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

Abstract

The electron states of gapped pseudospin-1 fermions of the $\alpha -{\mathcal{T}}_3$ lattice in the Coulomb field of a charged impurity are studied. The free $\alpha -{\mathcal{T}}_3$ model has three dispersive bands with two energy gaps between them depending on the parameter $\Theta$ which controls the coupling of atoms of honeycomb lattice with atoms in the center of each hexagon, thus, interpolating between graphene $\Theta =0$ and the dice model $\Theta =\pi /4$. 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 $\Theta$.

18 pages, 7 figures

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• The Coulomb impurity problem in graphene
• Vacuum Polarization and Screening of Supercritical Impurities in Graphene
• 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
• Supercritical Coulomb center and excitonic instability in graphene
• Magnetic field driven instability of charged center in graphene
• Tunable orbital susceptibility in $\alpha$-${\mathcal{T}}_3$ tight-binding models
• Coulomb center instability in bilayer graphene

Cited by in corpus (34)

• Floquet topological phase transition in $\alpha$-${\mathcal{T}}_3$ lattice
• Unconventional phases in a Haldane model of dice lattice
• Generalized WKB theory for electron tunneling in gapped $\alpha -{\mathcal{T}}_3$ lattices
• RKKY interaction in a doped pseudospin-1 fermion system at finite temperature
• Orbital susceptibility of T-graphene: Interplay of high-order van Hove singularities and Dirac cones
• Finite-temperature plasmons, damping and collective behavior for $\alpha -{\mathcal{T}}_3$ model
• Optical conductivity of semi-Dirac and pseudospin-1 models: Zitterbewegung approach
• Gap generation and flat band catalysis in dice model with local interaction
• Many-Body Effects and Optical Properties of Single- and Double Layer $\alpha$-${\mathcal{T}}_3$ Lattices
• Dynamical optical conductivity for gapped $\alpha -{\mathcal{T}}_3$ materials with a curved "flat" band
• Effect of magnetic field and chemical potential on the RKKY interaction in the $\alpha$-${\mathcal{T}}_3$ lattice
• Electron transitions for Dirac Hamiltonians with flat-bands under electromagnetic radiation and its application to the $\alpha -{\mathcal{T}}_3$ graphene model
• Magnon-magnon interaction and magnon relaxation time in ferromagnetic Cr2Ge2Te6 monolayer
• Superfluid density and collective modes of fermion superfluid in dice lattice
• Electronic states of pseudospin-1 fermions in $\alpha -{\mathcal{T}}_3$ lattice ribbons in a magnetic field
• Optical conductivity of bilayer dice lattices
• Effect of magnetic field on the electronic properties of an $\alpha$-$T_3$ ring
• Infinite bound states and hydrogen atom-like energy spectrum induced by a flat band
• Infinite bound states and $1/n$ energy spectrum induced by a Coulomb-like potential of type III in a flat band system
• Anomalous transport in pseudospin-1 fermions
• Proposed realization of critical regions in a one-dimensional flat band lattice with a quasi-periodic potential
• Orbital magnetization senses the topological phase transition in a spin-orbit coupled $\alpha$-$T_3$ system
• Coulomb impurity on a Dice lattice: atomic collapse and bound states
• Electrical and thermal transport through $\alpha -T_3$ NIS junction
• Bound states in the continuum (BIC) protected by self-sustained potential barriers in a flat band system
• Generation of isolated flat bands with tunable numbers through Moiré engineering
• Landau levels and snake states of pseudo-spin-1 Dirac-like electrons in gapped Lieb lattices
• Bound states and point interactions of the one-dimensional pseudospin-one Hamiltonian
• Differential entropy per particle as a probe of van Hove singularities and flat bands
• Influence of Dynamical Floquet Spectrum on the Plasmon Excitations and Exchange Energy of tilted monolayer 1T${}^{\prime }$MoS${}_2$
• Current distribution and group velocities for electronic states on $\alpha -{\mathcal{T}}_3$ lattice ribbons in a magnetic field
• Developing a semiclassical Wentzel-Kramers-Brillouin theory for $\alpha -{\mathcal{T}}_3$ model
• Geometry-Driven Moiré Engineering in Twisted Bilayers of High-Pseudospin Fermions
• Quantum Geometry Driven Finite-Momentum Exciton Fluctuations in Flat-Band Systems