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

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

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

Exchange interaction in quantum rings and wires in the Wigner-crystal limit

We present a controlled method for computing the exchange coupling in correlated one-dimensional electron systems based on the relation between the exchange constant and the pair-correlation function of spinless electrons. This relation is valid in several independent asymptotic regimes, including low electron density case, under the general condition of a strong spin-charge separation. Explicit formulas for the exchange constant are obtained for thin quantum rings and wires with realistic Coulomb interactions by calculating the pair-correlation function via a many-body instanton approach. A remarkably smooth interpolation between high and low electron density results is shown to be possible. These results are applicable to the case of one-dimensional wires of intermediate width as well. Our method can be easily generalized to other interaction laws, such as the inverse distance squared one of the Calogero-Sutherland-Moser model. We demonstrate excellent agreement with the known exact results for the latter model and show that they are relevant for a realistic experimental setup in which the bare Coulomb interaction is screened by an edge of a two-dimensional electron gas.Comment: 12 pages, 5 figure

Tunneling exponents in realistic quantum wires using the mean field approximation

It is demonstrated that the charge Tomonaga-Luttinger parameter $K_\rho$ of quantum wires can be estimated accurately using the Hartree-Fock approximation if carried out self consistently. The dependence of $K_\rho$ on the carrier density distinguishes different regimes of importance of correlations

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

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

Precipitation of T₁ and θ′ Phase in Al-4Cu-1Li-0.25Mn During Age Hardening: Microstructural Investigation and Phase-Field Simulation

Experimental and phase field studies of age hardening response of a high purity Al-4Cu-1Li-0.25Mn-alloy (mass %) during isothermal aging are conducted. In the experiments, two hardening phases are identified: the tetragonal θ′ (Al2Cu) phase and the hexagonal T1 (Al2CuLi) phase. Both are plate shaped and of nm size. They are analyzed with respect to the development of their size, number density and volume fraction during aging by applying different analysis techniques in TEM in combination with quantitative microstructural analysis. 3D phase-field simulations of formation and growth of θ′ phase are performed in which the full interfacial, chemical and elastic energy contributions are taken into account. 2D simulations of T1 phase are also investigated using multi-component diffusion without elasticity. This is a first step toward a complex phase-field study of T1 phase in the ternary alloy. The comparison between experimental and simulated data shows similar trends. The still unsaturated volume fraction indicates that the precipitates are in the growth stage and that the coarsening/ripening stage has not yet been reached