Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Vibrational instabilities in charge transport through molecular nanojunctions: The role of nonconservative current-induced electronic forces

Martin Mäck*, Riley J. Preston, Michael Thoss, and Samuel L. Rudge

  • *Contact author: martin.maeck@physik.uni-freiburg.de

Phys. Rev. B 112, 075430 – Published 27 August, 2025

DOI: https://doi.org/10.1103/rtr4-xnny

Abstract

Understanding the current-induced vibrational dynamics in molecular nanojunctions is critical for gaining insight into the stability of such systems. While it is well known that Joule heating at higher bias voltages plays an important role for the stability of the nanojunction, a different mechanism caused by current-induced nonconservative forces has been reported to cause vibrational instabilities already at much lower voltages. In this paper, we apply a mixed quantum-classical approach based on electronic friction and Langevin dynamics to a model system for which vibrational instabilities have previously been reported. The electronic friction and other electronic forces can be calculated exactly using nonequilibrium Green's functions. We perform Langevin simulations of the vibrational dynamics to calculate the steady-state vibrational excitation and compare the results to a simplified eigenmode analysis, identifying the parameter regimes in which runaway modes appear.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (93)

  1. A. von Hippel, Molecular engineering, Science 123, 315 (1956).
  2. A. Aviram and M. A. Ratner, Molecular rectifiers, Chem. Phys. Lett. 29, 277 (1974).
  3. A. Nitzan, Electron transmission through molecules and molecular interfaces, Annu. Rev. Phys. Chem. 52, 681 (2001).
  4. A. Nitzan and M. A. Ratner, Electron transport in molecular wire junctions, Science 300, 1384 (2003).
  5. J. C. Cuevas and E. Scheer, Molecular Electronics (World Scientific, Singapore, 2010).
  6. N. A. Zimbovskaya and M. R. Pederson, Electron transport through molecular junctions, Phys. Rep. 509, 1 (2011).
  7. J. P. Bergfield and M. A. Ratner, Forty years of molecular electronics: Non-equilibrium heat and charge transport at the nanoscale, Phys. Status Solidi (B) 250, 2249 (2013).
  8. M. Thoss and F. Evers, Perspective: Theory of quantum transport in molecular junctions, J. Chem. Phys. 148, 030901 (2018).
  9. M. Galperin, M. A. Ratner, and A. Nitzan, Molecular transport junctions: Vibrational effects, J. Phys.: Condens. Matter 19, 103201 (2007).
  10. J. Koch, F. von Oppen, and A. V. Andreev, Theory of the Franck-Condon blockade regime, Phys. Rev. B 74, 205438 (2006).
  11. F. von Oppen and J. Koch, Novel quantum transport effects in single-molecule transistors, in Advances in Solid State Physics (Springer, Berlin, 2008), pp. 99–109.
  12. R. Härtle and M. Thoss, Resonant electron transport in single-molecule junctions: Vibrational excitation, rectification, negative differential resistance, and local cooling, Phys. Rev. B 83, 115414 (2011).
  13. B. N. J. Persson and Ph. Avouris, Local bond breaking via STM-induced excitations: The role of temperature, Surf. Sci. 390, 45 (1997).
  14. M. Ring, D. Weber, P. Haiber, F. Pauly, P. Nielaba, and E. Scheer, Voltage-induced rearrangements in atomic-size contacts, Nano Lett. 20, 5773 (2020).
  15. C. Sabater, C. Untiedt, and J. M. van Ruitenbeek, Evidence for non-conservative current-induced forces in the breaking of Au and Pt atomic chains, Beilstein J. Nanotechnol. 6, 2338 (2015).
  16. C. Kaspar, A. Erpenbeck, J. Bätge, C. Schinabeck, and M. Thoss, Nonadiabatic vibronic effects in single-molecule junctions: A theoretical study using the hierarchical equations of motion approach, Phys. Rev. B 105, 195435 (2022).
