Comparison of the density-matrix renormalization group method applied to fractional quantum Hall systems in different geometries

We report a systematic study of the fractional quantum Hall effect (FQHE) using the density-matrix renormalization group (DMRG) method on two different geometries: the sphere and the cylinder. We provide convergence benchmarks based on model Hamiltonians known to possess exact zero-energy ground states, as well as an analysis of the number of sweeps and basis elements that need to be kept in order to achieve the desired accuracy.The ground state energies of the Coulomb Hamiltonian at $\nu=1/3$ and $\nu=5/2$ filling are extracted and compared with the results obtained by previous DMRG implementations in the literature. A remarkably rapid convergence in the cylinder geometry is noted and suggests that this boundary condition is particularly suited for the application of the DMRG method to the FQHE.Comment: 5 pages, 7 figure

Interface steps in field effect devices

The charge doped into a semiconductor in a field effect transistor (FET) is generally confined to the interface of the semiconductor. A planar step at the interface causes a potential drop due to the strong electric field of the FET, which in turn is screened by the doped carriers. We analyze the dipolar electronic structure of a single step in the Thomas-Fermi approximation and find that the transmission coefficient through the step is exponentially suppressed by the electric field and the induced carrier density as well as by the step height. In addition, the field enhancement at the step edge can facilitate the electric breakthrough of the insulating layer. We suggest that these two effects may lead to severe problems when engineering FET devices with very high doping. On the other hand steps can give rise to interesting physics in superconducting FETs by forming weak links and potentially creating atomic size Josephson junctions.Comment: 6 pages, 4 figures, submitted to J. Appl. Phy

Microscopic non-equilibrium theory of quantum well solar cells

We present a microscopic theory of bipolar quantum well structures in the photovoltaic regime, based on the non-equilibrium Green's function formalism for a multi band tight binding Hamiltonian. The quantum kinetic equations for the single particle Green's functions of electrons and holes are self-consistently coupled to Poisson's equation, including inter-carrier scattering on the Hartree level. Relaxation and broadening mechanisms are considered by the inclusion of acoustic and optical electron-phonon interaction in a self consistent Born approximation of the scattering self energies. Photogeneration of carriers is described on the same level in terms of a self energy derived from the standard dipole approximation of the electron-photon interaction. Results from a simple two band model are shown for the local density of states, spectral response, current spectrum, and current-voltage characteristics for generic single quantum well systems.Comment: 10 pages, 6 figures; corrected typos, changed caption Fig. 1, replaced Fig.

Second Generation of Composite Fermions in the Hamiltonian Theory

In the framework of a recently developed model of interacting composite fermions restricted to a single level, we calculate the activation gaps of a second generation of spin-polarized composite fermions. These composite particles consist each of a composite fermion of the first generation and a vortex-like excitation and may be responsible for the recently observed fractional quantum Hall states at unusual filling factors such as nu=4/11,5/13,5/17, and 6/17. Because the gaps of composite fermions of the second generation are found to be more than one order of magnitude smaller than those of the first generation, these states are less visible than the usual states observed at filling factors nu=p/(2ps+1). Their stability is discussed in the context of a pseudopotential expansion of the composite-fermion interaction potential.Comment: 5 pages, 3 figures; after publication in PRB, we have realized that a factor was missing in one of the expressions; the erroneous results are now corrected; an erratum has been sent to PR

Excitation gaps in fractional quantum Hall states: An exact diagonalization study

We compute energy gaps for spin-polarized fractional quantum Hall states in the lowest Landau level at filling fractions nu=1/3, 2/5,3/7 and 4/9 using exact diagonalization of systems with up to 16 particles and extrapolation to the infinite system-size limit. The gaps calculated for a pure Coulomb interaction and ignoring finite width effects, disorder and LL mixing agree with predictions of composite fermion theory provided the logarithmic corrections to the effective mass are included. This is in contrast with previous estimates, which, as we show, overestimated the gaps at nu=2/5 and 3/7 by around 15%. We also study the reduction of the gaps as a result of the non-zero width of the 2D layer. We show that these effects are accurately accounted for using either Gaussian or z*Gaussian' (zG) trial wavefunctions, which we show are significantly better variational wavefunctions than the Fang-Howard wavefunction. For quantum well parameters typical of heterostructure samples, we find gap reductions of around 20%. The experimental gaps, after accounting heuristically for disorder,are still around 40% smaller than the computed gaps. However, for the case of tetracene layers inmetal-insulator-semiconductor (MIS) devices we find that the measured activation gaps are close to those we compute. We discuss possible reasons why the difference between computed and measured activation gaps is larger in GaAs heterostructures than in MIS devices. Finally, we present new calculations using systems with up to 18 electrons of the gap at nu=5/2 including width corrections.Comment: 18 pages, 17 figure

Dynamic Substance Flow Analysis as a Valuable Risk Evaluation Tool – A Case Study for Brominated Flame Retardants as an Example of Potential Endocrine Disrupters

Most studies of potentially hazardous substances focus on aspects of their occurrence and fate in the environment (monitoring and modelling studies) to estimate the environmental impact and the potential exposure of humans. In order to evaluate emission sources, to recognise environmental impacts at an early stage, and to take efficient legislative or technical measures, it is essential to know their behaviour in the anthroposphere as a function of time. So far, only very few investigations of this type exist for chemicals. In regular risk assessments, only rather limited knowledge is available concerning the behaviour of chemicals in the anthroposphere (production data, substance quantities in products, recycling rates, emissions occurring during use, etc.) or their lifecycle, and no information at all about their behaviour as a function of time. For this reason, it is these aspects that were investigated in a case study within the framework of the national research programme NRP50 for selected brominated flame retardants with endocrine-disrupting potential (pentabromodiphenyl ether, hexabromocyclododecane) or the potential to degrade to such substances (decabromodiphenyl ether). A dynamic substance flow analysis (SFA) model was performed for Switzerland for the time period 1980–2020. In this review paper (a) we present a summary of typical results (system overview, consumption trends/application patterns, anthropogenic stocks and their changes, emission trends including major sources and environmental fate), (b) we summarize the effectiveness of recent risk-reduction measures in Switzerland and (c) we indicate serious remaining data gaps and recommend further important measures for risk reduction. For the future, we suggest improving the knowledge of the lifecycle of chemicals such as brominated flame retardants by applying SFA as a suitable tool to weight the effect of substance flows with respect to environmental emissions, and to serve as the basis for planning actions and measures to reduce such emissions. This is in line with one major conclusion of the NRP50 consensus platform 'Brominated Flame Retardants'

Dynamical Correlations in a Half-Filled Landau Level

We formulate a self-consistent field theory for the Chern-Simons fermions to study the dynamical response function of the quantum Hall system at $\nu=1/2$. Our scheme includes the effect of correlations beyond the random-phase approximation (RPA) employed to this date for this system. The resulting zero-frequency density response function vanishes as the square of the wave vector in the long-wavelength limit. The longitudinal conductivity calculated in this scheme shows linear dependence on the wave vector, like the experimentals results and the RPA, but the absolute values are higher than the experimental results.Comment: 4 pages, revtex, 3 figures included. Corrected typo

Magnons and skyrmions in fractional Hall ferromagnets

Recent experiments have established a qualitative difference between the magnetization temperature-dependences $M(T)$ of quantum Hall ferromagnets at integer and fractional filling factors. We explain this difference in terms of the relative energies of collective magnon and particle-hole excitations in the two cases. Analytic calculations for hard-core model systems are used to demonstrate that, in the fractional case, interactions suppress the magnetization at finite temperatures and that particle-hole excitations rather than long-wavelength magnons control $M(T)$ at low $T$.Comment: 4 pages, no figure

Quasi-Particle Tunneling in Anti-Pfaffian Quantum Hall State

We study tunneling phenomena at the edge of the anti-Pfaffian quantum Hall state at the filling factor $\nu=5/2$. The edge current in a single point-contact is considered. We focus on nonlinear behavior of two-terminal conductance with the increase in negative split-gate voltage. Expecting the appearance of the intermediate conductance plateau we calculate the value of its conductance by using the renormalization group (RG) analysis. Further, we show that non-perturbative quasi-particle tunneling is effectively described as perturbative electron tunneling by the instanton method. The two-terminals conductance is written as a function of the gate voltage. The obtained results enable us to distinguish the anti-Pfaffian state from the Pfaffian state experimentally.Comment: 5 pages, 4 figure