Electronic states of pseudospin-1 fermions in $\alpha -{\mathcal{T}}_3$ lattice ribbons in a magnetic field

Abstract

The electronic states on a finite width $\alpha -{\mathcal{T}}_3$ ribbon in a magnetic field are studied in the framework of low-energy effective theory. Both zigzag and armchair types of boundary conditions are analyzed. The analytical solutions are compared with the results of numerical tight-binding calculations. It is found that the flat band of zero energy survives for all types of boundary conditions. The analytical estimates for the spectral gap in a weak magnetic field are discussed. For zigzag type boundary conditions the approximate expressions for the edge and bulk electron states in the strong magnetic field are found.

arXiv comment14 pages, 7 figures

References in corpus (27)

• Electric Field Effect in Atomically Thin Carbon Films
• Electronic States of Graphene Nanoribbons
• Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals
• Artificial flat band systems: from lattice models to experiments
• Boundary conditions for Dirac fermions on a terminated honeycomb lattice
• Aharonov-Bohm cages in two-dimensional structures
• Flat bands in topological media
• From dia- to paramagnetic orbital susceptibility of Dirac cones
• Massless Dirac-Weyl Fermions in a T_3 Optical Lattice
• Dimensional crossover in topological matter: Evolution of the multiple Dirac point in the layered system to the flat band on the surface
• Magneto-optics of massless Kane fermions: Role of the flat band and unusual Berry phase
• Hall quantization and optical conductivity evolution with variable Berry phase in $\alpha$-$T_3$ model
• Magnetic properties of the $\alpha$-$T_3$ model: magneto-optical conductivity and the Hofstadter butterfly
• Phase Diagram of the Bose-Hubbard Model with T_3 symmetry
• Frequency-dependent polarizability, plasmons, and screening in the 2D pseudospin-1 dice lattice
• Photoinduced valley and electron-hole symmetry breaking in $\alpha$-$T_3$ lattice: The role of a variable Berry phase
• Magnetotransport properties of the $\alpha$-T${}_3$ model
• Minimal conductivity, topological Berry winding and duality in three-band semimetals
• Electron states for gapped pseudospin-1 fermions in the field of charged impurity
• Valley-polarized magnetoconductivity and particle-hole symmetry breaking in a periodically modulated $\alpha$-${\mathcal{T}}_3$ lattice
• Frequency dependent magneto-optical conductivity in the generalized $\alpha -T_3$ model
• Edge states, mass and spin gaps, and quantum Hall effect in graphene
• Unconventional quantum Hall effects in two-dimensional massive spin-1 fermion systems
• Magneto-optics of general pseudospin-s two-dimensional Dirac-Weyl fermions
• Electronic states of pseudospin-1 fermions in dice lattice ribbons
• Vortex correlations in a fully frustrated two-dimensional superconducting network
• Robust Bulk States

Cited by in corpus (8)

• Unconventional phases in a Haldane model of dice lattice
• RKKY interaction in a doped pseudospin-1 fermion system at finite temperature
• Strain-induced pseudo-magnetic field in $\alpha -{\mathcal{T}}_3$ lattice
• Electron transitions for Dirac Hamiltonians with flat-bands under electromagnetic radiation and its application to the $\alpha -{\mathcal{T}}_3$ graphene model
• Magnetic Fabry-Pérot interferometer for valley filtering in a honeycomb-dice model
• Coulomb impurity on a Dice lattice: atomic collapse and bound states
• Zigzag dice lattice ribbons: Distinct edge morphologies and structure-spectrum correspondences
• Current distribution and group velocities for electronic states on $\alpha -{\mathcal{T}}_3$ lattice ribbons in a magnetic field