Transmission Resonances Anomaly in 1D Disordered Quantum Systems

TL;DR

This paper investigates how in 1D disordered quantum systems, only some eigenstates contribute to conduction via resonant transmission, revealing a class of 'hidden' modes that do not enhance transport and are analogous to phenomena in classical wave systems.

Contribution

It uncovers the existence of hidden, non-conducting modes in 1D disordered systems and establishes their universal ratio to total states, linking quantum and classical wave behaviors.

Findings

Only part of the eigenstates show resonant transmission.

The ratio of transmission peaks to total eigenstates is approximately √(2/5).

Hidden modes' lifetimes do not increase with disorder, unlike ordinary states.

Abstract

Connections between the electron eigenstates and conductivity of one-dimensional disordered electron systems is studied in the framework of the tight-binding model. We show that for weak disorder only part of the states exhibit resonant transmission and contribute to the conductivity. The rest of the eigenvalues are not associated with peaks in transmission and the amplitudes of their wave functions do not exhibit a significant maxima within the sample. Moreover, unlike ordinary states, the lifetimes of these `hidden' modes either remain constant or even decrease (depending on the coupling with the leads) as the disorder becomes stronger. In a wide range of the disorder strengths, the averaged ratio of the number of transmission peaks to the total number of the eigenstates is independent of the degree of disorder and is close to the value $\sqrt{2/5}$, which was derived analytically in the weak-scattering approximation. These results are in perfect analogy to the spectral and transport properties of light in one-dimensional randomly inhomogeneous media, which provides strong grounds to believe that the existence of hidden, non-conducting modes is a general phenomenon inherent to 1D open random systems, and their fraction of the total density of states is the same for quantum particles and classical waves.