Landau levels and snake states of pseudo-spin-1 Dirac-like electrons in gapped Lieb lattices

Abstract

This work reports the three-band structure associated with a Lieb lattice with arbitrary nearest and next-nearest neighbors hopping interactions. For specific configurations, the system admits a flat band located between two dispersion bands. Three inequivalent Dirac valleys are identified so that the quasi-particles are effectively described by the spin-1 Dirac-type equation. Under external homogeneous magnetic fields, the Landau levels are exactly determined as the third-order polynomial equation for the energy can be solved using Cardano's formula. It is also shown that an external anti-symmetric field promotes the existence of current-carrying states, so-called snake states, confined at the interface where the external field changes its sign.

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Cited by in corpus (4)

• Lieb lattices and pseudospin-1 dynamics under barrier- and well-like electrostatic interactions
• Flat-band engineering of quasi-one-dimensional systems via supersymmetric transformations
• Bound states and point interactions of the one-dimensional pseudospin-one Hamiltonian
• Reflectionless pseudospin-1 Dirac systems via Darboux transformation and flat band solutions