Distribution of tunnelling times for quantum electron transport

TL;DR

This paper introduces a method to calculate the distribution of tunnelling times in quantum electron transport within dissipative environments, revealing Poissonian statistics and temperature-dependent behaviors in molecular junctions.

Contribution

The authors develop a practical approach to determine tunnelling time distributions using Markovian master equations, providing new insights into quantum tunnelling statistics and molecular orbital alignment.

Findings

Tunnelling time distribution is exponential, indicating Poissonian quantum tunnelling.

Temperature affects tunnelling times differently in p- and n-type molecular junctions.

Tunnelling time distribution can probe molecular orbital alignment relative to electrode Fermi energy.

Abstract

In electron transport, the tunnelling time is the time taken for an electron to tunnel out of a system after it has tunnelled in. We define the tunnelling time distribution for quantum processes in a dissipative environment and develop a practical approach for calculating it, where the environment is described by the general Markovian master equation. We illustrate the theory by using the rate equation to compute the tunnelling time distribution for electron transport through a molecular junction. The tunnelling time distribution is exponential, which indicates that Markovian quantum tunnelling is a Poissonian statistical process. The tunnelling time distribution is used not only to study the quantum statistics of tunnelling along the average electric current but also to analyse extreme quantum events where an electron jumps against the applied voltage bias. The average tunnelling time shows distinctly different temperature dependance for p- and n-type molecular junction and therefore provides a sensitive tool to probe the alignment of molecular orbitals relative to the electrode Fermi energy.