Are current-induced forces conservative?

Physical Review Letters

Volumn 92, Issue 17, 2004, Pages

  Di Ventra, M ^a   Chen, Y C ^a   Todorov, T N ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b QUEEN'S UNIVERSITY BELFAST   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ELECTROCHEMISTRY; ELECTRODES; ELECTROMIGRATION; ELECTRON ENERGY LEVELS; FORCE CONTROL; INTEGRAL EQUATIONS; IONS; LAGRANGE MULTIPLIERS; MICROELECTRONICS; MOLECULAR DYNAMICS; OPTICAL INTERCONNECTS; QUANTUM THEORY; VACUUM APPLICATIONS;

CURRENT-INDUCED FORCES; ENERGY FUNCTIONALS; FIRST-PRINCIPLES CALCULATIONS; MANY-BODY PROBLEMS;

ELECTRIC CURRENTS;

EID: 2942545076     PISSN: 00319007     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevLett.92.176803     Document Type: Article

References (30)

1. For a review see, e.g., R. S. Sorbello, in Solid State Physics, edited by H. Ehrenreich and F. Spaepen (Academic Press, New York, 1998), Vol. 51, p. 159, and references therein.
2. See, e.g., I. A. Blech and H. Sello, in Physics of Failure in Electronics, edited by T. S. Shilliday and J. Vaccaro (Rome Air Development Center, USAF, Rome, 1967), Vol. 5, p. 496.
3. N. D. Lang, Phys. Rev. B 45, 13599 (1992); 49, 2067 (1994).
4. N. D. Lang, Phys. Rev. B 45, 13599 (1992); 49, 2067 (1994).
5. N. Agraït, C. Untiedt, G. Rubio-Bollinger, and S. Vieira, Phys. Rev. Lett. 88, 216803 (2002).
6. K. Itakura, K. Yuki, S. Kurokawa, H. Yasuda, and A. Sakai, Phys. Rev. B 60, 11163 (1999).
7. H. Yasuda and A. Sakai, Phys. Rev. B 56, 1069 (1997).
8. T. N. Todorov, J. Hoekstra, and A. P. Sutton, Phys. Rev. Lett. 86, 3606 (2001).
9. Z. Yang and M. Di Ventra, Phys. Rev. B 67, 161311 (2003).
10. M. Brandbyge, K. Stokbro, J. Taylor, J. L. Mozos, and P. Ordejon, Phys. Rev. B 67, 193104 (2003).
11. B. Q. Wei, R. Vajtai, and P. M. Ajayan, Appl. Phys. Lett. 79, 1172 (2001).
12. M. Di Ventra, S. T. Pantelides, and N. D. Lang, Phys. Rev. Lett. 88, 046801 (2002); Phys. Rev. Lett. 89, 139902 (2002).
13. M. Di Ventra, S. T. Pantelides, and N. D. Lang, Phys. Rev. Lett. 88, 046801 (2002); Phys. Rev. Lett. 89, 139902 (2002).
14. R. Landauer and J. W. F. Woo, Phys. Rev. B 10, 1266 (1974); A. K. Das and R. Peierls, J. Phys. C 8, 3348 (1975); L. J. Sham, Phys. Rev. B 12, 3142 (1975); R. S. Sorbello and B. Dasgupta, Phys. Rev. B 16, 5193 (1977).
15. R. Landauer and J. W. F. Woo, Phys. Rev. B 10, 1266 (1974); A. K. Das and R. Peierls, J. Phys. C 8, 3348 (1975); L. J. Sham, Phys. Rev. B 12, 3142 (1975); R. S. Sorbello and B. Dasgupta, Phys. Rev. B 16, 5193 (1977).
16. R. Landauer and J. W. F. Woo, Phys. Rev. B 10, 1266 (1974); A. K. Das and R. Peierls, J. Phys. C 8, 3348 (1975); L. J. Sham, Phys. Rev. B 12, 3142 (1975); R. S. Sorbello and B. Dasgupta, Phys. Rev. B 16, 5193 (1977).
17. R. Landauer and J. W. F. Woo, Phys. Rev. B 10, 1266 (1974); A. K. Das and R. Peierls, J. Phys. C 8, 3348 (1975); L. J. Sham, Phys. Rev. B 12, 3142 (1975); R. S. Sorbello and B. Dasgupta, Phys. Rev. B 16, 5193 (1977).
18. Forces on ions need not be conservative even in the ground state, along closed trajectories that span a point of intersection of two distinct Born-Oppenheimer surfaces. In the present discussion, we shall assume that no such pathologies are present. We assume, furthermore, that no dissipative forces are present and that, as ions move, the electronic subsystem remains infinitesimally close to an instantaneous current-carrying steady state, corresponding to the instantaneous set of ionic positions.
