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Title: 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:
 [1];  [2]
  1. West Chester Univ., West Chester, PA (United States)
  2. 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}
}

Journal Article:

Citation Metrics:
Cited by: 3 works
Citation information provided by
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Figures / Tables:

FIG. 1 FIG. 1: Single-particle DOS as a function of energy. (a) and (b) show the typical situation, where electron-hole correlations arising from the ES stability criterion dig a narrow Coulomb gap out of a roughly constant DOS. If the total width of the DOS is ∼2W , then the Coulomb gapmore » width is ∼1/$$\sqrt{W}$$. (c) and (d) show the results from our numeric simulation for Δ = 10. The red dashed line shows the 3D Coulomb gap, Eq. (4). Shaded regions in these plots show the band of energies, as measured by our numeric simulations, that are used at the highest temperature at which we observe ES VRH [Eq. (5)]. Units of energy in this plot are e2/a0 and g(ε) is plotted in units of (e2a$$^{2}_{0}$$)−1.« less

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Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.