  17. D. Segal and A. Nitzan, Heating in current carrying molecular junctions, J. Chem. Phys. 117, 3915 (2002).
  18. Z. Huang, F. Chen, R. D'agosta, P. A. Bennett, M. Di Ventra, and N. Tao, Local ionic and electron heating in single-molecule junctions, Nat. Nanotechnol. 2, 698 (2007).
  19. R. Härtle, C. Benesch, and M. Thoss, Multimode vibrational effects in single-molecule conductance: A nonequilibrium Green's function approach, Phys. Rev. B 77, 205314 (2008).
  20. R. Volkovich, R. Härtle, M. Thoss, and U. Peskin, Bias-controlled selective excitation of vibrational modes in molecular junctions: A route towards mode-selective chemistry, Phys. Chem. Chem. Phys. 13, 14333 (2011).
  21. N. J. Tao, Electron transport in molecular junctions, Nat. Nanotechnol. 1, 173 (2006).
  22. M. Galperin, M. A. Ratner, A. Nitzan, and A. Troisi, Nuclear coupling and polarization in molecular transport junctions: Beyond tunneling to function, Science 319, 1056 (2008).
  23. Z. Ioffe, T. Shamai, A. Ophir, G. Noy, I. Yutsis, K. Kfir, O. Cheshnovsky, and Y. Selzer, Detection of heating in current-carrying molecular junctions by Raman scattering, Nat. Nanotechnol. 3, 727 (2008).
  24. M. J. Montgomery, T. N. Todorov, and A. P. Sutton, Power dissipation in nanoscale conductors, J. Phys.: Condens. Matter 14, 5377 (2002).
  25. A. Pecchia, G. Romano, and A. Di Carlo, Theory of heat dissipation in molecular electronics, Phys. Rev. B 75, 035401 (2007).
  26. C. Schinabeck, R. Härtle, and M. Thoss, Hierarchical quantum master equation approach to electronic-vibrational coupling in nonequilibrium transport through nanosystems: Reservoir formulation and application to vibrational instabilities, Phys. Rev. B 97, 235429 (2018).
  27. A. Erpenbeck, C. Schinabeck, U. Peskin, and M. Thoss, Current-induced bond rupture in single-molecule junctions, Phys. Rev. B 97, 235452 (2018).
  28. A. Erpenbeck, Y. Ke, U. Peskin, and M. Thoss, Current-induced dissociation in molecular junctions beyond the paradigm of vibrational heating: The role of antibonding electronic states, Phys. Rev. B 102, 195421 (2020).
  29. Y. Ke, A. Erpenbeck, U. Peskin, and M. Thoss, Unraveling current-induced dissociation mechanisms in single-molecule junctions, J. Chem. Phys. 154, 234702 (2021).
  30. Y. Ke, J. Dvořák, M. Čížek, R. Borrelli, and M. Thoss, Current-induced bond rupture in single-molecule junctions: Effects of multiple electronic states and vibrational modes, J. Chem. Phys. 159 (2023).
  31. H. Li, T. A. Su, V. Zhang, M. L. Steigerwald, C. Nuckolls, and L. Venkataraman, Electric field breakdown in single molecule junctions, J. Am. Chem. Soc. 137, 5028 (2015).
  32. H. Li, N. T. Kim, T. A. Su, M. L. Steigerwald, C. Nuckolls, P. Darancet, J. L. Leighton, and L. Venkataraman, Mechanism for Si-Sibond rupture in single molecule junctions, J. Am. Chem. Soc. 138, 16159 (2016).
  33. B. Capozzi, J. Z. Low, J. Xia, Z.-F. Liu, J. B. Neaton, L. M. Campos, and L. Venkataraman, Mapping the transmission functions of single-molecule junctions, Nano Lett. 16, 3949 (2016).
  34. R. Martel, P. Avouris, and I.-W. Lyo, Molecularly adsorbed oxygen species on Si(111)-(7×7): STM-induced dissociative attachment studies, Science 272, 385 (1996).
