In a quasi-one-dimensional system (a tube) with low concentration of defects n, the resistivity ρ has peaks (van-Hove singularities) as a function of the Fermi energy. We show that due to non-Born scattering effects a deep narrow gap should appear just in the center of each peak. The resistivity at the bottom of a gap (\({{\rho }_{{\min}}} \propto {{n}^{2}}\)) is dominated by scattering at rare “twin” pairs of close defects, while scattering at solitary defects is suppressed. The predicted effect is characteristic for multichannel systems, it cannot be observed in strictly one-dimensional one.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors. Physics and Material Properties (Springer, Berlin, 2010), Chap. 6.2.
Z. Zhang, D. A. Dikin, R. S. Ruoff, and V. Chandrasekhar, Europhys. Lett. 68, 713 (2004).
B. Babić and C. Schönenberger, Phys. Rev. B 70, 195408 (2004).
J. Kim, J. R. Kim, J.-O. Lee, J. W. Park, H. M. So, N. Kim, K. Kang, K. H. Yoo, and J. J. Kim, Phys. Rev. Lett. 90, 166403 (2003).
W. Yi, L. Lu, H. Hu, Z. W. Pan, and S. S. Xie, Phys. Rev. Lett. 91, 076801 (2003).
N. B. Brandt, D. V. Gitsu, A. A. Nikolaeva, and Ya. G. Ponomarev, Sov. Phys. JETP 45, 1226 (1977).
A. Nikolaeva, D. Gitsu, L. Konopko, M. J. Graf, and T. E. Huber, Phys. Rev. B 77, 075332 (2008).
K. Wakabayashi, Phys. Rev. B 64, 125428 (2001).
M. M. Pour, A. Lashkov, A. Radocea, X. Liu, T. Sun, A. Lipatov, R. A. Korlacki, M. Shekhirev, N. R. Aluru, J. W. Lyding, V. Sysoev, and A. Sinitskii, Nat. Commun. 8, 820 (2017).
G. Bastard, J. A. Brum, and R. Ferreira, Semiconductor Heterostructures and Nanostructures, Solid State Physics (Academic, New York, 1991), Chap. 8, p. 229.
T. J. Thornton, M. Pepper, H. Ahmed, D. Andrews, and G. J. Davies, Phys. Rev. Lett. 56, 1198 (1986).
H. Z. Zheng, H. P. Wei, D. C. Tsui, and G. Weimann, Phys. Rev. B 34, 5635 (1986).
J. C. Chen, Y. Lin, K. Ting Lin, T. Ueda, and S. Komiyama, Appl. Phys. Lett. 94, 012105 (2009).
U. Fano, Phys. Rev. 124, 1866 (1961).
A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, Rev. Mod. Phys. 82, 2257 (2010).
A. S. Ioselevich and N. S. Peshcherenko, JETP Lett. 108, 825 (2018).
A. S. Ioselevich and N. S. Peshcherenko, Phys. Rev. B 99, 035414 (2019).
N. S. Peshcherenko and A. S. Ioselevich, Phys. Rev. B 102, 134208 (2020).
I. M. Lifshits, S. A. Gredeskul, and L. A. Pastur, Introduction to the Theory of Disordered Systems (Wiley-VCH, New York, 1988).
Yu. A. Bychkov and A. M. Dykhne, JETP Lett. 3, 202 (1966).
Yu. A. Bychkov and A. M. Dykhne, JETP 24, 1285 (1967).
I. A. Ado, I. A. Dmitriev, P. M. Ostrovsky, and M. Titov, Phys. Rev. Lett. 117, 046601 (2016).
A. Kumar and P. F. Bagwell, Phys. Rev. B 43, 9012 (1991).
ACKNOWLEDGMENTS
We are grateful to I.S. Burmistrov and P.M. Ostrovsky for valuable comments.
Funding
This work was supported by the Basic Research Program of The Higher School of Economics. N. Peshcherenko acknowledges the support of the Foundation for Advancement of Theoretical Physics and Mathematics Basis, project no. 20-1-5-150-1.
Author information
Authors and Affiliations
Corresponding authors
Supplementary Information
Rights and permissions
About this article
Cite this article
Ioselevich, A.S., Peshcherenko, N.S. Two-Impurity Scattering in Quasi-One-Dimensional Systems. Jetp Lett. 114, 45–50 (2021). https://doi.org/10.1134/S0021364021130038
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0021364021130038