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

TL;DR

This paper analyzes the origins of Fano resonance asymmetries in quantum conductance, revealing three types based on different interference effects and deriving formulas for Fano parameters including magnetic field effects.

Contribution

It introduces a microscopic formula for conductance in open quantum systems that accounts for three distinct Fano asymmetry types without background integrals.

Findings

Identifies three types of Fano asymmetry based on interference origins.

Derives a formula expressing conductance solely through discrete eigenstates.

Shows Fano parameters can become complex under magnetic fields.

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.