Abstract A group‐theoretical analysis is given of the eigenstates of a charged particle when a magnetic field and a periodic potential are simultaneously present. The field is assumed totally or partially irrational with respect to the crystalline structure. The representations of the magnetic translation group are generated from free electron Landau states for convenience, but no discrepancies with the Frobenius method arise. The results are as follows: if H is parallel to a lattice direction, k · H is a good quantum number; otherwise, k · H may be assigned a fixed value for all members of a representation but is not numerically unique. According to group theory, there is a fixed finite δ k ⊥ which separates members of the same representation, and hence, equal energy. However, consideration of the energy matrix shows that there is complete degeneracy in k y for totally irrational fields; this case is thus close to the case of free electrons. In the cases intermediate between zero and totally irrational field boundary conditions may be crucial for the energy spectrum, as illustrated by an example.
A transition temperature to the charge density wave (CDW) state is calculated by the mean field approximation for a two-dimensional electrons in strong magnetic fields. Firstly ...
We investigate the quantum Hall (QH) states near the charge-neutral Dirac point of a high mobility graphene sample in high magnetic fields. We find that the QH states at filling...
Abstract The localization by a magnetic field of electrons in an inversion layer of silicon has been investigated, with fields both transverse and parallel to the surface being ...
Graphene is a two-dimensional carbon material with a honeycomb lattice and Dirac-like low-energy excitations. When Zeeman and spin-orbit interactions are neglected, its Landau l...
An extension of the phenomenological London equations to take into account a space variation of the concentration of superconducting electrons is presented. The theory differs f...
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