Consistent analytical solution for the response of a nanoscale circuit to a mode-locked laser

TL;DR

This paper develops analytical algorithms to solve the Schrödinger equation for nanoscale circuits, providing consistent solutions that account for quantum coherence over long electron mean free paths, which traditional methods may not capture.

Contribution

It introduces new analytical algorithms for solving the Schrödinger equation in nanoscale circuits, ensuring solution consistency and addressing quantum coherence effects.

Findings

Existence of consistent solutions demonstrated

Algorithms for eigenvalue determination developed

Full analytical solutions for nanoscale circuits provided

Abstract

It is now common practice to solve the Schr\"odinger equation to estimate the tunneling current between two electrodes at specified potentials, or the transmission through a potential barrier by assuming that there is an incident, reflected, and transmitted wave. However, these two approaches may not be appropriate for applications with nanoscale circuits. A new approach is required because the electron man-free path may be as long as 68.2 nm in metals so it is possible that the wavefunction may be coherent throughout a nanoscale circuit. We define several algorithms for determining the eigenvalues with different sets of the circuit parameters, thus demonstrating the existence of consistent solutions for nanoscale circuits. We also present another algorithm that is being applied to determine the full solution for nanoscale circuits. All of this is done using only analytical solutions of the Schr\"odinger equation.