Resonant Spectrum Analysis of the Conductance of Open Quantum System and Three Types of Fano Parameter

Abstract

We explain the Fano peak (an asymmetric resonance peak) as an interference effect involving resonant states. We reveal that there are three types of Fano asymmetry according to their origins: the interference between a resonant state and an anti-resonant state, that between a resonant state and a bound state, and that between two resonant states. We show that the last two show the asymmetric energy dependence given by Fano, but the first one shows a slightly different form. In order to show the above, we analytically and microscopically derive a formula where we express the conductance purely in terms of the summation over all discrete eigenstates including resonant states and anti-resonant states, without any background integrals. We thereby obtain microscopic expressions of the Fano parameters that describe the three types of the Fano asymmetry. One of the expressions indicate that the corresponding Fano parameter becomes complex under an external magnetic field.

29 pages, 22 figures, considerably expanded from the first version, this time with corrections of references. To be published in J. Phys. Soc. Jpn. No. 10 (2011)

References in corpus (11)

• Quantum conductance of graphene nanoribbons with edge defects
• Interference Effects on Kondo-Assisted Transport through Double Quantum Dots
• Exact scattering eigenstates, many-body bound states, and nonequilibrium current of an open quantum dot system
• The absolute position of a resonance peak
• Electronic transmission in a model quantum wire with side coupled quasiperiodic chains: Fano resonance and related issues
• Statistics of Resonances in a Semi-infinite Disordered Chain
• Resonances in one-dimensional Disordered Chain
• Spin-polarized quantum transport through a T-shape quantum dot-array: a model of spin splitter
• Calculation of the Self-energy of Open Quantum Systems
• Initial state maximizing the nonexponentially decaying survival probability for unstable multilevel systems
• Fermi Liquid Theory for the Persistent Current Past a Side-Coupled Quantum Dot

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