The Integrated Density of States for 1D Nanostructures at Zero Bias Limit

TL;DR

This paper investigates the asymptotic behavior of the integrated density of states in 1D nanostructures at zero bias, revealing that while the density of states lacks a regular limit, the integrated density of states does, using a novel quasiclassical approach.

Contribution

The paper introduces a new method for analyzing the spectrum of Stark-Wannier operators, providing a rigorous proof of the integrated density of states behavior at zero bias in 1D nanostructures.

Findings

Density of states has no regular limit at zero bias

Integrated density of states has a well-defined limit

New quasiclassical asymptotics approach for Stark-Wannier operators

Abstract

By methods of quasiclassical asymptotics the behaviour of the integrated density of states for 1D periodic nanostructures at the zero bias limit is studied. It is shown that the density of states at the zero bias limit has no regular limit while the integrated density of states has. The rigorous proof of this phenomenon given in the paper is based on a novel approach for the quasiclassical asymptotics on the spectrum of the Stark-Wannier operators. A connection of this phenomenon with the zero bias limits of the current through the nanostructures and their conductivity is briefly discussed.