# Electron transfer statistics and thermal fluctuations in molecular junctions

## Abstract

We derive analytical expressions for probability distribution function (PDF) for electron transport in a simple model of quantum junction in presence of thermal fluctuations. Our approach is based on the large deviation theory combined with the generating function method. For large number of electrons transferred, the PDF is found to decay exponentially in the tails with different rates due to applied bias. This asymmetry in the PDF is related to the fluctuation theorem. Statistics of fluctuations are analyzed in terms of the Fano factor. Thermal fluctuations play a quantitative role in determining the statistics of electron transfer; they tend to suppress the average current while enhancing the fluctuations in particle transfer. This gives rise to both bunching and antibunching phenomena as determined by the Fano factor. The thermal fluctuations and shot noise compete with each other and determine the net (effective) statistics of particle transfer. Exact analytical expression is obtained for delay time distribution. The optimal values of the delay time between successive electron transfers can be lowered below the corresponding shot noise values by tuning the thermal effects.

- Authors:

- Department of Inorganic and Physical Chemistry, Indian Institute of Science, Bangalore 560012 (India)

- Publication Date:

- OSTI Identifier:
- 22416164

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Physics; Journal Volume: 142; Journal Issue: 8; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ASYMMETRY; DISTRIBUTION FUNCTIONS; ELECTRIC CONTACTS; ELECTRON TRANSFER; ELECTRONS; FANO FACTOR; FLUCTUATIONS; NOISE; PARTICLES; PROBABILITY; SEMICONDUCTOR JUNCTIONS; TEMPERATURE DEPENDENCE; TIME DELAY

### Citation Formats

```
Goswami, Himangshu Prabal, and Harbola, Upendra.
```*Electron transfer statistics and thermal fluctuations in molecular junctions*. United States: N. p., 2015.
Web. doi:10.1063/1.4908230.

```
Goswami, Himangshu Prabal, & Harbola, Upendra.
```*Electron transfer statistics and thermal fluctuations in molecular junctions*. United States. doi:10.1063/1.4908230.

```
Goswami, Himangshu Prabal, and Harbola, Upendra. Sat .
"Electron transfer statistics and thermal fluctuations in molecular junctions". United States.
doi:10.1063/1.4908230.
```

```
@article{osti_22416164,
```

title = {Electron transfer statistics and thermal fluctuations in molecular junctions},

author = {Goswami, Himangshu Prabal and Harbola, Upendra},

abstractNote = {We derive analytical expressions for probability distribution function (PDF) for electron transport in a simple model of quantum junction in presence of thermal fluctuations. Our approach is based on the large deviation theory combined with the generating function method. For large number of electrons transferred, the PDF is found to decay exponentially in the tails with different rates due to applied bias. This asymmetry in the PDF is related to the fluctuation theorem. Statistics of fluctuations are analyzed in terms of the Fano factor. Thermal fluctuations play a quantitative role in determining the statistics of electron transfer; they tend to suppress the average current while enhancing the fluctuations in particle transfer. This gives rise to both bunching and antibunching phenomena as determined by the Fano factor. The thermal fluctuations and shot noise compete with each other and determine the net (effective) statistics of particle transfer. Exact analytical expression is obtained for delay time distribution. The optimal values of the delay time between successive electron transfers can be lowered below the corresponding shot noise values by tuning the thermal effects.},

doi = {10.1063/1.4908230},

journal = {Journal of Chemical Physics},

number = 8,

volume = 142,

place = {United States},

year = {Sat Feb 28 00:00:00 EST 2015},

month = {Sat Feb 28 00:00:00 EST 2015}

}