Artifical atoms in interacting graphene quantum dots

We describe the theory of few Coulomb-correlated electrons in a magnetic quantum dot formed in graphene. While the corresponding nonrelativistic (Schr\"odinger) problem is well understood, a naive generalization to graphene's "relativistic" (Dirac-Weyl) spectrum encounters divergencies and is ill-defined. We employ Sucher's projection formalism to overcome these problems. Exact diagonalization results for the two-electron quantum dot, i.e., the artificial helium atom in graphene, are presented.Comment: 4+ pages, 2 figure

Theory of momentum resolved tunneling into a short quantum wire

Motivated by recent tunneling experiments in the parallel wire geometry, we calculate results for momentum resolved tunneling into a short one-dimensional wire, containing a small number of electrons. We derive some general theorems about the momentum dependence, and we carry out exact calculations for up to N=4 electrons in the final state, for a system with screened Coulomb interactions that models the situation of the experiments. We also investigate the limit of large $N$ using a Luttinger-liquid type analysis. We consider the low-density regime, where the system is close to the Wigner crystal limit, and where the energy scale for spin excitations can be much lower than for charge excitations, and we consider temperatures intermediate between the relevant spin energies and charge excitations, as well as temperatures below both energy scales.Comment: 19 pages, 13 figures, clarified text in a few points, added 1 figure, updated reference

Exchange Coupling in a One-Dimensional Wigner Crystal

We consider a long quantum wire at low electron densities. In this strong interaction regime a Wigner crystal may form, in which electrons comprise an antiferromagnetic Heisenberg spin chain. The coupling constant J is exponentially small, as it originates from tunneling of two neighboring electrons through the segregating potential barrier. We study this exponential dependence, properly accounting for the many-body effects and the finite width of the wire.Comment: 4 pages, 3 figure

Gapped Phases of Quantum Wires

We investigate possible nontrivial phases of a two-subband quantum wire. It is found that inter- and intra-subband interactions may drive the electron system of the wire into a gapped state. If the nominal electron densities in the two subbands are sufficiently close to each other, then the leading instability is the inter-subband charge-density wave (CDW). For large density imbalance, the interaction in the inter-subband Cooper channel may lead to a superconducting instability. The total charge-density mode, responsible for the conductance of an ideal wire, always remains gapless, which enforces the two-terminal conductance to be at the universal value of 2e^2/h per occupied subband. On the contrary, the tunneling density of states (DOS) in the bulk of the wire acquires a hard gap, above which the DOS has a non-universal singularity. This singularity is weaker than the square-root divergency characteristic for non-interacting quasiparticles near a gap edge due to the "dressing" of massive modes by a gapless total charge density mode. The DOS for tunneling into the end of a wire in a CDW-gapped state preserves the power-law behavior due to the frustration the edge introduces into the CDW order. This work is related to the vast literature on coupled 1D systems, and most of all, on two-leg Hubbard ladders. Whenever possible, we give derivations of the important results by other authors, adopted for the context of our study.Comment: 30 pages, 6 figures, to appear in "Interactions and Transport Properties of Lower Dimensional Systems", Lecture Notes in Physics, Springe

Spin and Charge Luttinger-Liquid Parameters of the One-Dimensional Electron Gas

Low-energy properties of the homogeneous electron gas in one dimension are completely described by the group velocities of its charge (plasmon) and spin collective excitations. Because of the long range of the electron-electron interaction, the plasmon velocity is dominated by an electrostatic contribution and can be estimated accurately. In this Letter we report on Quantum Monte Carlo simulations which demonstrate that the spin velocity is substantially decreased by interactions in semiconductor quantum wire realizations of the one-dimensional electron liquid.Comment: 13 pages, figures include

Remote-sensing-based analysis of the 1996 surge of Northern Inylchek Glacier, central Tien Shan, Kyrgyzstan

The evolution of Northern Inylchek Glacier and its proglacial lake - Upper Lake Merzbacher - during its 1996 surge and the surrounding decades is analyzed with remote sensing imagery. Overall retreat of the glacier from 1943 to 1996 enlarged the lake to 4 km long and ≈ 100 m deep. The surge in 1996 initiated between 12 September and 7 October and advanced the glacier by 3.7 km to override most of Upper Lake Merzbacher. The surge phase probably ended in December 1996 and involved mean flow velocities across the lower trunk of the glacier that reached 50 m d− 1 over a 32-day period. Water displaced by the surge from Upper Lake Merzbacher, totalling 1.5 × 108 m3 in volume, accelerated filling of Lower Lake Merzbacher downvalley and helped trigger this marginal ice-dammed lake to outburst in a jökulhlaup around late November/early December. The characteristics and duration of the surge render it as similar to temperate glacier surges elsewhere. It may have been facilitated by low basal friction caused by water-saturated sediments in the upper lake bed. Furthermore, bathymetric measurements show that the surge evacuated much sediment into the upper lake, causing its depth to reduce from 20 to 30 m in 1996 to 8 m by 2005 and 2 m by 2011; the corresponding deposition rates imply glacier-catchment specific mean sediment yields of 1.4 to 3.4 × 103 Mg km− 2 a− 1 in the years after the surge. Our study documents novel interactions within a cascade system of glaciers and lakes that exhibits surging and outburst-flood behavior

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