Flat-band ferromagnetism in a topological Hubbard model

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 term 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 \nu=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.Comment: 16 pages, 5 figure

Analysis of a SU(4) generalization of Halperin's wave function as an approach towards a SU(4) fractional quantum Hall effect in graphene sheets

Inspired by the four-fold spin-valley symmetry of relativistic electrons in graphene, we investigate a possible SU(4) fractional quantum Hall effect, which may also arise in bilayer semiconductor quantum Hall systems with small Zeeman gap. SU(4) generalizations of Halperin's wave functions [Helv. Phys. Acta 56, 75 (1983)], which may break differently the original SU(4) symmetry, are studied analytically and compared, at nu=2/3, to exact-diagonalization studies.Comment: 4+epsilon pages, 4 figures; published version with minor correction

On the self-similarity in quantum Hall systems

The Hall-resistance curve of a two-dimensional electron system in the presence of a strong perpendicular magnetic field is an example of self-similarity. It reveals plateaus at low temperatures and has a fractal structure. We show that this fractal structure emerges naturally in the Hamiltonian formulation of composite fermions. After a set of transformations on the electronic model, we show that the model, which describes interacting composite fermions in a partially filled energy level, is self-similar. This mathematical property allows for the construction of a basis of higher generations of composite fermions. The collective-excitation dispersion of the recently observed 4/11 fractional-quantum-Hall state is discussed within the present formalism.Comment: 7 pages, 4 figures; version accepted for publication in Europhys. Lett., new version contains energy calculations for collective excitations of the 4/11 stat

Electron interactions in graphene in a strong magnetic field

Graphene in the quantum Hall regime exhibits a multi-component structure due to the electronic spin and chirality degrees of freedom. While the applied field breaks the spin symmetry explicitly, we show that the fate of the chirality SU(2) symmetry is more involved: the leading symmetry-breaking terms differ in origin when the Hamiltonian is projected onto the central (n=0) rather than any of the other Landau levels. Our description at the lattice level leads to a Harper equation; in its continuum limit, the ratio of lattice constant a and magnetic length l_B assumes the role of a small control parameter in different guises. The leading symmetry-breaking terms are direct (n=0) and exchange (n different from 0) terms, which are algebraically small in a/l_B. We comment on the Haldane pseudopotentials for graphene, and evaluate the easy-plane anisotropy of the graphene ferromagnet.Comment: 4 pages, 1 figure; revised version contains a more detailed comparison with experimental results; accepted for publication in PR

Optical Absorption by Dirac Excitons in Single-Layer Transition-Metal Dichalcogenides

We develop an analytically solvable model able to qualitatively explain nonhydrogenic exciton spectra observed recently in two-dimensional (2d) semiconducting transition metal dichalcogenides. Our exciton Hamiltonian explicitly includes additional angular momentum associated with the pseudospin degree of freedom unavoidable in 2d semiconducting materials with honeycomb structure. We claim that this is the key ingredient for understanding the nonhydrogenic exciton spectra that was missing so far.Comment: 4+ pages, 2 figure

Measure of Diracness in two-dimensional semiconductors

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 investigated. In general, their electrons have a mixed character -- they can be massive Dirac fermions as well as simple Schr\"odinger 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.Comment: 6 pages, 2 figures ; new version (with minor modifications) accepted for publication in EP