Lattice generalization of the Dirac equation to general spin and the role of the flat band

Abstract

We provide a novel setup for generalizing the two-dimensional pseudospin S=1/2 Dirac equation, arising in graphene's honeycomb lattice, to general pseudospin-S. We engineer these band structures as a nearest-neighbor hopping Hamiltonian involving stacked triangular lattices. We obtain multi-layered low energy excitations around half-filling described by a two-dimensional Dirac equation of the form H=v_F S\cdot p, where S represents an arbitrary spin-S (integer or half-integer). For integer-S, a flat band appears, whose presence modifies qualitatively the response of the system. Among physical observables, the density of states, the optical conductivity and the peculiarities of Klein tunneling are investigated. We also study Chern numbers as well as the zero-energy Landau level degeneracy. By changing the stacking pattern, the topological properties are altered significantly, with no obvious analogue in multilayer graphene stacks.

14 pages, 6 figures, 1 table, revised version with a new section on experimental possibilities

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Cited by in corpus (87)

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• Hall effect of triplons in a dimerized quantum magnet
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• Klein tunneling and supercollimation of pseudospin-1 electromagnetic waves
• Tunable topological Weyl semimetal from simple cubic lattices with staggered fluxes
• High-temperature surface superconductivity in rhombohedral graphite
• 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
• Frequency-dependent polarizability, plasmons, and screening in the 2D pseudospin-1 dice lattice
• Magnetotransport properties of the $\alpha$-T${}_3$ model
• Disordered flat bands on the kagome lattice
• Minimal conductivity, topological Berry winding and duality in three-band semimetals
• Diverging dc conductivity due to a flat band in disordered pseudospin-1 Dirac-Weyl fermions
• Berry Curvature and Quantum Metric in $N$-band systems -- an Eigenprojector Approach
• 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
• Optical properties of a semi-Dirac material
• Linear optical conductivity of chiral multifold fermions
• Nematic, topological and Berry phases when a flat and a parabolic band touch
• Unconventional quantum Hall effects in two-dimensional massive spin-1 fermion systems
• Coexistence of spin-1/2 and spin-1 Dirac-Weyl fermions in the edge-centered honeycomb lattice
• Anisotropic exceptional points of arbitrary order
• Dynamics of a quasiparticle in the $\alpha$-T${}_3$ model: Role of pseudospin polarization and transverse magnetic field on \textbf{\textit{zitterbewegung}}
• Magneto-optics of general pseudospin-s two-dimensional Dirac-Weyl fermions
• From Birefringent Electrons to a Marginal or Non-Fermi Liquid of Relativistic Spin-1/2 Fermions: An Emergent Superuniversality
• Generalized WKB theory for electron tunneling in gapped $\alpha -{\mathcal{T}}_3$ lattices
• Stable Flatbands, Topology, and Superconductivity of Magic Honeycomb Networks
• Anomalous localization behaviors in disordered pseudospin systems: Beyond the conventional Anderson picture
• Robust Marginal Fermi Liquid In Birefringent Semimetals
• Flat bands and long range Coulomb interactions: conducting or insulating?
• Generalized Triple-Component Fermions: Lattice Model, Fermi arcs, and Anomalous Transport
• Optical conductivity of semi-Dirac and pseudospin-1 models: Zitterbewegung approach
• Topology-optimized Dual-Polarization Dirac Cones
• Optical response of two-dimensional Dirac materials with a flat band
• Super-Andreev reflection and longitudinal shift of pseudospin-one fermions
• Solitons in one-dimensional lattices with a flat band
• Asymmetric spatial structure of zero modes for birefringent Dirac fermions
• Effect of magnetic field and chemical potential on the RKKY interaction in the $\alpha$-${\mathcal{T}}_3$ lattice
• Magnetoplasmons for the $\alpha$-T${}_3$ model with filled Landau levels
• Photoinduced interfacial chiral modes in threefold topological semimetal
• Anderson localization of two-dimensional massless pseudospin-1 Dirac particles in a correlated random one-dimensional scalar potential
• Non-equilibrium transport in the pseudospin-1 Dirac-Weyl system
• Tunable multiple layered Dirac cones in optical lattices
• Magneto-optical conductivity of anisotropic two-dimensional Dirac-Weyl materials
• Magnon-magnon interaction and magnon relaxation time in ferromagnetic Cr2Ge2Te6 monolayer
• Enhancement of thermoelectric performance of a nanoribbon made of alpha-${\mathcal{T}}_3$ lattice
• Conical intersections for light and matter waves
• Superscattering of pseudospin-1 wave in photonic lattice
• Superfluid density and collective modes of fermion superfluid in dice lattice
• Dynamic polarization and plasmons in kekulé-patterned graphene: Signatures of the broken valley degeneracy
• Instabilities of a birefringent semi-metal
• Coexistence of spin-1 fermion and Dirac fermion on the triangular kagome lattice
• Quantum phase transitions of multi-species Dirac fermions
• High-degeneracy points protected by site-permutation symmetries
• Optoelectronic Fingerprints of Interference between Different Charge Carriers in Graphene Superlattices and Analogies to Twisted Graphene Bilayers
• Persistence of the flat band in a kagome magnet with dipolar interactions
• Geometrical quench and dynamical quantum phase transition in the $\alpha -T_3$ lattice
• Non-Universal Critical Behaviors in Disordered Pseudospin-1 Systems
• Transport properties in non-Fermi liquid phases of nodal-point semimetals
• Dynamical polarization, optical conductivity and plasmon mode of a linear triple component fermionic system
• Relativistic non-Fermi liquid from interacting birefringent fermions: A robust superuniversality
• Infinite bound states and hydrogen atom-like energy spectrum induced by a flat band
• Optical conductivity of tilted higher pseudospin Dirac-Weyl cones
• Chaos based Berry phase detector
• Electronic Properties of $\alpha -{\mathcal{T}}_3$ Quantum Dots in Magnetic Fields
• Optical properties of two dimensional Dirac Weyl materials with a flatband
• Triply degenerate nodal lines in topological and non-topological metals
• Tunneling in an anisotropic cubic Dirac semi-metal
• Correlations at higher-order exceptional points in non-Hermitian models
• Chern-Simons theory and atypical Hall conductivity in the Varma phase
• Geometry fluctuations in a two-dimensional quantum antiferromagnet
• Landau levels and snake states of pseudo-spin-1 Dirac-like electrons in gapped Lieb lattices
• SU(3) fermions in a three-band Graphene-like model
• Selective Kondo strong coupling in magnetic impurity flat-band lattices
• Pseudospin-2 in photonic chiral borophene
• Mode conversion and resonant absorption in inhomogeneous materials with flat bands
• Optical conductivity of triple point fermions
• Anomalous in-gap edge states in two-dimensional pseudospin-1 Dirac insulators
• Preformed Cooper pairs in flat-band semimetals
• Simulating the Klein tunneling of pseudospin-one Maxwell particles with trapped ions
• Band structure and optical response of Kekulé-modulated $\alpha -{\mathcal{T}}_3$ model
• Unconventional transport properties in systems with triply degenerate quadratic band crossings
• 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
• Parity Anomaly of Lattice Maxwell Fermions in Two Spatial Dimensions
• Volkov-Pankratov states in a driven semimetal for a generic interface