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Optical Ceiling on Polaron Mobility in Disordered Molecular Semiconductors: Lessons from Eumelanin

  • Alvan Hunt
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Abstract

Polaron hopping in disordered molecular semiconductors such as eumelanin is set by energetic disorder σ and reorganization energy λ. We show that the reduced polaron absorption band encodes this transport problem. Its value at zero energy fixes the mean hop rate, which bounds the mobility in any dimension. For Gaussian disorder and classical vibrations its centroid is Eop=λ+(1−c)σ2/kBT, its variance obeys the Hush relation, and the bound is the Marcus rate at λ→ Eop; a 1D lower bound vanishes at kBT*=(1−c)σ2/λ, read from optics.

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Cite

BibTeXRIS
BibTeX
@misc{hunt2026optical,
  title = {{Optical Ceiling on Polaron Mobility in Disordered Molecular Semiconductors: Lessons from Eumelanin}},
  author = {Alvan Hunt},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.04986},
  eprint = {2611.04986},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.04986},
}
RIS
TY  - UNPB
TI  - Optical Ceiling on Polaron Mobility in Disordered Molecular Semiconductors: Lessons from Eumelanin
AU  - Alvan Hunt
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2611.04986
UR  - https://arxiv.org/abs/2611.04986
AB  - Polaron hopping in disordered molecular semiconductors such as eumelanin is set by energetic disorder σ and reorganization energy λ. We show that the reduced polaron absorption band encodes this transport problem. Its value at zero energy fixes the mean hop rate, which bounds the mobility in any dimension. For Gaussian disorder and classical vibrations its centroid is E_op=λ+(1−c)σ^2/k_BT, its variance obeys the Hush relation, and the bound is the Marcus rate at λ→ E_op; a 1D lower bound vanishes at k_BT^*=(1−c)σ^2/λ, read from optics.
ER  -