Long Range Spatial Correlations in One- Dimensional Anderson Models Greg M. Petersen Nancy Sandler...
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Transcript of Long Range Spatial Correlations in One- Dimensional Anderson Models Greg M. Petersen Nancy Sandler...
Long Range Spatial Correlations in One-
Dimensional Anderson Models
Greg M. PetersenNancy Sandler
Ohio UniversityDepartment of Physics and Astronomy
1D Anderson Transition?
Greg M. Petersen
Evidence For
Dunlap, Wu, and Phillips, PRL (1990)
Moura and Lyra, PRL (1998)
Evidence Against
Kotani and Simon, Commun. Math. Phys (1987)
García-García and Cuevas, PRB (2009)
Cain et al. EPL (2011)
Abrahams et al. PRL (1979)Johnston and Kramer Z Phys. B (1986)
E/t
The Model
α=.1
α=.5
α=1
Greg M. Petersen
Generation Method: 1. Find spectral density 2. Generate {V(k)} from Gaussian with variance S(k) 3. Apply conditions V(k) = V*(-k) 4. Take inverse FT to get {Є
i}
Recursive Green's Function Method
Greg M. Petersen
Klimeck http://nanohub.org/resources/165 (2004)
Lead LeadConductor
Also get DOS
Verification of Single Parameter Scaling
Greg M. Petersen
Slope
All Localized
Transfer Matrix Method
Greg M. Petersen
Less Localized More Localized
Crossover Energy
Analysis of the Crossing Energy
Greg M. Petersen
More Localized
Less Localized
Participation Ratio
Greg M. Petersen
- Wavefunctions are characterized by fractal exponents.
Fractal Exponent D of IPR
Greg M. Petersen
E=0.1
E=1.3
E=2.5
Character of eigenstates changes for alpha less than 1.
Exam
Greg M. Petersen
Cain et al. EPL (2011) – no transition
Petersen, Sandler (2012)- no transition
Moura and Lyra, PRL (1998)- transition
Conclusions
- All states localize
- Single parameter scaling is verified
Thank you for your attention!
- Found more and less localized regions
Greg M. Petersen
- Determined dependence of W/t on crossing energy- Calculated the fractal dimension D by IPR
- D is conditional dependent on alpha