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The Effect of Next-Nearest Neighbour Hopping in the One, Two, and Three Dimensional Holstein Model
Carl J Chandler1, Christian Prosko1, F Marsiglio1
1Department of Physics, University of Alberta, Edmonton, Alberta, T6G 2E1, Canada.
Scientific Reports
|September 3, 2016
Summary
Including next-nearest neighbour hopping in the Holstein model increases the polaron effective mass. This study precisely calculated this effect across dimensions, offering insights into electron-phonon interactions.
Area of Science:
- Condensed Matter Physics
- Quantum Mechanics
- Materials Science
Background:
- The Holstein model describes electron-phonon interactions, crucial for understanding material properties.
- Previous studies focused on nearest-neighbor hopping, limiting a full understanding of polaron behavior.
Purpose of the Study:
- To investigate the impact of next-nearest neighbor (NNN) hopping on polaron effective mass.
- To extend the analysis to one, two, and three dimensions.
- To develop methods for mapping NNN Holstein models to the standard model.
Main Methods:
- Application of a modified Trugman method for exact calculations.
- Perturbative calculations.
- Development of a heuristic scaling factor for coupling strength and ion frequency.
Main Results:
- NNN hopping significantly increases the polaron effective mass.
- The effect on effective mass is observed across all considered dimensions.
- A method to approximate NNN Holstein model results using the original model was developed.
Conclusions:
- Next-nearest neighbor hopping is a critical factor influencing polaron effective mass.
- The findings necessitate re-evaluation of models that neglect longer-range electron-phonon interactions.
- This research provides a more comprehensive understanding of polaron dynamics in condensed matter systems.
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