Polaron Effects in Quench Dynamics

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Quench Dynamics in Interacting and Superconducting Nanojunctions

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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.

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References

  1. Nazarov Y, Blanter Y (2009) Quantum transport: introduction to nanoscience. Cambridge University Press, Cambridge

    Google Scholar 

  2. Blanter Y, BĂĽttiker M (2000) Shot noise in mesoscopic conductors. Phys Rep 336:1

    Article  ADS  Google Scholar 

  3. 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

    Article  ADS  Google Scholar 

  4. 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

    Article  ADS  Google Scholar 

  5. 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

    Article  ADS  Google Scholar 

  6. 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

    Article  ADS  Google Scholar 

  7. 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

    Article  ADS  Google Scholar 

  8. Thibault K, Gabelli J, Lupien C, Reulet B (2015) Pauli-Heisenberg oscillations in electron quantum transport. Phys Rev Lett 114:236604

    Article  ADS  Google Scholar 

  9. Neder I, Marquardt F (2007) Coherence oscillations in dephasing by non-Gaussian shot noise. New J Phys 9:112

    Article  Google Scholar 

  10. Van Kampen N (2011) Stochastic processes in physics and chemistry. North-Holland personal library. Elsevier Science, Amsterdam

    Google Scholar 

  11. Brandes T (2008) Waiting times and noise in single particle transport. Annalen der Physik 17:477

    Article  ADS  MATH  Google Scholar 

  12. Albert M, Flindt C, BĂĽttiker M (2011) Distributions of waiting times of dynamic single-electron emitters. Phys Rev Lett 107:086805

    Article  ADS  Google Scholar 

  13. 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

    Article  ADS  Google Scholar 

  14. Albert M, Haack G, Flindt C, BĂĽttiker M (2012) Electron waiting times in mesoscopic conductors. Phys Rev Lett 108:186806

    Article  ADS  Google Scholar 

  15. Thomas KH, Flindt C (2014) Waiting time distributions of noninteracting fermions on a tight-binding chain. Phys Rev B 89:245420

    Article  ADS  Google Scholar 

  16. Esposito M, Harbola U, Mukamel S (2009) Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems. Rev Mod Phys 81:1665

    Article  ADS  MathSciNet  MATH  Google Scholar 

  17. Tang G-M, Xu F, Wang J (2014) Waiting time distribution of quantum electronic transport in the transient regime. Phys Rev B 89:205310

    Article  ADS  Google Scholar 

  18. 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

    Article  ADS  Google Scholar 

  19. Holstein T (1959) Studies of polaron motion: part i. the molecular-crystal model. Ann Phys 8:325

    Article  ADS  MATH  Google Scholar 

  20. LeRoy BJ, Lemay SG, Kong J, Dekker C (2004) Electrical generation and absorption of phonons in carbon nanotubes. Nature 432:371 EP

    Article  ADS  Google Scholar 

  21. 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

    Article  ADS  Google Scholar 

  22. 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

    ADS  Google Scholar 

  23. Flensberg K (2003) Tunneling broadening of vibrational sidebands in molecular transistors. Phys Rev B 68:205323

    Article  ADS  Google Scholar 

  24. Galperin M, Nitzan A, Ratner MA (2006) Inelastic tunneling effects on noise properties of molecular junctions. Phys Rev B 74:075326

    Article  ADS  Google Scholar 

  25. Galperin M, Ratner MA, Nitzan A (2007) Molecular transport junctions: vibrational effects. J Phys: Condens Matter 19:103201

    ADS  Google Scholar 

  26. MĂĽhlbacher L, Rabani E (2008) Real-time path integral approach to nonequilibrium many-body quantum systems. Phys Rev Lett 100:176403

    Article  ADS  Google Scholar 

  27. Monreal RC, Flores F, MartĂ­n-Rodero A (2010) Nonequilibrium transport in molecular junctions with strong electron-phonon interactions. Phys Rev B 82:235412

    Article  ADS  Google Scholar 

  28. 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

    Article  ADS  Google Scholar 

  29. Dong B, Ding GH, Lei XL (2013) Full counting statistics of a single-molecule quantum dot. Phys Rev B 88:075414

    Article  ADS  Google Scholar 

  30. Jovchev A, Anders FB (2013) Influence of vibrational modes on quantum transport through a nanodevice. Phys Rev B 87:195112

