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

Quantum Hall ferromagnetism in graphene: a SU(4) bosonization approach

We study the quantum Hall effect in graphene at filling factors \nu = 0 and \nu = \pm, concentrating on the quantum Hall ferromagnetic regime, within a non-perturbative bosonization formalism. We start by developing a bosonization scheme for electrons with two discrete degrees of freedom (spin-1/2 and pseudospin-1/2) restricted to the lowest Landau level. Three distinct phases are considered, namely the so-called spin-pseudospin, spin, and pseudospin phases. The first corresponds to a quarter-filled (\nu =-1) while the others to a half-filled (\nu = 0) lowest Landau level. In each case, we show that the elementary neutral excitations can be treated approximately as a set of n-independent kinds of boson excitations. The boson representation of the projected electron density, the spin, pseudospin, and mixed spin-pseudospin density operators are derived. We then apply the developed formalism to the effective continuous model, which includes SU(4) symmetry breaking terms, recently proposed by Alicea and Fisher. For each quantum Hall state, an effective interacting boson model is derived and the dispersion relations of the elementary excitations are analytically calculated. We propose that the charged excitations (quantum Hall skyrmions) can be described as a coherent state of bosons. We calculate the semiclassical limit of the boson model derived from the SU(4) invariant part of the original fermionic Hamiltonian and show that it agrees with the results of Arovas and co-workers for SU(N) quantum Hall skyrmions. We briefly discuss the influence of the SU(4) symmetry breaking terms in the skyrmion energy.Comment: 16 pages, 4 figures, final version, extended discussion about the boson-boson interaction and its relation with quantum Hall skyrmion

Sorption of sulfadiazine on Brazilian soils

AbstractAntimicrobials, among them sulfonamides are widely used in veterinary medicine and can contaminate the environment. The degree to which antimicrobials adsorb onto soil particles varies widely, as does the mobility of these drugs. Sulfadiazine (SDZ) was used to study the adsorption–desorption in Brazilian soil–water systems, using batch equilibrium experiments. Sorption of SDZ was carried out using four types of soils. Adsorption and desorption data were well fitted with Freundlich isotherms in log form (r>0.999) and (0.984<r<0.999), respectively. An adsorption–desorption hysteresis phenomenon was apparent in all soils ranging from 0.517 to 0.827. The experimental results indicate that the Freundlich sorption coefficient (KF) values for SDZ ranged from 0.45 to 2.6μg1−1/n(cm3)1/ng−1

Photoluminescence spectrum of an interacting two-dimensional electron gas at \nu=1

We report on the theoretical photoluminescence spectrum of the interacting two-dimensional electron gas at filling factor one (\nu=1). We considered a model similar to the one adopted to study the X-ray spectra of metals and solved it analytically using the bosonization method previously developed for the two-dimensional electron gas at \nu=1. We calculated the emission spectra of the right and the left circularly polarized radiations for the situations where the distance between the two-dimensional electron gas and the valence band hole are smaller and greater than the magnetic length. For the former, we showed that the polarized photoluminescence spectra can be understood as the recombination of the so-called excitonic state with the valence band hole whereas, for the latter, the observed emission spectra can be related to the recombination of a state formed by a spin down electron bound to n spin waves. This state seems to be a good description for the quantum Hall skyrmion.Comment: Revised version, 10 pages, 5 figures, accepted to Phys. Rev.

Flat-band ferromagnetism in a correlated topological insulator on a honeycomb lattice

We study the flat-band ferromagnetic phase of a spinfull and time-reversal symmetric Haldane-Hubbard model on a honeycomb lattice within a bosonization formalism for flat-band Z$_2$ topological insulators. Such a study extend our previous one [L. S. G. Leite and R. L. Doretto, Phys. Rev. B {\bf 104}, 155129 (2021)] concerning the flat-band ferromagnetic phase of a correlated Chern insulator described by a Haldane-Hubbard model. We consider the topological Hubbard model at $1/4$ filling of its corresponding noninteracting limit and in the nearly flat band limit of its lower free-electronic bands. We show that it is possible to define boson operators associated with two distinct spin-flip excitations, one that changes (mixed-lattice excitations) and a second one that preserves (same-lattice excitations) the index related with the two triangular sublattices. Within the bosonization scheme, the fermionic model is mapped into an effective interacting boson model, whose quadratic term is considered at the harmonic approximation in order to determine the spin-wave excitation spectrum. For both mixed and same-lattice excitations, we find that the spin-wave spectrum is gapped and has two branches, with an energy gap between the lower and the upper bands at the $K$ and $K'$ points of the first Brillouin zone. Such a behavior is distinct from the one of the corresponding correlated Chern insulator, whose spin-wave spectrum has a Goldstone mode at the center of the first Brillouin zone and Dirac points at $K$ and $K'$ points. We also find some evidences that the spin-wave bands for the same-lattice excitations might be topologically nontrivial even in the completely flat band limit.Comment: 16 pages, 8 figures, companion paper to our previous arXiv:2106.00468, final versio

