Electron states for gapped pseudospin-1 fermions in the field of a charged impurity

Abstract

The electron states of gapped pseudospin-1 fermions of the α − T3 lattice in the Coulomb field of a charged impurity are studied. The free α − T3 model has three dispersive bands with two energy gaps between them depending on the parameter Θ which controls the coupling of atoms of honeycomb lattice with atoms in the center of each hexagon, thus, interpolating between graphene Θ = 0 and the dice model Θ = π/4. The middle band becomes flat one with zero energy in the dice model. The bound electron states are found in the two cases: the centrally symmetric potential well and a regularized Coulomb potential of the charged impurity. As the charge of impurity increases, bound state energy levels descend from the upper and central continua and dive at certain critical charges into the central and lower continuum, respectively. In the dice model, it is found that the flat band survives in the presence of a potential well, however, is absent in the case of the Coulomb potential. The analytical results are presented for the energy levels near continuum boundaries in the potential well. For the genuine Coulomb potential, we present the recursion relations that determine the coefficients of the series expansion of wave functions of bound states. It is shown that the condition for the termination of the series expansion gives two equations relating energy and charge values. Hence, analytical solutions can exist for a countably infinite set of values of impurity charge at fixed Θ.

Compact localized states and localization dynamics in the dice lattice

“…The dice lattice is a honeycomb lattice with an additional sublattice placed at the hexagonal center, and the additional sublattice is coupled to the three sublattices of the original honeycomb lattice [54]. The couplings of the dice lattice are uniform in contrast to the α-T 3 lattice with distinct couplings from the hexagonal vertexes to the hexagonal center [62][63][64][65][66][67]. The dice lattice under consideration shown in Fig.…”

Thermal Collective Excitations in Novel Two-Dimensional Dirac-Cone Materials

“…A bit later, first evidence of really existing or fabricated materials with α-T 3 electronic structure began mounting up. This includes Josephson arrays, optical arrangement based on the laser beams, Kagome and Lieb lattices with optical waveguides, Hg 1Àx Cd x Te for a specific electron doping density, dielectric photonic crystals having zero-refractive index and a few others [48,49]. So far, α-T 3 model is believed to be the most promising innovative low-dimensional systems, and is one of the mostly investigated material in modern condensed matter physics.…”

Electrical confinement in a spectrum of two-dimensional Dirac materials with classically integrable, mixed, and chaotic dynamics

“…The details for solving the corresponding eigenvalue problem are presented in Appendix A. Quantum scattering from a circular cavity has been studied for graphene (α = 0) [52,54,68,69] and pseudospin-1 (α = 1) [33,70] systems. There has also been a study of scattering from a centrally symmetric potential in α-T 3 materials [16]. Because of the circular symmetry in the potential profile, the scattering problem can be solved analytically.…”

“…Because of the existence of three distinct bands, the low-energy excitations need to be described by a spinor wave function of three components, corresponding effectively to pseudospin-1 quasiparticles that obey the Dirac-Weyl equation. In between the pseudospin-1/2 and pseudospin-1 extremes lies a spectrum of pseudospin quasiparticles that can be generated by the corresponding spectrum of α-T 3 lattices [6][7][8][9][10][11][12][13][14][15][16].…”