  35. M. Tsutsui, M. Taniguchi, and T. Kawai, Local heating in metal-molecule-metal junctions, Nano Lett. 8, 3293 (2008).
  36. Y. Asai, Nonequilibrium phonon effects on transport properties through atomic and molecular bridge junctions, Phys. Rev. B 78, 045434 (2008).
  37. J.-T. Lü, M. Brandbyge, and P. Hedegård, Blowing the fuse: Berry's phase and runaway vibrations in molecular conductors, Nano Lett. 10, 1657 (2010).
  38. J.-T. Lü, T. Gunst, P. Hedegård, and M. Brandbyge, Current-induced dynamics in carbon atomic contacts, Beilstein J. Nanotechnol. 2, 814 (2011).
  39. D. Dundas, E. J. McEniry, and T. N. Todorov, Current-driven atomic waterwheels, Nat. Nanotechnol. 4, 99 (2009).
  40. R. S. Sorbello, Theory of electromigration, in Solid State Physics, Solid State Physics, edited by H. Ehrenreich and F. Spaepen (Academic, New York, 1998), Vol. 51, pp. 159–231.
  41. J.-T. Lü, R. B. Christensen, J.-S. Wang, P. Hedegård, and M. Brandbyge, Current-induced forces and hot spots in biased nanojunctions, Phys. Rev. Lett. 114, 096801 (2015).
  42. T. Gunst, J.-T. Lü, P. Hedegård, and M. Brandbyge, Phonon excitation and instabilities in biased graphene nanoconstrictions, Phys. Rev. B 88, 161401(R) (2013).
  43. R. B. Christensen, J.-T. Lü, P. Hedegård, and M. Brandbyge, Current-induced runaway vibrations in dehydrogenated graphene nanoribbons, Beilstein J. Nanotechnol. 7, 68 (2016).
  44. J.-T. Lü, B.-Z. Hu, P. Hedegård, and M. Brandbyge, Semi-classical generalized Langevin equation for equilibrium and nonequilibrium molecular dynamics simulation, Prog. Surf. Sci. 94, 21 (2019).
  45. J.-T. Lü, M. Brandbyge, P. Hedegård, T. N. Todorov, and D. Dundas, Current-induced atomic dynamics, instabilities, and Raman signals: Quasiclassical Langevin equation approach, Phys. Rev. B 85, 245444 (2012).
  46. N. Bode, S. V. Kusminskiy, R. Egger, and F. von Oppen, Scattering theory of current-induced forces in mesoscopic systems, Phys. Rev. Lett. 107, 036804 (2011).
  47. T. N. Todorov, D. Dundas, J.-T. Lü, M. Brandbyge, and P. Hedegård, Current-induced forces: A simple derivation, Eur. J. Phys. 35, 065004 (2014).
  48. J. Koch, M. Semmelhack, F. von Oppen, and A. Nitzan, Current-induced nonequilibrium vibrations in single-molecule devices, Phys. Rev. B 73, 155306 (2006).
  49. M. Leijnse and M. R. Wegewijs, Kinetic equations for transport through single-molecule transistors, Phys. Rev. B 78, 235424 (2008).
  50. J. Koch and F. von Oppen, Franck-condon blockade and giant fano factors in transport through single molecules, Phys. Rev. Lett. 94, 206804 (2005).
  51. S. L. Rudge and D. S. Kosov, Nonrenewal statistics in quantum transport from the perspective of first-passage and waiting time distributions, Phys. Rev. B 99, 115426 (2019).
  52. S. L. Rudge and D. S. Kosov, Counting quantum jumps: A summary and comparison of fixed-time and fluctuating-time statistics in electron transport, J. Chem. Phys. 151, 034107 (2019).
  53. M. Esposito and M. Galperin, Transport in molecular states language: Generalized quantum master equation approach, Phys. Rev. B 79, 205303 (2009).
  54. A. Mitra, I. Aleiner, and A. J. Millis, Phonon effects in molecular transistors: Quantal and classical treatment, Phys. Rev. B 69, 245302 (2004).
  55. A. Erpenbeck, R. Härtle, and M. Thoss, Effect of nonadiabatic electronic-vibrational interactions on the transport properties of single-molecule junctions, Phys. Rev. B 91, 195418 (2015).
