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• W4385949745 abstract "We consider a quantum ring of a certain radius $R$ built from a sheet of the $ensuremath{alpha}text{ensuremath{-}}{T}_{3}$ lattice and solve for its spectral properties in the presence of an external magnetic field. The energy spectrum consists of a conduction band, a valence band, and a zero-energy flat band, all having a number of discrete levels which can be characterized by the angular momentum quantum number $m$. The energy levels in the flat band are infinitely degenerate irrespective of the value of $ensuremath{alpha}$. We reveal a twofold degeneracy of the levels in the conduction band as well as in the valence band for $ensuremath{alpha}=0$ and $ensuremath{alpha}=1$. However, the $m=0$ level for $ensuremath{alpha}=1$ is an exception. Corresponding to an intermediate value of $ensuremath{alpha}$, namely, $0<ensuremath{alpha}<1$, the energy levels become nondegenerate. The scenario for the degeneracy of the energy levels remains unaltered when the ring is threaded by a magnetic flux which is an integer multiple of the flux quantum. We comment on the energy levels which are relevant for low-energy physics by studying their radius dependence in the presence of a magnetic field. We also calculate the persistent current, which exhibits quantum oscillations as a function of the magnetic field with a period of one flux quantum at a particular Dirac point, which is often referred to as a valley. The total persistent current comprising the contributions from both the valleys is zero in the cases corresponding to $ensuremath{alpha}=0$ and $ensuremath{alpha}=1$. However, the total current oscillates with a periodicity of one flux quantum for any intermediate value of $ensuremath{alpha}$. We also explore the effect of a mass term (that breaks the sublattice symmetry) in the Hamiltonian. In the absence of a magnetic field, the energy levels in the flat band become dispersive, except for the $m=0$ level in the case of $ensuremath{alpha}=1$. In the presence of the field, each of the flat band levels becomes dispersive for any $ensuremath{alpha}ensuremath{ne}0$. Finally, we also see the effect of the mass term on the behavior of the persistent current, which shows a periodicity of one flux quantum, but the total current remains finite for all values of $ensuremath{alpha}$." @default.
• W4385949745 created "2023-08-18" @default.
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• W4385949745 date "2023-08-17" @default.
• W4385949745 modified "2023-10-05" @default.
• W4385949745 title "Effect of magnetic field on the electronic properties of an <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi>α</mml:mi><mml:mtext>−</mml:mtext><mml:msub><mml:mi>T</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math> ring" @default.
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• W4385949745 doi "https://doi.org/10.1103/physrevb.108.085423" @default.
• W4385949745 hasPublicationYear "2023" @default.
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