We study the flat-band ferromagnetic phase of a topological Hubbard model within a bosonization formalism and, in particular, determine the spin-wave excitation spectrum. We consider a square lattice Hubbard model at 1/4-filling whose free-electron t
erm is the pi-flux model with topologically nontrivial and nearly flat energy bands. The electron spin is introduced such that the model either explicitly breaks time-reversal symmetry (correlated flat-band Chern insulator) or is invariant under time-reversal symmetry (correlated flat-band $Z_2$ topological insulator). We generalize for flat-band Chern and topological insulators the bosonization formalism [Phys. Rev. B 71, 045339 (2005)] previously developed for the two-dimensional electron gas in a uniform and perpendicular magnetic field at filling factor u=1. We show that, within the bosonization scheme, the topological Hubbard model is mapped into an effective interacting boson model. We consider the boson model at the harmonic approximation and show that, for the correlated Chern insulator, the spin-wave excitation spectrum is gapless while, for the correlated topological insulator, gapped. We briefly comment on the possible effects of the boson-boson (spin-wave--spin-wave) coupling.
We analyze the low-energy properties of two-dimensional direct-gap semiconductors, such as for example the transition-metal dichalcogenides MoS$_2$, WS$_2$, and their diselenide analogues MoSe$_2$, WSe$_2$, etc., which are currently intensively inves
tigated. In general, their electrons have a mixed character -- they can be massive Dirac fermions as well as simple Schrodinger particles. We propose a measure (Diracness) for the degree of mixing between the two characters and discuss how this quantity can in principle be extracted experimentally, within magneto-transport measurements, and numerically via ab initio calculations.
The electrodynamics of a two-dimensional gas of massless fermions in graphene is studied by a collisionless hydrodynamic approach. A low-energy dispersion relation for the collective modes (plasmons) is derived both in the absence and in the presence
of a perpendicular magnetic field. The results for graphene are compared to those for a standard two-dimensional gas of massive electrons. We further compare the results within the classical hydrodynamic approach to the full quantum mechanical calculation in the random phase approximation. The low-energy dispersion relation is shown to be a good approximation at small wave vectors. The limitations of this approach at higher order is also discussed.
We review different scenarios for the motion and merging of Dirac points in two dimensional crystals. These different types of merging can be classified according to a winding number (a topological Berry phase) attached to each Dirac point. For each
scenario, we calculate the Landau level spectrum and show that it can be quantitatively described by a semiclassical quantization rule for the constant energy areas. This quantization depends on how many Dirac points are enclosed by these areas. We also emphasize that different scenarios are characterized by different numbers of topologically protected zero energy Landau levels
We present a theoretical description of Bernstein modes that arise as a result of the coupling between plasmon-like collective excitations (upper-hybrid mode) and inter-Landau-level excitations, in graphene in a perpendicular magnetic field. These mo
des, which are apparent as avoided level crossings in the spectral function obtained in the random-phase approximation, are described to great accuracy in a phenomenological model. Bernstein modes, which may be measured in inelastic light-scattering experiments or in photo-conductivity spectroscopy, are a manifestation of the Coulomb interaction between the electrons and may be used for a high-precision measurement of the upper-hybrid mode at small non-zero wave vectors.
We study collective electronic excitations in graphene in the integer quantum Hall regime, concentrating mainly on excitations with spin reversal such as spin-flip and spin-wave excitations. We show that these excitations are correctly accounted for
in the time-dependent Hartree-Fock and strong magnetic field approximations, in contrast to spin-conserving (magneto-exciton) modes which involve a strong Landau-level mixing at non-zero wave vectors. The collective excitations are discussed in view of prominent theorems, such as Kohns and Larmors. Whereas the latter remains valid in graphene and yields insight into the understanding of spin-dependent modes, Kohns theorem does not apply to relativistic electrons in graphene. We finally calculate the exchange correction to the chemical potential in the weak magnetic field limit.
A doped graphene layer in the integer quantum Hall regime reveals a highly unusual particle-hole excitation spectrum, which is calculated from the dynamical polarizability in the random phase approximation. We find that the elementary neutral excitat
ions in graphene in a magnetic field are unlike those of a standard two-dimensional electron gas (2DEG): in addition to the upper-hybrid mode, the particle-hole spectrum is reorganized in linear magneto-plasmons that disperse roughly parallel to $omega=v_F q$, instead of the usual horizontal (almost dispersionless) magneto-excitons. These modes could be detected in an inelastic light scattering experiment.
We discuss charged topological spin textures in quantum Hall ferromagnets in which the electrons carry a pseudospin as well as the usual spin degree of freedom, as is the case in bilayer GaAs or monolayer graphene samples. We develop a theory which t
reats spin and pseudospin on a manifestly equal footing, which may also be of help in visualizing the relevant spin textures. We in particular consider the entanglement of spin and pseudospin in the presence of realistic anisotropies. An entanglement operator is introduced which generates families of degenerate Skyrmions with differing entanglement properties. We propose a local characterization of the latter, and touch on the role entangled Skyrmions play in the nuclear relaxation time of quantum Hall ferromagnets.
We describe a peculiar fine structure acquired by the in-plane optical phonon at the Gamma-point in graphene when it is brought into resonance with one of the inter-Landau-level transitions in this material. The effect is most pronounced when this la
ttice mode (associated with the G-band in graphene Raman spectrum) is in resonance with inter-Landau-level transitions 0 -> (+,1) and (-,1) -> 0, at a magnetic field B_0 ~ 30 T. It can be used to measure the strength of the electron-phonon coupling directly, and its filling-factor dependence can be used experimentally to detect circularly polarized lattice modes.
