Luttinger liquids with boundaries: Power-laws and energy scales

We present a study of the one-particle spectral properties for a variety of models of Luttinger liquids with open boundaries. We first consider the Tomonaga-Luttinger model using bosonization. For weak interactions the boundary exponent of the power-law suppression of the spectral weight close to the chemical potential is dominated by a term linear in the interaction. This motivates us to study the spectral properties also within the Hartree-Fock approximation. It already gives power-law behavior and qualitative agreement with the exact spectral function. For the lattice model of spinless fermions and the Hubbard model we present numerically exact results obtained using the density-matrix renormalization-group algorithm. We show that many aspects of the behavior of the spectral function close to the boundary can again be understood within the Hartree-Fock approximation. For the repulsive Hubbard model with interaction U the spectral weight is enhanced in a large energy range around the chemical potential. At smaller energies a power-law suppression, as predicted by bosonization, sets in. We present an analytical discussion of the crossover and show that for small U it occurs at energies exponentially (in -1/U) close to the chemical potential, i.e. that bosonization only holds on exponentially small energy scales. We show that such a crossover can also be found in other models.Comment: 16 pages, 9 figures included, submitted for publicatio

Flow equations for Hamiltonians: Contrasting different approaches by using a numerically solvable model

To contrast different generators for flow equations for Hamiltonians and to discuss the dependence of physical quantities on unitarily equivalent, but effectively different initial Hamiltonians, a numerically solvable model is considered which is structurally similar to impurity models. By this we discuss the question of optimization for the first time. A general truncation scheme is established that produces good results for the Hamiltonian flow as well as for the operator flow. Nevertheless, it is also pointed out that a systematic and feasible scheme for the operator flow on the operator level is missing. For this, an explicit analysis of the operator flow is given for the first time. We observe that truncation of the series of the observable flow after the linear or bilinear terms does not yield satisfactory results for the entire parameter regime as - especially close to resonances - even high orders of the exact series expansion carry considerable weight.Comment: 25 pages, 10 figure

The optical conductivity of graphene in the visible region of the spectrum

We compute the optical conductivity of graphene beyond the usual Dirac cone approximation, giving results that are valid in the visible region of the conductivity spectrum. The effect of next nearest neighbor hoping is also discussed. Using the full expression for the optical conductivity, the transmission and reflection coefficients are given. We find that even in the optical regime the corrections to the Dirac cone approximation are surprisingly small (a few percent). Our results help in the interpretation of the experimental results reported by Nair {\it et al.} [Science {\bf 320}, 1308 (2008)].Comment: 8 pages, 6 figure

Universal Dynamic Conductivity and Quantized Visible Opacity of Suspended Graphene

We show that the optical transparency of suspended graphene is defined by the fine structure constant, alpha, the parameter that describes coupling between light and relativistic electrons and is traditionally associated with quantum electrodynamics rather than condensed matter physics. Despite being only one atom thick, graphene is found to absorb a significant (pi times alpha=2.3%) fraction of incident white light, which is a consequence of graphene's unique electronic structure. This value translates into universal dynamic conductivity G =e^2/4h_bar within a few percent accuracy

Chirality probe of twisted bilayer graphene in the linear transport regime

We propose a minimal transport experiment in the linear regime that can probe the chirality of twisted moir\'e structures. First, we point out that usual two-terminal conductance measurements cannot access the chirality of a system. Only with a third contact and in the presence of an in-plane magnetic field, a chiral system displays non-reciprocal transport even if all contacts are symmetric. We thus propose to use the third lead as a voltage probe and show that opposite enantiomers give rise to different voltage drops on the third lead. The third lead can also be used as a current probe in the case of layer-discriminating contacts that can detect different handedness even in the absence of a magnetic field. Our exact symmetry considerations are supported by numerical calculations that confirm our conclusions and also demonstrate that there is a change of chirality around the magic angle.Comment: 13 pages, 6 figure

Effect of Holstein phonons on the optical conductivity of gapped graphene

We study the optical conductivity of a doped graphene when a sublattice symmetry breaking is occurred in the presence of the electron-phonon interaction. Our study is based on the Kubo formula that is established upon the retarded self-energy. We report new features of both the real and imaginary parts of the quasiparticle self-energy in the presence of a gap opening. We find an analytical expression for the renormalized Fermi velocity of massive Dirac Fermions over broad ranges of electron densities, gap values and the electron-phonon coupling constants. Finally we conclude that the inclusion of the renormalized Fermi energy and the band gap effects are indeed crucial to get reasonable feature for the optical conductivity.Comment: 12 pages, 4 figures. To appear in Eur. Phys. J.

Zigzag materials: selective interchain couplings control the coexistence of one-dimensional physics and deviations from it

The coexistence in the low-temperature spin-conducting phases of the zigzag materials BaCo2V2O8 and SrCo2V2O8 of one-dimensional (1D) physics with important deviations from it is not well understood. The studies of this paper account for an important selection rule that follows from interchain spin states being coupled more strongly within the spin dynamical structure factor of such zigzag materials whenever they are connected by a specific symmetry operation of the underlying lattice. In the case of excited states, this symmetry operation is only a symmetry in spin-space ifno electronic spin flip is performed within the generation of such states. Our results on both the role of selective interchain couplings in protecting the 1D physics and being behind deviations from it and on the dynamical properties being controlled by scattering of singlet pairs of physical spins 1/2 open the door to a key advance in the understanding of the physics of the spin chains in BaCo2V2O8 and SrCo2V2O8.Comment: 24 pages, 13 figure

Evaluation of the Impact of the Plastic BioSand Filter on Health and Drinking Water Quality in Rural Tamale, Ghana

A randomized controlled trial of the plastic BioSand filter (BSF) was performed in rural communities in Tamale (Ghana) to assess reductions in diarrheal disease and improvements in household drinking water quality. Few studies of household water filters have been performed in this region, where high drinking water turbidity can be a challenge for other household water treatment technologies. During the study, the longitudinal prevalence ratio for diarrhea comparing households that received the plastic BSF to households that did not receive it was 0.40 (95% confidence interval: 0.05, 0.80), suggesting an overall diarrheal disease reduction of 60%. The plastic BSF achieved a geometric mean reduction of 97% and 67% for E. coli and turbidity, respectively. These results suggest the plastic BSF significantly improved drinking water quality and reduced diarrheal disease during the short trial in rural Tamale, Ghana. The results are similar to other trials of household drinking water treatment technologies

Tomonaga-Luttinger model with an impurity for a weak two-body interaction

The Tomonaga-Luttinger model with impurity is studied by means of flow equations for Hamiltonians. The system is formulated within collective density fluctuations but no use of the bosonization formula is made. The truncation scheme includes operators consisting of up to four fermion operators and is valid for small electron-electron interactions. In this regime, the exact expression for the anomalous dimension is recovered. Furthermore, we verify the phase diagram of Kane and Fisher also for intermediate impurity strength. The approach can be extended to more general one-body potentials.Comment: 10 pages, 1 figur