  56. M. Galperin, A. Nitzan, and M. A. Ratner, Resonant inelastic tunneling in molecular junctions, Phys. Rev. B 73, 045314 (2006).
  57. D. A. Ryndyk, M. Hartung, and G. Cuniberti, Nonequilibrium molecular vibrons: An approach based on the nonequilibrium Green function technique and the self-consistent Born approximation, Phys. Rev. B 73, 045420 (2006).
  58. T. Novotný, F. Haupt, and W. Belzig, Nonequilibrium phonon backaction on the current noise in atomic-sized junctions, Phys. Rev. B 84, 113107 (2011).
  59. Y. Tanimura and R. Kubo, Time evolution of a quantum system in contact with a nearly Gaussian-Markoffian noise bath, J. Phys. Soc. Jpn. 58, 101 (1989).
  60. C. Schinabeck and M. Thoss, Hierarchical quantum master equation approach to current fluctuations in nonequilibrium charge transport through nanosystems, Phys. Rev. B 101, 075422 (2020).
  61. J. Jin, X. Zheng, and Y. Yan, Exact dynamics of dissipative electronic systems and quantum transport: Hierarchical equations of motion approach, J. Chem. Phys. 128, 234703 (2008).
  62. R. Härtle, G. Cohen, D. R. Reichman, and A. J. Millis, Decoherence and lead-induced interdot coupling in nonequilibrium electron transport through interacting quantum dots: A hierarchical quantum master equation approach, Phys. Rev. B 88, 235426 (2013).
  63. R. Härtle, C. Schinabeck, M. Kulkarni, D. Gelbwaser-Klimovsky, M. Thoss, and U. Peskin, Cooling by heating in nonequilibrium nanosystems, Phys. Rev. B 98, 081404 (2018).
  64. C. Schinabeck, A. Erpenbeck, R. Härtle, and M. Thoss, Hierarchical quantum master equation approach to electronic-vibrational coupling in nonequilibrium transport through nanosystems, Phys. Rev. B 94, 201407 (2016).
  65. H. Wang and M. Thoss, Numerically exact quantum dynamics for indistinguishable particles: The multilayer multiconfiguration time-dependent Hartree theory in second quantization representation, J. Chem. Phys. 131, 024114 (2009).
  66. H. Wang, I. Pshenichnyuk, R. Härtle, and M. Thoss, Numerically exact, time-dependent treatment of vibrationally coupled electron transport in single-molecule junctions, J. Chem. Phys. 135, 244506 (2011).
  67. H. Wang and M. Thoss, Employing an interaction picture to remove artificial correlations in multilayer multiconfiguration time-dependent Hartree simulations, J. Chem. Phys. 145, 164105 (2016).
  68. M. Head-Gordon and J. C. Tully, Molecular dynamics with electronic frictions, J. Chem. Phys. 103, 10137 (1995).
  69. N. Bode, S. V. Kusminskiy, R. Egger, and F. von Oppen, Current-induced forces in mesoscopic systems: A scattering-matrix approach, Beilstein J. Nanotechnol. 3, 144 (2012).
  70. W. Dou and J. E. Subotnik, Electronic friction near metal surfaces: A case where molecule-metal couplings depend on nuclear coordinates, J. Chem. Phys. 146 (2016).
  71. W. Dou and J. E. Subotnik, A many-body states picture of electronic friction: The case of multiple orbitals and multiple electronic states, J. Chem. Phys. 145, 054102 (2016).
  72. R. J. Maurer, M. Askerka, V. S. Batista, and J. C. Tully, Ab initio tensorial electronic friction for molecules on metal surfaces: Nonadiabatic vibrational relaxation, Phys. Rev. B 94, 115432 (2016).
  73. W. Dou, G. Miao, and J. E. Subotnik, Born-Oppenheimer dynamics, electronic friction, and the inclusion of electron-electron interactions, Phys. Rev. Lett. 119, 046001 (2017).
