Abstract
Fisher-Lee relation \hbox{$\bm{t}= {i}\bm{\Gamma}_L^{1/2}\bm{G}\bm{\Gamma}^{1/2}_R$} t = i Γ L 1 / 2 G Γ R 1 / 2 is a well-established tool to decode the mode information from Green’s function and coupling parameters. Using the Bloch eigen-modes of the leads, we show that the \hbox{$\bm{\Gamma}^{1/2}_{L/R}$} Γ L / R 1 / 2 term can be expressed by the Bloch eigen-mode vectors and the wave velocities which give unambiguous algorithm of \hbox{$\bm{\Gamma}^{1/2}_{L/R}$} Γ L / R 1 / 2 in the Fish-Lee relation. Using this approach, we present an accurate and convenient technique to analyze all transport modes and also the dominant channels of an electronic transport system in tight-binding model. We study graphene nanoribbon structures to demonstrate the typical application of our technique.
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Tae-Hee Han, Youngbin Lee, Mi-Ri Choi, Seong-Hoon Woo, Sang-Hoon Bae, Byung Hee Hong, Jong-Hyun Ahn, Tae-Woo Lee, Nat. Photon. 6, 105 (2012)
D.J. van Woerkom, A. Geresdi, L.P. Kouwenhoven, Nat. Phys. 11, 547 (2015)
F. Bonaccorso, L. Colombo, G. Yu, M. Stoller, V. Tozzini, A.C. Ferrari, R.S. Ruoff, V. Pellegrini, Science 347, 1246501 (2015)
Juekuan Yang et al., Phys. Rev. Lett. 112, 205901 (2014)
S. Lee, D. Broido, K. Esfarjani, G. Chen, Nat. Commun. 6, 6290 (2015)
K.F. Mak, H. Felipe, K. He, J. Deslippe, N. Petrone, J. Hone, J. Shan, S.G. Louie, T.F. Heinz, Phys. Rev. Lett. 112, 207401 (2014)
S. Takei, Y. Tserkovnyak, Phys. Rev. Lett. 112, 227201 (2014)
S. Hild, T. Fukuhara, P. Schauß, J. Zeiher, M. Knap, E. Demler, I. Bloch, C. Gross, Phys. Rev. Lett. 113, 147205 (2014)
W. Han, R.K. Kawakami, Phys. Rev. Lett. 107, 047207 (2011)
L. Ju et al., Nature 520, 650 (2015)
G. Fiori, F. Bonaccorso, G. Iannaccone, T. Palacios, D. Neumaier, A. Seabaugh, S.K. Banerjee, L. Colombo, Nat. Nanotechnol. 9, 768 (2014)
Z.Y. Ong, G. Zhang, Phys. Rev. B 91, 174302 (2015)
I. Rungger, S. Sanvito, Phys. Rev. B 78, 035407 (2008)
K. Baker, Singular value decomposition tutorial, The Ohio State University, 2005
M. Wimmer, Ph.D. thesis, University of Regensburg, 2009
T. Ando, Phys. Rev. B 44, 8017 (1991)
P.A. Khomyakov, G. Brocks, V. Karpan, M. Zwierzycki, P.J. Kelly, Phys. Rev. B 72, 035450 (2005)
T. Ono, Y. Egami, K. Hirose, Phys. Rev. B 86, 195406 (2012)
K. Xia, M. Zwierzycki, M. Talanana, P. Kelly, G. Bauer, Phys. Rev. B 73, 064420 (2006)
J.Z. Huang, W.C. Chew, Y. Wu, L.J. Jiang, J. Appl. Phys. 112, 013711 (2012)
Yanxia Xing, Lei Zhang, Jian Wang, Phys. Rev. B 84, 035110 (2011)
G.H. Golub, C.F. Van Loan, in Matrix computations (JHU Press, 2012), Vol. 3
L. Brey, H. Fertig, Phys. Rev. B 73, 235411 (2006)
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Jin, C., Lan, J., Zhao, X. et al. Mode-detailed analysis of transmission based directly on Green’s functions. Eur. Phys. J. B 89, 187 (2016). https://doi.org/10.1140/epjb/e2016-70106-7
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DOI: https://doi.org/10.1140/epjb/e2016-70106-7