32,25 (1960).
D.B. Gutman and Yuval Gefen “Shot noise at high temperatures”, cond-mat/0201007
D.B. Gutman and Y Gefen Phys. Rev. B. 64, 205317 (2001).
H. Lee, L.S. Levitov and A.Yu. Yakovets Phys. Rev. B 51, 4079, (1995).
for the discussion of application of random-matrix theory to shot noise see M. J. M. de Jong, C. W. J. Beenakker in ”Mesoscopic Electron Transport,” edited by L.L. Sohn, L.P. Kouwenhoven, and G. Schoen, NATO ASI Series Vol. 345 (Kluwer Academic Publishers, Dordrecht, 1997).
K.E. Nagaev Phys. Rev. B 52, 4740, (1995).
V.I. Kozub and A.M. Rudin Phys. Rev. B, 52, 7853, (1995).
A.M. Finkel’s tein Physica B 197,636 (1994).
A. Kamenev, A. Andreev Phys. Rev. B 60, 2218 (1999).
A. Schmid Z. Physik 271251 (1974); B.L. Altshuler and A.G. Aronov JETP Lett. 30 483 (1979).
A.Ju. Zyuzin, B.Z. Spivak, Zh. Eksp. Theor. Fiz. 93,994 (1987) (Sov. Phys. JETP 66, 560 (1987)).
K. E. Nagaev “Cascade Boltzmann-Langevin approach to higher-order current correlations in diffusive metal contacts”, cond-mat/0203503.
Recently the regression procedure has been applied for a closed disordered cavity: K.E. Nagaev, P. Samuelsson, S. Pilgram “Cascade approach to current fluctuations in a chaotic cavity”, cond-mat/0208147
R. Peierls Helv. Phys. Acta 7, Suppl. 2, 24 (1934).
As a side remark, we note that if the condition ≪ 1 is not satisfied the deviation from the kinetic theory may be substantial. In particular the renormalization of conductance by electron-electron interaction (Altshuler-Aronov effect) is pronounced when is small[30].
B.L. Altshuler and A.G. Aronov in Electron Electron interaction in the disordered metals, (Elsevier Science Publishers B.V., New-York, 1985).
Yu. V. Nazarov Ann. Phys. (Leipzig) 8, Spec. Issue, 193 (1999). We believe that the result in this paper contains a small error.
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Gutman, D.B., Gefen, Y., Mirlin, A.D. (2003). High Cumulants of Current Fluctuations Out of Equilibrium. In: Nazarov, Y.V. (eds) Quantum Noise in Mesoscopic Physics. NATO Science Series, vol 97. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0089-5_23
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DOI: https://doi.org/10.1007/978-94-010-0089-5_23
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