Frequency dependent magneto-optical conductivity in the generalized $\alpha -T_3$ model

Abstract

We have studied a generalized three band crossing model in 2D, the generalized $\alpha -T_3$ lattice, ranging from the pseudospin-1 Dirac equation through a quadratic+flat band touching to the pseudospin-1/2 Dirac equation. A general method is presented to determine the operator form of the Green's function, being gauge and representation independent. This yields the Landau level structure in a quantizing magnetic field and the longitudinal and transversal magneto-optical conductivities of the underlying system Although the magneto-optical selection rules allow for many transitions between Landau levels, the dominant one stems from exciting a particle from/to the flat band to/from a propagating band. The Hall conductivity from each valley is rational (not quantized at all), in agreement with Berry phase considerations, though their sum is always integer quantized.

11 pages, 9 figures

References in corpus (7)

• The electronic properties of graphene
• Magneto-optical conductivity in Graphene
• Observation of a localized flat-band state in a photonic Lieb lattice
• Observation of bound states in Lieb photonic lattices
• Magnetotransport properties of the $\alpha$-T${}_3$ model
• Tunable orbital susceptibility in $\alpha$-${\mathcal{T}}_3$ tight-binding models
• Magneto-optical and optical probes of gapped ground states of bilayer graphene

Cited by in corpus (34)

• Photoinduced valley and electron-hole symmetry breaking in $\alpha$-$T_3$ lattice: The role of a variable Berry phase
• Floquet topological phase transition in $\alpha$-${\mathcal{T}}_3$ lattice
• Electron states for gapped pseudospin-1 fermions in the field of charged impurity
• Unconventional phases in a Haldane model of dice lattice
• Quantum-statistical theory for laser-tuned transport and optical conductivities of dressed electrons in $α-\mc{T}_3$ materials
• Unconventional quantum Hall effects in two-dimensional massive spin-1 fermion systems
• Dynamics of a quasiparticle in the $\alpha$-T${}_3$ model: Role of pseudospin polarization and transverse magnetic field on \textbf{\textit{zitterbewegung}}
• Floquet engineering of low-energy dispersions and dynamical localization in a periodically kicked three-band system
• 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
• Probing Topological signatures in an optically driven $\alpha$-$T_3$ Lattice
• Optical response of two-dimensional Dirac materials with a flat band
• Effect of magnetic field and chemical potential on the RKKY interaction in the $\alpha$-${\mathcal{T}}_3$ lattice
• Dynamical optical conductivity for gapped $\alpha -{\mathcal{T}}_3$ materials with a curved "flat" band
• Magnetoplasmons for the $\alpha$-T${}_3$ model with filled Landau levels
• Electron transitions for Dirac Hamiltonians with flat-bands under electromagnetic radiation and its application to the $\alpha -{\mathcal{T}}_3$ graphene model
• Enhancement of thermoelectric performance of a nanoribbon made of alpha-${\mathcal{T}}_3$ lattice
• Electronic states of pseudospin-1 fermions in $\alpha -{\mathcal{T}}_3$ lattice ribbons in a magnetic field
• Optical conductivity of bilayer dice lattices
• Geometrical quench and dynamical quantum phase transition in the $\alpha -T_3$ lattice
• Effect of magnetic field on the electronic properties of an $\alpha$-$T_3$ ring
• Chaos based Berry phase detector
• Holstein polaron in a pseudospin-$1$ quantum spin Hall system: first and second order topological phase transitions
• Tunneling valley Hall effect induced by coherent geometric phase
• Anomalous transport in pseudospin-1 fermions
• Optical properties of two dimensional Dirac Weyl materials with a flatband
• Superfluidity of dipolar magnetoexcitons in doped double-layered $\alpha$-${\mathcal{T}}_3$ lattice in a strong magnetic field
• Orbital magnetization senses the topological phase transition in a spin-orbit coupled $\alpha$-$T_3$ system
• Superfluidity of dipolar excitons in a double layer of $\alpha -T_3$ with a mass term
• SU(3) fermions in a three-band Graphene-like model
• Bound states and point interactions of the one-dimensional pseudospin-one Hamiltonian
• Developing a semiclassical Wentzel-Kramers-Brillouin theory for $\alpha -{\mathcal{T}}_3$ model
• Transport properties of the pseudospin-3/2 Dirac-Weyl fermions in the double-barrier-modulated two-dimensional system
• Surface states and finite size effects in triple-fold semimetals