Abstract
The charge and current fluctuations provide an essential information to understand the transport phenomenon through the system. On the other hand, the transient response of the physical observables contain information about the characteristic system time scales, which can be important to fabricate devices operating at high frequency or for designing single electron sources and single electron detectors. In this context, it is of fundamental importance to develop new theoretical methods to characterize the charge fluctuations in the time domain. The concept of Waiting Time Distributions (WTD), originally used in the field of quantum optics and stochastic processes, has been recently extended to characterize the electron quantum transport. Although the first works were focused on the incoherent regime, a more recent extension to the coherent regime has been done for non-interacting devices. Another approach to the problem is provided by the NGFs. In this chapter we analyze the WTD and the transient charge and current fluctuations of a molecular junction coupled to metallic electrodes in the coherent regime.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Nazarov Y, Blanter Y (2009) Quantum transport: introduction to nanoscience. Cambridge University Press, Cambridge
Blanter Y, BĂĽttiker M (2000) Shot noise in mesoscopic conductors. Phys Rep 336:1
Castro LC, John DL, Pulfrey DL, Pourfath M, Gehring A, Kosina H (2005) Method for predicting fT for carbon nanotube FETs. IEEE Trans Nanotechnol 4:699
Liao Y-C, Lin L, Bao M, Cheng R, Qu Y, Bai J, Liu Y, Wang KL, Huang Y, Duan X (2010) High-speed graphene transistors with a self-aligned nanowire gate. Nature 467: 305 EP
Fève G, Mahé A, Berroir J-M, Kontos T, Plaçais B, Glattli DC, Cavanna A, Etienne B, ** Y (2007) An on-demand coherent single-electron source. Science 316:1169
Bocquillon E, Freulon V, Berroir J-M, Degiovanni P, Plaçais B, Cavanna A, ** Y, Fève G (2013) Coherence and indistinguishability of single electrons emitted by independent sources. Science 339:1054
Dubois J, Jullien T, Portier F, Roche P, Cavanna A, ** Y, Wegscheider W, Roulleau P, Glattli DC (2013) Minimal-excitation states for electron quantum optics using levitons. Nature 502:659 EP
Thibault K, Gabelli J, Lupien C, Reulet B (2015) Pauli-Heisenberg oscillations in electron quantum transport. Phys Rev Lett 114:236604
Neder I, Marquardt F (2007) Coherence oscillations in dephasing by non-Gaussian shot noise. New J Phys 9:112
Van Kampen N (2011) Stochastic processes in physics and chemistry. North-Holland personal library. Elsevier Science, Amsterdam
Brandes T (2008) Waiting times and noise in single particle transport. Annalen der Physik 17:477
Albert M, Flindt C, BĂĽttiker M (2011) Distributions of waiting times of dynamic single-electron emitters. Phys Rev Lett 107:086805
Rajabi L, Pöltl C, Governale M (2013) Waiting time distributions for the transport through a quantum-dot tunnel coupled to one normal and one superconducting lead. Phys Rev Lett 111:067002
Albert M, Haack G, Flindt C, BĂĽttiker M (2012) Electron waiting times in mesoscopic conductors. Phys Rev Lett 108:186806
Thomas KH, Flindt C (2014) Waiting time distributions of noninteracting fermions on a tight-binding chain. Phys Rev B 89:245420
Esposito M, Harbola U, Mukamel S (2009) Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems. Rev Mod Phys 81:1665
Tang G-M, Xu F, Wang J (2014) Waiting time distribution of quantum electronic transport in the transient regime. Phys Rev B 89:205310
Tang G-M, Wang J (2014) Full-counting statistics of charge and spin transport in the transient regime: a nonequilibrium Green’s function approach. Phys Rev B 90:195422
Holstein T (1959) Studies of polaron motion: part i. the molecular-crystal model. Ann Phys 8:325
LeRoy BJ, Lemay SG, Kong J, Dekker C (2004) Electrical generation and absorption of phonons in carbon nanotubes. Nature 432:371 EP
Sapmaz S, Jarillo-Herrero P, Blanter YM, Dekker C, van der Zant HSJ (2006) Tunneling in suspended carbon nanotubes assisted by longitudinal phonons. Phys Rev Lett 96:026801
Leturcq R, Stampfer C, Inderbitzin K, Durrer L, Hierold C, Mariani E, Schultz MG, von Oppen F, Ensslin K (2009) Franck-Condon blockade in suspended carbon nanotube quantum dots. Nat Phys 5:327 EP
Flensberg K (2003) Tunneling broadening of vibrational sidebands in molecular transistors. Phys Rev B 68:205323
Galperin M, Nitzan A, Ratner MA (2006) Inelastic tunneling effects on noise properties of molecular junctions. Phys Rev B 74:075326
Galperin M, Ratner MA, Nitzan A (2007) Molecular transport junctions: vibrational effects. J Phys: Condens Matter 19:103201
MĂĽhlbacher L, Rabani E (2008) Real-time path integral approach to nonequilibrium many-body quantum systems. Phys Rev Lett 100:176403