    Article  ADS  Google Scholar 

  31. Jauho A-P, Wingreen NS, Meir Y (1994) Time-dependent transport in interacting and noninteracting resonant-tunneling systems. Phys Rev B 50:5528

    Article  ADS  Google Scholar 

  32. 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

    Article  ADS  Google Scholar 

  33. Albrecht KF, Martín-Rodero A, Monreal RC, Mühlbacher L, Levy Yeyati A (2013) Long transient dynamics in the Anderson-Holstein model out of equilibrium. Phys Rev B 87:085127

    Google Scholar 

  34. Perfetto E, Stefanucci G (2013) Image charge effects in the nonequilibrium Anderson-Holstein model. Phys Rev B 88:245437

    Article  ADS  Google Scholar 

  35. 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

    Google Scholar 

  36. Perfetto E, Stefanucci G (2015) Transient dynamics in the Anderson-Holstein model with interfacial screening. J Comput Electron 14:352

    Article  Google Scholar 

  37. 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

    ADS  Google Scholar 

  38. Souto RS, Yeyati AL, MartĂ­n-Rodero A, Monreal RC (2014) Dressed tunneling approximation for electronic transport through molecular transistors. Phys Rev B 89:085412

    Google Scholar 

  39. Tang G, **ng Y, Wang J (2017) Short-time dynamics of molecular junctions after projective measurement. Phys Rev B 96:075417

    Article  ADS  Google Scholar 

  40. 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

    Article  Google Scholar 

  41. Kosov DS (2017) Non-renewal statistics for electron transport in a molecular junction with electron-vibration interaction. J Chem Phys 147:104109

    Article  ADS  Google Scholar 

  42. Kosov DS (2017) Waiting time distribution for electron transport in a molecular junction with electron-vibration interaction. J Chem Phys 146:074102

    Article  ADS  Google Scholar 

  43. Kamenev A (2011) Field theory of non-equilibrium systems. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  44. Gogolin AO, Komnik A (2006) Towards full counting statistics for the Anderson impurity model. Phys Rev B 73:195301

    Article  ADS  Google Scholar 

  45. 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

    Article  ADS  Google Scholar 

  46. Entin-Wohlman O, Imry Y, Aharony A (2010) Transport through molecular junctions with a nonequilibrium phonon population. Phys Rev B 81:113408

    Article  ADS  Google Scholar 

  47. Urban DF, Avriller R, Yeyati AL (2010) Nonlinear effects of phonon fluctuations on transport through nanoscale junctions. Phys Rev B 82:121414

    Google Scholar 

  48. 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

    Article  ADS  Google Scholar 

  49. Keldysh LV (1964) Diagram technique for nonequilibrium processes. Zh. Eksp. Teor. Fiz. 47:1515 (1964). [Sov Phys JETP 20:1018 (1965)]

    Google Scholar 

  50. Koch J, von Oppen F (2005) Franck-Condon blockade and giant Fano factors in transport through single molecules. Phys Rev Lett 94:206804

    Article  ADS  Google Scholar 

  51. 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

    Article  Google Scholar 

  52. 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

    Article  ADS  Google Scholar 

  53. Avriller R, Yeyati AL (2009) Electron-phonon interaction and full counting statistics in molecular junctions. Phys Rev B 80:041309

    Google Scholar 

  54. Schmidt TL, Komnik A (2009) Charge transfer statistics of a molecular quantum dot with a vibrational degree of freedom. Phys Rev B 80:041307

    Article  ADS  Google Scholar 

  55. Haupt F, NovotnĂ˝ T, Belzig W (2009) Phonon-assisted current noise in molecular junctions. Phys Rev Lett 103:136601

    Article  ADS  Google Scholar 

  56. Kumar M, Avriller R, Yeyati AL, van Ruitenbeek JM (2012) Detection of vibration-mode scattering in electronic shot noise. Phys Rev Lett 108:146602

    Article  ADS  Google Scholar 

  57. Avriller R, Souto RS, MartĂ­n-Rodero A, Yeyati AL (2019) Buildup of vibron-mediated electron correlations in molecular junctions. Phys Rev B 99:121403

    Article  ADS  Google Scholar 

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Correspondence to Rubén Seoane Souto .

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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

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