19. M. Di Ventra and S. T. Pantelides, Phys. Rev. B 61, 16207 (2000).
20. T. N. Todorov, J. Hoekstra, and A. P. Sutton, Philos. Mag. B 80, 421 (2000).
21. The problem is not just "academic," but can also have an impact in nanoscale electronics. As an example, consider a perfect, defect-free quasi-two-dimensional wire and identify two points in it such that a straight line connecting them separates the wire into two equivalent regions. If the force is nonconservative, then you can move an atom from one point to the other along different paths in the two equivalent regions such that the work done by the current-induced force is different for the different paths. As a consequence, it is in principle possible to break equivalent regions of a defect-free wire differently. While this effect might not be important in macroscopic wires, it is relevant in nanoscale conductors made of a relatively small number of atoms. A further implication of the problem is this. If current-induced forces are not conservative, then their cross derivatives with respect to ionic positions are not necessarily equal, and hence the dynamical response matrix for a current-carrying structure is not necessarily symmetric, in which case the conventional notion of phonons would be lost in the presence of current.
22. T. N. Todorov, J. Phys. Condens. Matter 13, 10125 (2001); J. Phys. Condens. Matter 14, 3049 (2002).
23. T. N. Todorov, J. Phys. Condens. Matter 13, 10125 (2001); J. Phys. Condens. Matter 14, 3049 (2002).
24. Analogs of Eq. (1) in basis sets that depend parametrically on the ionic positions are available as well [17].
25. For simplicity, we may here imagine a jellium wire.
26. It is clear that this "vacuum resonance" will get more and more sensitive to external perturbations as the electrode separation increases and the resonance gets narrower and narrower. This does not alter the conclusions of our Letter; it simply implies that, in practice, this resonance may be destroyed easily by external perturbations and be difficult to detect in experiments.
27. The single-particle wave functions are expanded in plane waves. The number of plane waves in the direction of current flow has been increased with increasing electrode separation, while keeping the number of plane waves in the perpendicular direction constant This way we have an estimated error of about 10% in the current and about 0.5 mRy/a.u. in the force irrespective of distance. The maximum jellium-jellium edge separation we can consider to keep the errors within the above values is 16 a.u. Other details can be found in Refs. [14,22].
28. M. Di Ventra and N. D. Lang, Phys. Rev. B 65, 045402 (2002); Z. Yang, A. Tackett, and M. Di Ventra, Phys. Rev. B 66, 041405 (2002).
29. M. Di Ventra and N. D. Lang, Phys. Rev. B 65, 045402 (2002); Z. Yang, A. Tackett, and M. Di Ventra, Phys. Rev. B 66, 041405 (2002).
30. The sign of the force on the resonant Si atom in the present geometry is consistent with previous calculations on analogous geometries (see, e.g., Refs. [3,8,14,15]). However, we expect that, in general, this sign will depend on the geometry, phase, and interference details of the resonant wave functions as well as on the chemical identity of the atom. For an atom next to a long current-carrying wire, the sign of the force may depend, furthermore, on the chemical, structural, and geometrical properties of the wire.