Abstract.
We report on a novel order N algorithm, that allows efficient computation of the Landauer-Büttiker conductance formula in heterojunctions of any complexity. The method is based on the recursive construction of a bi-orthogonal basis, in which non-hermitian hamiltonian matrices are first tridiagonalized, and continued-fraction expansion further used to accurately compute off-diagonal Green’s function matrix elements. The method, of broad range of applicability, is here validated on tight-binding hamiltonians for nanotube-based intramolecular junctions.
References
Molecular Electronics: Science and Technology (Annals of the New York Academy of Sciences), edited by A. Aviram, M. Ratner, (The New York Academy of Sciences, New York, 1998), Vol. 852
A. Javey, J. Guo, Q. Wian, M. Lundstrom, H. Dai, Nature 424, 654 (2003); Ph. Avouris, MRS Bulletin, June 2004, p. 43
M. Brandbyge et al., Phys. Rev. B. 65, 165401 (2002); J. Taylor, M. Brandbyge, K. Stokbro, Phys. Rev. Lett. 89, 138301 (2002); J.J. Palacios et al., Phys. Rev. Lett. 90, 106801 (2003); S. K. Nielsen et al., Phys. Rev. Lett. 89, 66804 (2002); E. Louis et al., Phys. Rev. B 67, 155321 (2003)
C. Krezminski et al., Phys. Rev. B 64, 085405 (2001); C. Krzeminski, C. Delerue, G. Allan, J. Phys. Chem. B. 27, 6321 (2001); Y.M. Niquet et al., Phys. Rev. B 65, 165334 (2002); C. Delerue, M. Lannoo, G. Allan, Phys. Stat. Sol. 227, 115 (2001)
R. Haydock, in Solid State Physics, edited by H. Ehrenreich, F. Seitz, D. Turnbull (Academic Press New-York, 1980), Vol. 35, 215
Recursion Method and its Applications, edited by D.G. Petitfor, D.L. Weaire, Springer Series in Solid States Sciences, Vol. 58 (Springer Verlag, Berlin, 1985); The Recursion Method: Application to Many-Body Dynamics, edited by V.S. Viswanath, G. Müller, Lectures Notes in Physics, Vol. 23 (Springer Verlag, Berlin, 1994)
S. Goedecker, Rev. Mod. Phys. 71, 1085 (1999); S. Goedecker, L. Colombo, Phys. Rev. Lett 73, 122 (1994); P. Ordejon et al., Phys. Rev. Lett 75, 1324 (1995); C.S. Jayanthi et al., Phys. Rev. B 57, 3799 (1998); S. Bagnier, P. Dallot, G. Zérah, Phys. Rev. E 61, 6999 (2000); T. Hoshi, T. Fujiwara, J. Phys. Soc. Jpn. 72, 2429 (2003); R. Takayama, T. Hoshi, T. Fujiwara, J. Phys. Soc. Jpn 73, 1519 (2004)
C. Lanczos, J. Res. Nat. Bur. Stand. 45, 255 (1950)
D.J. Lohrmann et al., Phys. Rev. B 40, 8404 (1989)
S.K. Bose, K. Winer, O.K. Andersen, Phys. Rev. B 37, 6262 (1988); S.K. Bose et al., Phys. Rev. B 37, 9955 (1988); S.K. Bose et al., Phys. Rev. B 41, 7988 (1990)
R. Kubo, J. Phys. Soc. Jpn. 12, 570 (1957); D. Fisher, P.A. Lee, Phys. Rev. B 23, 6852 (1981)
P.E.A. Turchi, D. Mayou, Phys. Rev. B 64, 075113 (2001); L.E. Ballentine, M. Kollar, J. Phys. C. 19, 981 (1986); S. Roche, D. Mayou, Phys. Rev. Lett. 79, 2518 (1997)
S. Roche, R. Saito, Phys. Rev. Lett. 87, 246803 (2001); S. Roche, F. Triozon, A. Rubio, D. Mayou, Phys. Rev. B 64, 121401 (2001); S. Latil, S. Roche, D. Mayou, J.C. Charlier, Phys. Rev. Lett. 92, 256805 (2004); F. Triozon, S. Roche, A. Rubio, D. Mayou, Phys. Rev. B 69, 121410 (2004)
R. Landauer, IBM J. Res. Dev. 32, 306 (1988); M. Büttiker, IBM J. Res. Dev. 32, 317 (1988)
S. Datta, Superlattices and Microstructures 28, 253 (2000)
R. Haydock, M. J. Kelly, J. Phys. C. 8, L290 (1975)
C. Benoit et al., Modelling Simul. Mater. Sci. Eng. 3, 161 (1995); C. Benoit, G. Poussigue, Eur. Phys. J. AP 23, 117 (2003); C. Benoit, J. Phys.: Condens. Matter 6, 3137 (1994)
J.P. Gaspard, F. Cyrot-Lackmann, J. Phys. C: Solid St. Phys. 6 3077 (1973); S. Roche, Phys. Rev. B 59, 2284 (1999); P.E.A. Turchi, D. Mayou, J.P. Julien, Phys. Rev. B 56, 1726–1742 (1997)
P.E.A. Turchi, F. Ducastelle, G. Tréglia, J. Phys. C 15, 2891 (1982).
L. Chico et al., Phys. Rev. Lett. 76, 971 (1996)
W. Fa et al., Phys. Rev. B 69, 235413 (2004)
L. Chico et al., Phys. Rev. B 54, 2600–2606 (1996); L. Chico et al., Phys. Rev. B 61, 10511 (2000)
Ph. Lambin et al., Chem. Phys. Lett. 245, 85 (1995); J.C. Charlier, T.W. Ebbesen, Ph. Lambin, Phys. Rev. B 53, 11108 (1996); F. Triozon, Ph. Lambin, S. Roche, Nanotechnology 16, 230 (2005)
T.W Odom, J.-L. Huang, C.M Lieber J. Phys.: Condens. Matter 14 No 6, R145–R167 (2002); H. Kim et al., Phys. Rev. Lett. 90, 216107 (2003)
F. García-Moliner, V. R. Velasco, Physics Reports 200, 83 (1991); G. Grosso, S. Moroni, G. Pastori Parravicini, Phys. Rev. B 67, 12328 (1989); M. Buongiorno Nardelli, J.-L. Fattebert, J. Bernholc, Phys. Rev. B 64, 245423 (2001); A. McKinnon, J. Phys. C. 13, L1031 (1980); A. Cresti et al., Phys. Rev. B 68, 075306 (2003)
L. Chico, M.P. López Sancho, M. C. Mu\(\tilde{n}\)oz, Phys. Rev. Lett. 81, 1278–1281 (1998); L. Chico W. Jaskólski, Phys. Rev. B 69, 085406 (2004); C.G. Rocha, T.G. Dargam, A. Latgé Phys. Rev. B 65, 165431 (2002); R. Tamura, Phys. Rev. B 67, 121408 (2003)
J. Guo, Supriyo Datta, M. Lundstrom, IEEE Transactions on Electron Devices 51, 172 (2004); Y. Xue, M.A. Ratner, Appl. Phys. Lett. 83, 2429 (2003)
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Triozon, F., Roche, S. Efficient linear scaling method for computing the Landauer-Büttiker conductance. Eur. Phys. J. B 46, 427–431 (2005). https://doi.org/10.1140/epjb/e2005-00260-x
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DOI: https://doi.org/10.1140/epjb/e2005-00260-x