Abstract
Starting from the zero modes of the Dirac-Weyl equation for Landau levels in the symmetric gauge, we propose a novel mechanism to construct the eigenvalues and its eigenfunctions. We show that the problem may be addressed without numerical calculation and only solving the Dirac-Weyl equation for the zero modes. Specifically, the eigenstates associated to the negative magnetic field configurations may be constructed from the zero mode with positive chirality. In addition, we obtain that the eigenstates associated to the positive magnetic field configurations may be constructed from the zero mode with negative chirality. Finally, we show that our mechanism may be used to obtain the eigenvalues and eigenfunctions of the Hamiltonian corresponding to bilayer graphene system.
Highlights
The problem of a single electron confined to two dimensions and exposed to a magnetic field was explored by Darwin [1], Fock [2] and Landau [3]
We have shown that for negative magnetic field configurations the eigenstates may be constructed from the zero mode with positive chirality whereas for positive magnetic field the eigenstates are constructed form the zero mode with negative chirality
This is a consequence of the Aharonov-Casher theorem, which establishes that for a negative magnetic flux the zeroenergy solutions can exist only for positive spin direction, whereas if the magnetic flux is positive the zero-energy solutions can exist only for negative spin direction
Summary
Starting from the zero modes of the Dirac-Weyl equation for Landau levels in the symmetric gauge, we licence. Propose a novel mechanism to construct the eigenvalues and its eigenfunctions. Any further distribution of this work must maintain problem may be addressed without numerical calculation and only solving the Dirac-Weyl equation attribution to the for the zero modes. The eigenstates associated to the negative magnetic field configurations author(s) and the title of the work, journal citation may be constructed from the zero mode with positive chirality. Eigenstates associated to the positive magnetic field configurations may be constructed from the zero mode with negative chirality. We show that our mechanism may be used to obtain the eigenvalues and eigenfunctions of the Hamiltonian corresponding to bilayer graphene system
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
