How a Fano Resonance Crosses the Mobility Edge in Quantum Waveguides
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How a Fano Resonance Crosses the Mobility Edge in Quantum Waveguides1 Y. S. Joea,b,*, V. Vargiamidisc, A. M. Satanind, E. R. Hedina, and Y. D. Kimb a Center
for Computational Nanoscience, Department of Physics and Astronomy, Ball State University, Muncie, IN 47306, USA b Department of Physics, Kyung Hee University, Seoul, 02447 Republic of Korea c Aristotle University, Thessaloniki, GR-54124 Greece d Lobachevsky State University of Nizhny Novgorod (NNGU), Nizhny Novgorod, 603950 Russia * e-mail: [email protected] Received September 6, 2017
Abstract—A new scenario for the occurrence of a Fano resonance in the transmission probability of electron waveguides is investigated using a coupled-channel theory. Both a quantum dot and an antidot with either short- or finite-range interaction are embedded in the electron waveguide. Particularly, when the Fano reso4/3 nance occurs close to the mobility edge (channel threshold), it is shown that Γ ~ U 12 , where Γ is the resonance width and U12 is the coupling strength between bound state and continuum. This is in contrast to the 2 usual result Γ ~ U 12 , which is valid when the resonance occurs far from the mobility edge. Furthermore, it is shown that increasing the size of both dot and antidot leads to larger resonance width.
DOI: 10.1134/S1063776118050035
1. INTRODUCTION The asymmetric Fano resonance has been a characteristic feature of interacting quantum systems. In electronic transport through microstructures, Fano resonances have attracted a great deal of attention for various reasons; namely, they can form the basis for the creation of new resonant nanoelectronic devices, they can be used for studying phase coherence and phase evolution of electrons, etc. Resonances of the Fano type have been treated theoretically in various condensed matter systems including transport through quasi-one-dimensional wires with attractive impurities or embedded quantum dots [1–8]. The Fano effect has also been observed in a large variety of experiments including transport through various mesoscopic systems [9–12]. Fano resonances have also been studied in plasmonic materials and metamaterials [13–15] and in the conductance of graphene nanoribbons [16]. A particular class of mesoscopic systems in which the Fano effect manifests is the quantum waveguide with embedded quantum dots [1, 3, 5, 7]. In this case, the bound state in the dot is coupled to the continuum of states resulting in a resonant (quasibound) state. The coexistence of two separate transmission channels (one through the quasibound state and the other 1 The article is published in the original.
through the continuum) and the interference between them gives rise to the Fano resonance. Fano resonances have a line shape of the form [17]
(e + q)2 (1) , 2 e +1 where T(e ) is the transmission probability, e = (E – ER)/Γ is the dimensionless energy from resonance, Γ is the resonance width, q is the (Fano) asymmetry parameter, and Tbg is the background (nonresonant) transmission. As mentioned above, the resonance l
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