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Honeycomb structures in magnetic fields
- Publication Year :
- 2020
-
Abstract
- Funder: University of Cambridge Centre for Doctoral Training<br />We consider the nearest-neighbour tight binding model of the honeycomb lattice in magnetic fields and discover surprizing new analytical results that fully explain fractal spectra and experimentally observed asymmetries in the density of states of molecular graphene. We describe a fractal Cantor spectrum for irrational magnetic flux through a honeycomb, and establish the existence of zero energy Dirac cones for each rational flux with fully explicit estimates on the cone angle. Our results give a substantially more refined description of subtleties in the de Haas–van Alphen and quantum Hall effects, and provide the first quantitative bounds on transport coefficients for the tight-binding model under disorder.
- Subjects :
- Statistics and Probability
Paper
Cantor spectrum
magnetic
General Physics and Astronomy
FOS: Physical sciences
01 natural sciences
quantum Hall effect
Mathematics - Spectral Theory
honeycomb
0103 physical sciences
FOS: Mathematics
0101 mathematics
010306 general physics
Spectral Theory (math.SP)
Mathematical Physics
Anderson model
Physics
Quantum Physics
Condensed matter physics
010102 general mathematics
Statistical and Nonlinear Physics
Mathematical Physics (math-ph)
5104 Condensed Matter Physics
Magnetic field
Honeycomb structure
Modeling and Simulation
Quantum Physics (quant-ph)
51 Physical Sciences
semiclassical analysis
de Haas van Alphen effect
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....1be96b15bbe7591e7732769e05634191