Monreal RC, Flores F, MartĂn-Rodero A (2010) Nonequilibrium transport in molecular junctions with strong electron-phonon interactions. Phys Rev B 82:235412
Maier S, Schmidt TL, Komnik A (2011) Charge transfer statistics of a molecular quantum dot with strong electron-phonon interaction. Phys Rev B 83:085401
Dong B, Ding GH, Lei XL (2013) Full counting statistics of a single-molecule quantum dot. Phys Rev B 88:075414
Jovchev A, Anders FB (2013) Influence of vibrational modes on quantum transport through a nanodevice. Phys Rev B 87:195112
Jauho A-P, Wingreen NS, Meir Y (1994) Time-dependent transport in interacting and noninteracting resonant-tunneling systems. Phys Rev B 50:5528
Albrecht KF, Wang H, MĂĽhlbacher L, Thoss M, Komnik A (2012) Bistability signatures in nonequilibrium charge transport through molecular quantum dots. Phys Rev B 86:081412
Albrecht KF, MartĂn-Rodero A, Monreal RC, MĂĽhlbacher L, Levy Yeyati A (2013) Long transient dynamics in the Anderson-Holstein model out of equilibrium. Phys Rev B 87:085127
Perfetto E, Stefanucci G (2013) Image charge effects in the nonequilibrium Anderson-Holstein model. Phys Rev B 88:245437
Souto RS, Avriller R, Monreal RC, MartĂn-Rodero A, Yeyati AL (2015) Transient dynamics and waiting time distribution of molecular junctions in the polaronic regime. Phys Rev B 92:125435
Perfetto E, Stefanucci G (2015) Transient dynamics in the Anderson-Holstein model with interfacial screening. J Comput Electron 14:352
Ding G-H, **ong B, Dong B (2016) Transient currents of a single molecular junction with a vibrational mode. J Phys: Condens Matter 28:065301
Souto RS, Yeyati AL, MartĂn-Rodero A, Monreal RC (2014) Dressed tunneling approximation for electronic transport through molecular transistors. Phys Rev B 89:085412
Tang G, **ng Y, Wang J (2017) Short-time dynamics of molecular junctions after projective measurement. Phys Rev B 96:075417
Tang G, Yu Z, Wang J (2017) Full-counting statistics of energy transport of molecular junctions in the polaronic regime. New J Phys 19:083007
Kosov DS (2017) Non-renewal statistics for electron transport in a molecular junction with electron-vibration interaction. J Chem Phys 147:104109
Kosov DS (2017) Waiting time distribution for electron transport in a molecular junction with electron-vibration interaction. J Chem Phys 146:074102
Kamenev A (2011) Field theory of non-equilibrium systems. Cambridge University Press, Cambridge
Gogolin AO, Komnik A (2006) Towards full counting statistics for the Anderson impurity model. Phys Rev B 73:195301
Dash LK, Ness H, Godby RW (2011) Nonequilibrium inelastic electronic transport: polarization effects and vertex corrections to the self-consistent Born approximation. Phys Rev B 84:085433
Entin-Wohlman O, Imry Y, Aharony A (2010) Transport through molecular junctions with a nonequilibrium phonon population. Phys Rev B 81:113408
Urban DF, Avriller R, Yeyati AL (2010) Nonlinear effects of phonon fluctuations on transport through nanoscale junctions. Phys Rev B 82:121414
Utsumi Y, Entin-Wohlman O, Ueda A, Aharony A (2013) Full-counting statistics for molecular junctions: fluctuation theorem and singularities. Phys Rev B 87:115407
Keldysh LV (1964) Diagram technique for nonequilibrium processes. Zh. Eksp. Teor. Fiz. 47:1515 (1964). [Sov Phys JETP 20:1018 (1965)]
Koch J, von Oppen F (2005) Franck-Condon blockade and giant Fano factors in transport through single molecules. Phys Rev Lett 94:206804
Covito F, Eich FG, Tuovinen R, Sentef MA, Rubio A (2018) Transient charge and energy flow in the wide-band limit. J Chem Theory Comput 14:2495
de la Vega L, MartĂn-Rodero A, AgraĂŻt N, Yeyati AL (2006) Universal features of electron-phonon interactions in atomic wires. Phys Rev B 73:075428
Avriller R, Yeyati AL (2009) Electron-phonon interaction and full counting statistics in molecular junctions. Phys Rev B 80:041309
Schmidt TL, Komnik A (2009) Charge transfer statistics of a molecular quantum dot with a vibrational degree of freedom. Phys Rev B 80:041307
Haupt F, NovotnĂ˝ T, Belzig W (2009) Phonon-assisted current noise in molecular junctions. Phys Rev Lett 103:136601
Kumar M, Avriller R, Yeyati AL, van Ruitenbeek JM (2012) Detection of vibration-mode scattering in electronic shot noise. Phys Rev Lett 108:146602
Avriller R, Souto RS, MartĂn-Rodero A, Yeyati AL (2019) Buildup of vibron-mediated electron correlations in molecular junctions. Phys Rev B 99:121403
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Seoane Souto, R. (2020). Polaron Effects in Quench Dynamics. In: Quench Dynamics in Interacting and Superconducting Nanojunctions. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-030-36595-0_4
Download citation
DOI: https://doi.org/10.1007/978-3-030-36595-0_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-36594-3
Online ISBN: 978-3-030-36595-0
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)