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Dirac wave transmission in Lévy-disordered systems
Jonas R F Lima1, Luiz Felipe C Pereira2, Anderson L R Barbosa1
1Departamento de Física, Universidade Federal Rural de Pernambuco, 52171-900, Recife, PE, Brazil.
Physical Review. E
|April 20, 2019
Summary
Electronic waves in disordered systems transition between anomalous and standard localization. This behavior, unique to Dirac equation waves, depends on incidence energy and angle, unlike Schrödinger equation waves.
Area of Science:
- Condensed Matter Physics
- Quantum Mechanics
- Wave Propagation
Background:
- Disordered systems exhibit wave localization phenomena.
- Lévy-type disorder influences wave transport properties.
- Dirac and Schrödinger equations describe distinct quantum wave behaviors.
Purpose of the Study:
- Investigate electronic wave propagation under Lévy-type disorder.
- Analyze phase transitions in wave localization.
- Compare Dirac and Schrödinger equation responses to disorder.
Main Methods:
- Numerical calculations using the transfer matrix method.
- Analysis of systems with potential barriers.
- Characterization of localization regimes via phase diagrams.
Main Results:
- Dirac equation waves show energy-dependent transitions: anomalous -> standard -> anomalous localization.
- Schrödinger equation waves do not exhibit these transitions.
- A phase diagram (incidence angle vs. energy) for localization regimes was obtained.
Conclusions:
- Lévy-type disorder induces unique phase transitions in Dirac wave localization.
- Transmission dispersion and fluctuations characterize localization transitions.
- Critical incidence angles significantly impact system transmittance.
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