Bosonization Approach For Bilayer Quantum Hall Systems At νt=1

We develop a nonperturbative bosonization approach for bilayer quantum Hall systems at νT=1, which allows us to systematically study the existence of an exciton condensate in these systems. An effective boson model is derived and the excitation spectrum is calculated in both the Bogoliubov and the Popov approximations. In the latter case, we show that the ground state of the system is an exciton condensate only when the distance between the layers is very small compared to the magnetic length, indicating that the system possibly undergoes another phase transition before the incompressible-compressible one. The effect of a finite electron interlayer tunneling is included and a quantitative phase diagram is proposed. © 2006 The American Physical Society.9718(1997) Perspectives in Quantum Hall Effects, , edited by S. Das Sarma and A. Pinczuk (Wiley, New York)Eisenstein, J.P., MacDonald, A.H., (2004) Nature (London), 432, p. 691. , NATUAS 0028-0836 10.1038/nature03081Eisenstein, J.P., (2004) Science, 305, p. 950. , SCIEAS 0036-8075 10.1126/science.1099386Murphy, S.Q., (1994) Phys. Rev. Lett., 72, p. 728. , PRLTAO 0031-9007 10.1103/PhysRevLett.72.728Girvin, S.M., cond-mat/0108181Spielman, I.B., (2000) Phys. Rev. Lett., 84, p. 5808. , PRLTAO 0031-9007 10.1103/PhysRevLett.84.5808Spielman, I.B., (2001) Phys. Rev. Lett., 87, p. 036803. , PRLTAO 0031-9007 10.1103/PhysRevLett.87.036803Fertig, H.A., Straley, J.P., (2003) Phys. Rev. Lett., 91, p. 046806. , PRLTAO 0031-9007 10.1103/PhysRevLett.91.046806Kellogg, M., (2004) Phys. Rev. Lett., 93, p. 036801. , PRLTAO 0031-9007 10.1103/PhysRevLett.93.036801Wiersma, R.D., (2004) Phys. Rev. Lett., 93, p. 266805. , PRLTAO 0031-9007 10.1103/PhysRevLett.93.266805Wen, X.G., Zee, A., (1992) Phys. Rev. Lett., 69, p. 1811. , PRLTAO 0031-9007 10.1103/PhysRevLett.69.1811Fertig, H.A., (1989) Phys. Rev. B, 40, p. 1087. , PRBMDO 0163-1829 10.1103/PhysRevB.40.1087MacDonald, A.H., (1990) Phys. Rev. Lett., 65, p. 775. , PRLTAO 0031-9007 10.1103/PhysRevLett.65.775Joglekar, Y.N., MacDonald, A.H., (2001) Phys. Rev. B, 64, p. 155315. , PRBMDO 0163-1829 10.1103/PhysRevB.64.155315Fertig, H.A., Murthy, G., (2005) Phys. Rev. Lett., 95, p. 156802. , PRLTAO 0031-9007 10.1103/PhysRevLett.95.156802Doretto, R.L., Caldeira, A.O., Girvin, S.M., (2005) Phys. Rev. B, 71, p. 045339. , PRBMDO 0163-1829 10.1103/PhysRevB.71.045339Kallin, C., Halperin, B.I., (1984) Phys. Rev. B, 30, p. 5655. , PRBMDO 0163-1829 10.1103/PhysRevB.30.5655Fetter, A.L., Walecka, J.D., (2003) Quantum Theory of Many-Particle Systems, , Dover, MineolaStoof, H.T.C., Bijlsma, M., (1993) Phys. Rev. E, 47, p. 939. , PLEEE8 1063-651X 10.1103/PhysRevE.47.939Shi, H., Griffin, A., (1998) Phys. Rep., 304, p. 1. , PRPLCM 0370-1573 10.1016/S0370-1573(98)00015-5Chen, X.M., Quinn, J.J., (1992) Phys. Rev. B, 45, p. 11054. , PRBMDO 0163-1829 10.1103/PhysRevB.45.1105