Magnetic properties of the $\alpha$-$T_3$ model: magneto-optical conductivity and the Hofstadter butterfly

Abstract

The $\alpha$-$T_3$ model extrapolates between the pseudospin $S=1/2$ honeycomb lattice of graphene and the pseudospin $S=1$ dice lattice via parameter $\alpha$. We present calculations of the magnetic properties of this hybrid pseudospin model, namely the absorptive magneto-optical conductivity and the Hofstadter butterfly spectra. In the magneto-optics curves, signatures of the hybrid system corollary a doublet structure present in the peaks, resulting from differing Landau level energies in the $K$ and $K^{\prime }$ valleys. In the Hofstadter spectra, we detail the evolution of the Hofstadter butterfly as it changes its periodicity by a factor of three as we vary between the two limiting cases of the $\alpha$-$T_3$ model.

12 pages, 11 figures, submitted to Phys. Rev. B on May 30, 2016

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• Quantum-statistical theory for laser-tuned transport and optical conductivities of dressed electrons in $α-\mc{T}_3$ materials
• 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
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• Generalized WKB theory for electron tunneling in gapped $\alpha -{\mathcal{T}}_3$ lattices
• Flat Bands and Ferrimagnetic Order in Electronically Correlated Dice-Lattice Ribbons
• Probing Topological signatures in an optically driven $\alpha$-$T_3$ Lattice
• Finite-temperature plasmons, damping and collective behavior for $\alpha -{\mathcal{T}}_3$ model
• Many-Body Effects and Optical Properties of Single- and Double Layer $\alpha$-${\mathcal{T}}_3$ Lattices
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• 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
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• Enhancement of thermoelectric performance of a nanoribbon made of alpha-${\mathcal{T}}_3$ lattice
• Superfluid density and collective modes of fermion superfluid in dice lattice
• An analytic evaluation of Kane fermion magneto-optics in two and three dimensions
• Majorana corner states on the 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
• Magneto-optical properties of bilayer transition metal dichalcogenides
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• Valley-contrasting interband transitions and excitons in symmetrically biased dice model
• Optical conductivity of tilted higher pseudospin Dirac-Weyl cones
• Superfluidity of dipolar magnetoexcitons in doped double-layered $\alpha$-${\mathcal{T}}_3$ lattice in a strong magnetic field
• Superfluidity of dipolar excitons in a double layer of $\alpha -T_3$ with a mass term
• Orbital magnetization senses the topological phase transition in a spin-orbit coupled $\alpha$-$T_3$ system
• Moiré semiconductors on twisted bilayer dice lattice
• Electrical and thermal transport through $\alpha -T_3$ NIS junction
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• SU(3) fermions in a three-band Graphene-like model
• Quantum pumping with adiabatically modulated barriers in three-band pseudospin-1 Dirac-Weyl systems
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• Developing a semiclassical Wentzel-Kramers-Brillouin theory for $\alpha -{\mathcal{T}}_3$ model
• Transport in armchair graphene nanoribbons and in ordinary waveguides
• Transport properties of the pseudospin-3/2 Dirac-Weyl fermions in the double-barrier-modulated two-dimensional system
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• Superconductivity and geometric superfluid weight of a tunable flat band system
• Pseudospin-one particles in the time-periodic dice lattice: A new approach to transport control