Renormalized phonon spectrum of polyacetylene and similar materials

Motivated to understand the phonon spectrum renormalization in the ground state of the half-filled SSH model, we use the Born-Oppenheimer approximation together with the harmonic approximation to evaluate the all-to-all real-space ionic force constants generated through the electron-phonon interacti...

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Bibliographic Details
Published in:arXiv.org 2021-10
Main Authors: Fomichev, Stepan, Berciu, Mona
Format: Article
Language:English
Subjects:
Approximation
Born-Oppenheimer approximation
Carbyne
Chain branching
Chains
Dimerization
Electron phonon interactions
Ground state
Lattice instability
Mathematical analysis
Phonons
Polyacetylene
Zero point energy
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Summary:Motivated to understand the phonon spectrum renormalization in the ground state of the half-filled SSH model, we use the Born-Oppenheimer approximation together with the harmonic approximation to evaluate the all-to-all real-space ionic force constants generated through the electron-phonon interaction. Using these force constants, we compute the renormalized phonon spectrum and study its behaviour as a function of the Peierls distortion. For the undimerized chain we confirm the presence of a large Kohn anomaly at \(2k_F\), signalling a strong lattice instability. For the dimerized chain, we find an optical branch separated by a gap from the acoustic one, while the Kohn anomaly manifests as phonon softening. To find the equilibrium dimerization, we minimize the ground state energy, crucially including the contribution of the renormalized phonon zero-point energy (ZPE). Our results show strong agreement with prior \textit{ab initio} studies for trans-polyacetylene and linear acetylenic carbon (carbyne), validating our method which is much simpler, and moreover can be easily generalized to study other problems in higher dimensions.
ISSN:2331-8422