  74. W. Dou and J. E. Subotnik, Universality of electronic friction: Equivalence of von Oppen's nonequilibrium Green's function approach and the Head-Gordon-Tully model at equilibrium, Phys. Rev. B 96, 104305 (2017).
  75. W. Dou and J. E. Subotnik, Perspective: How to understand electronic friction, J. Chem. Phys. 148, 230901 (2018).
  76. F. Chen, K. Miwa, and M. Galperin, Current-induced forces for nonadiabatic molecular dynamics, J. Phys. Chem. A 123, 693 (2019).
  77. F. Chen, K. Miwa, and M. Galperin, Electronic friction in interacting systems, J. Chem. Phys. 150, 174101 (2019).
  78. R. J. Preston, M. F. Gelin, and D. S. Kosov, First-passage time theory of activated rate chemical processes in electronic molecular junctions, J. Chem. Phys. 154, 114108 (2021).
  79. A. Nocera, C. A. Perroni, V. Marigliano Ramaglia, and V. Cataudella, Stochastic dynamics for a single vibrational mode in molecular junctions, Phys. Rev. B 83, 115420 (2011).
  80. R. J. Preston, T. D. Honeychurch, and D. S. Kosov, Cooling molecular electronic junctions by AC current, J. Chem. Phys. 153, 121102 (2020).
  81. R. J. Preston, V. F. Kershaw, and D. S. Kosov, Current-induced atomic motion, structural instabilities, and negative temperatures on molecule-electrode interfaces in electronic junctions, Phys. Rev. B 101, 155415 (2020).
  82. R. J. Preston, T. D. Honeychurch, and D. S. Kosov, Emergence of negative viscosities and colored noise under current-driven Ehrenfest molecular dynamics, Phys. Rev. B 106, 195406 (2022).
  83. S. L. Rudge, Y. Ke, and M. Thoss, Current-induced forces in nanosystems: A hierarchical equations of motion approach, Phys. Rev. B 107, 115416 (2023).
  84. S. L. Rudge, C. Kaspar, R. L. Grether, S. Wolf, G. Stock, and M. Thoss, Nonadiabatic dynamics of molecules interacting with metal surfaces: A quantum-classical approach based on Langevin dynamics and the hierarchical equations of motion, J. Chem. Phys. 160, 184106 (2024).
  85. M. Mäck, M. Thoss, and S. L. Rudge, Nonadiabatic dynamics of molecules interacting with metal surfaces: Extending the hierarchical equations of motion and Langevin dynamics approach to position-dependent metal-molecule couplings, J. Chem. Phys. 161, 064106 (2024).
  86. H.-H. Teh, W. Dou, and J. E. Subotnik, Antisymmetric Berry frictional force at equilibrium in the presence of spin-orbit coupling, Phys. Rev. B 104, L201409 (2021).
  87. H.-H. Teh, W. Dou, and J. E. Subotnik, Spin polarization through a molecular junction based on nuclear Berry curvature effects, Phys. Rev. B 106, 184302 (2022).
  88. A. Altland and B. Simons, Condensed Matter Field Theory, 3rd ed. (Cambridge University Press, Cambridge, 2023).
  89. R. J. Preston and D. S. Kosov, A physically realizable molecular motor driven by the Landauer blowtorch effect, J. Chem. Phys. 158, 224106 (2023).
  90. M. Sachs, B. Leimkuhler, and V. Danos, Langevin dynamics with variable coefficients and nonconservative forces: From stationary states to numerical methods, Entropy 19, 647 (2017).
  91. Y. Meir and N. S. Wingreen, Landauer formula for the current through an interacting electron region, Phys. Rev. Lett. 68, 2512 (1992).
  92. A. Erpenbeck, Y. Ke, U. Peskin, and M. Thoss, How an electrical current can stabilize a molecular nanojunction, Nanoscale 15, 16333 (2023).
  93. A. Erpenbeck and M. Thoss, Hierarchical quantum master equation approach to vibronic reaction dynamics at metal surfaces, J. Chem. Phys. 151, 191101 (2019).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation