The quantized Hall conductance of a single atomic wire: A proposal based on synthetic dimensions

We propose a method by which the quantization of the Hall conductance can be directly measured in the transport of a one-dimensional atomic gas. Our approach builds on two main ingredients: (1) a constriction optical potential, which generates a mesoscopic channel connected to two reservoirs, and (2) a time-periodic modulation of the channel, specifically designed to generate motion along an additional synthetic dimension. This fictitious dimension is spanned by the harmonic-oscillator modes associated with the tightly-confined channel, and hence, the corresponding "lattice sites" are intimately related to the energy of the system. We analyze the quantum transport properties of this hybrid two-dimensional system, highlighting the appealing features offered by the synthetic dimension. In particular, we demonstrate how the energetic nature of the synthetic dimension, combined with the quasi-energy spectrum of the periodically-driven channel, allows for the direct and unambiguous observation of the quantized Hall effect in a two-reservoir geometry. Our work illustrates how topological properties of matter can be accessed in a minimal one-dimensional setup, with direct and practical experimental consequences.

Conductance quantization and snake states in graphene magnetic waveguides

We consider electron waveguides (quantum wires) in graphene created by suitable inhomogeneous magnetic fields. The properties of uni-directional snake states are discussed. For a certain magnetic field profile, two spatially separated counter-propagating snake states are formed, leading to conductance quantization insensitive to backscattering by impurities or irregularities of the magnetic field.Comment: 5 pages, 4 figures, final version accepted as Rapid Comm. in PR

Analyse zur Netto-Lebensmittelproduktion und zum Ackerflächenbedarf von Rindermastsystemen

Die zukünftigen Rahmenbedingungen lassen eine steigende Ressourcenkonkurrenz zwischen Nahrungs- und Futtermittelproduktion erwarten. Gerade die Rindermast wird in diesem Zusammenhang sehr oft kritisch betrachtet. Das Ziel der vorliegenden Arbeit war es daher, unterschiedlich intensive Rindermastsysteme hinsichtlich ihres Ackerflächenbedarfs und ihres Beitrags zur Netto- Lebensmittelproduktion zu untersuchen. Die Analysen beruhen auf Daten eines Mastversuchs mit Kalbinnen, Ochsen und Stieren der Rasse Fleckvieh auf Grassilage- bzw. Maissilagebasis. Die Tiere der Grassilagegruppen wurden auf drei unterschiedlichen Kraftfutterniveaus (extensiv, niedrig, hoch) und die Maissilagegruppen auf hohem Kraftfutterniveau gemästet. Die Lebensmittelkonversionseffizienz (LKE, humanernährungstauglicher Output/ humanernährungstauglicher Input) verringert sich bei den Grassilage- Fütterungsgruppen mit steigender Kraftfuttergabe und war für die Maissilage- Fütterungsgruppen sowohl auf Basis Bruttoenergie als auch Rohprotein an niedrigsten. Im Mittel über alle Versuchsgruppen lag die LKE-Energie mit 0,29 (0,6-0,56) und LKE- Protein mit 0,44 (0,21- 0,87) unter den derzeitigen Bedingungen deutlich unter 1, was einer negativen Netto- Lebensmittelproduktion entspricht. Allerdings muss berücksichtigt werden, dass die Proteinqualität auf der Output- Seite um den Faktor 1,5 bis 1,9 höher war als auf der Input- Seite. Kombiniert man diese qualitativen Unterschiede mit den quantitativen Änderungen im humanernährungstauglichen Protein, so steigern extensiv gefütterte Kalbinnen und Ochsen die Wertigkeit des Proteins Für die menschliche Ernährung. Mit steigender Fütterungsintensität stieg die Nährstoffversorgung über Futtermittel von Ackerflächen in den Grassilagegruppen deutlich an und der höchste Ackerflächenbedarf ergab sich in den Maissilagegruppen

Electron Correlations in a Quantum Dot with Bychkov-Rashba Coupling

We report on a theoretical approach developed to investigate the influence of Bychkov-Rashba interaction on a few interacting electrons confined in a quantum dot. We note that the spin-orbit coupling profoundly influences the energy spectrum of interacting electrons in a quantum dot. Inter-electron interaction causes level crossings in the ground state and a jump in magnetization. As the coupling strength is increased, that jump is shifted to lower magnetic fields. Low-field magnetization will therefore provide a direct probe of the spin-orbit coupling strength in a quantum dot

