Enhancement of hopping conductivity by spontaneous fractal ordering of low-energy sites
Abstract
Variable-range hopping conductivity has long been understood in terms of a canonical prescription for relating the single-particle density of states to the temperature-dependent conductivity. Here we demonstrate that this prescription breaks down in situations where a large and long-ranged random potential develops. In particular, we examine a canonical model of a completely compensated semiconductor, and we show that at low temperatures hopping proceeds along self-organized, low-dimensional subspaces having fractal dimension d = 2. We derive and study numerically the spatial structure of these subspaces, as well as the conductivity and density of states that result from them. One of our prominent findings is that fractal ordering of low energy sites greatly enhances the hopping conductivity and allows Efros-Shklovskii type conductivity to persist up to unexpectedly high temperatures.
- Authors:
-
- West Chester Univ., West Chester, PA (United States)
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
- Publication Date:
- Research Org.:
- Energy Frontier Research Centers (EFRC) (United States). Center for Excitonics (CE); Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES)
- OSTI Identifier:
- 1388200
- Alternate Identifier(s):
- OSTI ID: 1310839
- Grant/Contract Number:
- SC0001088
- Resource Type:
- Journal Article: Accepted Manuscript
- Journal Name:
- Physical Review B
- Additional Journal Information:
- Journal Volume: 94; Journal Issue: 8; Related Information: CE partners with Massachusetts Institute of Technology (lead); Brookhaven National Laboratory; Harvard University; Journal ID: ISSN 2469-9950
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
Citation Formats
Chen, Tianran, and Skinner, Brian. Enhancement of hopping conductivity by spontaneous fractal ordering of low-energy sites. United States: N. p., 2016.
Web. doi:10.1103/PhysRevB.94.085146.
Chen, Tianran, & Skinner, Brian. Enhancement of hopping conductivity by spontaneous fractal ordering of low-energy sites. United States. https://doi.org/10.1103/PhysRevB.94.085146
Chen, Tianran, and Skinner, Brian. 2016.
"Enhancement of hopping conductivity by spontaneous fractal ordering of low-energy sites". United States. https://doi.org/10.1103/PhysRevB.94.085146. https://www.osti.gov/servlets/purl/1388200.
@article{osti_1388200,
title = {Enhancement of hopping conductivity by spontaneous fractal ordering of low-energy sites},
author = {Chen, Tianran and Skinner, Brian},
abstractNote = {Variable-range hopping conductivity has long been understood in terms of a canonical prescription for relating the single-particle density of states to the temperature-dependent conductivity. Here we demonstrate that this prescription breaks down in situations where a large and long-ranged random potential develops. In particular, we examine a canonical model of a completely compensated semiconductor, and we show that at low temperatures hopping proceeds along self-organized, low-dimensional subspaces having fractal dimension d = 2. We derive and study numerically the spatial structure of these subspaces, as well as the conductivity and density of states that result from them. One of our prominent findings is that fractal ordering of low energy sites greatly enhances the hopping conductivity and allows Efros-Shklovskii type conductivity to persist up to unexpectedly high temperatures.},
doi = {10.1103/PhysRevB.94.085146},
url = {https://www.osti.gov/biblio/1388200},
journal = {Physical Review B},
issn = {2469-9950},
number = 8,
volume = 94,
place = {United States},
year = {Mon Aug 29 00:00:00 EDT 2016},
month = {Mon Aug 29 00:00:00 EDT 2016}
}
Web of Science
Figures / Tables:
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