Strain Relaxation in Graded InGaAs and InP Buffer Layers on GaAs (001)

We investigate compositionally graded Inxo≤x≤0.5Ga1-xAs and InP buffer layers which are prepared by molecular beam epitaxy on (001) GaAs substrate. The initial In content xo is equal to 0, 0.12, 0.18, 0.24, and 0.5 for the different samples. The In composition of the graded buffer increases linearly between xo and 0.5 with a fixed slope of 50% In-content per μm. The idea was to combine the advantage of surface flatness in homogeneous buffer layers and the reduced density of threading dislocations on the surface for graded buffer layers. The best compromise in terms of photoluminescence intensity and linewidth, electron mobility and crystal quality is achieved for xo = 0.18. For comparison to the InGaAs layers, we investigated also homogenous InP buffer layers on GaAs substrate. A strong photoluminescence peak with a linewidth of 5 meV is observed for 1 μm InP grown at 450°C applying a GaP decomposition source. The density of threading dislocations in the surface region is lower than in relaxed In0.5Ga0.5As layers but still by far not as low as for the graded buffer layers

Bosonization of strongly interacting electrons

Strong repulsive interactions in a one-dimensional electron system suppress the exchange coupling J of electron spins to a value much smaller than the Fermi energy E_F. The conventional theoretical description of such systems based on the bosonization approach and the concept of Tomonaga-Luttinger liquid is applicable only at energies below J. In this paper we develop a theoretical approach valid at all energies below the Fermi energy, including a broad range of energies between J and E_F. The method involves bosonization of the charge degrees of freedom, while the spin excitations are treated exactly. We use this technique to calculate the spectral functions of strongly interacting electron systems at energies in the range J<<epsilon<< E_F$. We show that in addition to the expected features at the wavevector k near the Fermi point k_F, the spectral function has a strong peak centered at k=0. Our theory also provides analytical description of the spectral function singularities near 3k_F (the "shadow band" features).Comment: 21 pages, 4 figure

Tomonaga-Luttinger liquid parameters of magnetic waveguides in graphene

Electronic waveguides in graphene formed by counterpropagating snake states in suitable inhomogeneous magnetic fields are shown to constitute a realization of a Tomonaga-Luttinger liquid. Due to the spatial separation of the right- and left-moving snake states, this non-Fermi liquid state induced by electron-electron interactions is essentially unaffected by disorder. We calculate the interaction parameters accounting for the absence of Galilei invariance in this system, and thereby demonstrate that non-Fermi liquid effects are significant and tunable in realistic geometries

Effective charge-spin models for quantum dots

It is shown that at low densities, quantum dots with few electrons may be mapped onto effective charge-spin models for the low-energy eigenstates. This is justified by defining a lattice model based on a many-electron pocket-state basis in which electrons are localised near their classical ground-state positions. The equivalence to a single-band Hubbard model is then established leading to a charge-spin ($t-J-V$) model which for most geometries reduces to a spin (Heisenberg) model. The method is refined to include processes which involve cyclic rotations of a ``ring'' of neighboring electrons. This is achieved by introducing intermediate lattice points and the importance of ring processes relative to pair-exchange processes is investigated using high-order degenerate perturbation theory and the WKB approximation. The energy spectra are computed from the effective models for specific cases and compared with exact results and other approximation methods.Comment: RevTex, 24 pages, 7 figures submitted as compressed and PostScript file

Signatures of electron correlations in the transport properties of quantum dots

The transition matrix elements between the correlated $N$ and $N\!+\!1$ electron states of a quantum dot are calculated by numerical diagonalization. They are the central ingredient for the linear and non--linear transport properties which we compute using a rate equation. The experimentally observed variations in the heights of the linear conductance peaks can be explained. The knowledge of the matrix elements as well as the stationary populations of the states allows to assign the features observed in the non--linear transport spectroscopy to certain transition and contains valuable information about the correlated electron states.Comment: 4 pages (revtex,27kB) + 3 figures in one file ziped and uuencoded (postscript,33kB), to appear in Phys.Rev.B as Rapid Communicatio