Does Luttinger liquid behaviour survive in an atomic wire on a surface?

We form a highly simplified model of an atomic wire on a surface by the coupling of two one-dimensional chains, one with electron-electron interactions to represent the wire and and one with no electron-electron interactions to represent the surface. We use exact diagonalization techniques to calculate the eigenstates and response functions of our model, in order to determine both the nature of the coupling and to what extent the coupling affects the Luttinger liquid properties we would expect in a purely one-dimensional system. We find that while there are indeed Luttinger liquid indicators present, some residual Fermi liquid characteristics remain.Comment: 14 pages, 7 figures. Submitted to J Phys

Friedel oscillations in a gas of interacting one-dimensional fermionic atoms confined in a harmonic trap

Using an asymptotic phase representation of the particle density operator $\hat{\rho}(z)$ in the one-dimensional harmonic trap, the part $\delta \hat{\rho}_F(z)$ which describes the Friedel oscillations is extracted. The expectation value $$ with respect to the interacting ground state requires the calculation of the mean square average of a properly defined phase operator. This calculation is performed analytically for the Tomonaga-Luttinger model with harmonic confinement. It is found that the envelope of the Friedel oscillations at zero temperature decays with the boundary exponent $\nu = (K+1)/2$ away from the classical boundaries. This value differs from that known for open boundary conditions or strong pinning impurities. The soft boundary in the present case thus modifies the decay of Friedel oscillations. The case of two components is also discussed.Comment: Revised version to appear in Journal of Physics B: Atomic, Molecular and Optical Physic

Renormalization-group study of a magnetic impurity in a Luttinger liquid

A generalized Anderson model for a magnetic impurity in an interacting one-dimensional electron gas is studied via a mapping onto a classical Coulomb gas. For weak potential scattering, the local-moment parameter regime expands as repulsive bulk interactions become stronger, but the Kondo scale for the quenching of the impurity moment varies nonmonotonically. There also exist two regimes dominated by backward potential scattering: one in which the impurity is nonmagnetic, and another in which an unquenched local moment survives down to very low temperatures.Comment: REVTeX, 4 pages, 3 epsf-embedded EPS figure

An Exactly Solvable Kondo Problem for Interacting One-Dimensional Fermions

The single impurity Kondo problem in the one-dimensional $\delta$-potential Fermi gas is exactly solved for two sets of special coupling constants via Bethe ansatz. It is found that ferromagnetic Kondo screening does occur in one case which confirms the Furusaki-Nagaosa conjecture while in the other case it does not, which we explain in a simple physical picture. The surface energy, the low temperature specific heat and the Pauli susceptibility induced by the impurity and thereby the Kondo temperature are derived explicitly.Comment: 8 pages, LATEX, REVTE

Perturbation theory for optical excitations in the one-dimensional extended Peierls--Hubbard model

For the one-dimensional, extended Peierls--Hubbard model we calculate analytically the ground-state energy and the single-particle gap to second order in the Coulomb interaction for a given lattice dimerization. The comparison with numerically exact data from the Density-Matrix Renormalization Group shows that the ground-state energy is quantitatively reliable for Coulomb parameters as large as the band width. The single-particle gap can almost triple from its bare Peierls value before substantial deviations appear. For the calculation of the dominant optical excitations, we follow two approaches. In Wannier theory, we perturb the Wannier exciton states to second order. In two-step perturbation theory, similar in spirit to the GW-BSE approach, we form excitons from dressed electron-hole excitations. We find the Wannier approach to be superior to the two-step perturbation theory. For singlet excitons, Wannier theory is applicable up to Coulomb parameters as large as half band width. For triplet excitons, second-order perturbation theory quickly fails completely.Comment: 32 pages, 12 figures, submtted to JSTA

Boundary Effects on Spectral Properties of Interacting Electrons in One Dimension

The single electron Green's function of the one-dimensional Tomonaga-Luttinger model in the presence of open boundaries is calculated with bosonization methods. We show that the critical exponents of the local spectral density and of the momentum distribution change in the presence of a boundary. The well understood universal bulk behavior always crosses over to a boundary dominated regime for small energies or small momenta. We show this crossover explicitly for the large-U Hubbard model in the low-temperature limit. Consequences for photoemission experiments are discussed.Comment: revised and reformatted paper to appear in Phys. Rev. Lett. (Feb. 1996). 5 pages (revtex) and 3 embedded figures (macro included). A complete postscript file is available from http://FY.CHALMERS.SE/~eggert/luttinger.ps or by request from [email protected]

New selection rules for resonant Raman scattering on quantum wires

The bosonisation technique is used to calculate the resonant Raman spectrum of a quantum wire with two electronic sub-bands occupied. Close to resonance, the cross section at frequencies in the region of the inter sub-band transitions shows distinct peaks in parallel polarisation of the incident and scattered light that are signature of collective higher order spin density excitations. This is in striking contrast to the conventional selection rule for non-resonant Raman scattering according to which spin modes can appear only in perpendicular polarisation. We predict a new selection rule for the excitations observed near resonance, namely that, apart from charge density excitations, only spin modes with positive group velocities can appear as peaks in the spectra in parallel configuration close to resonance. The results are consistent with all of the presently available experimental data.Comment: 7 pages, 2 figure

Frequency scaling of photo-induced tunneling

The DC current-voltage characteristics, induced by a driving electric field with frequency Omega, of a one dimensional electron channel with a tunnel barrier is calculated. Electron-electron interaction of finite-range is taken into account. For intermediate interaction strengths, the non-linear differential conductance shows cusp-like minima at bias voltages integer multiples of hbar Omega / e that are a consequence of the finite non-zero range of the interaction but are independent of the shape of the driving electric field. However, the frequency-scaling of the photo-induced current shows a cross-over between Omega^{-1} and Omega^{-2}, and depends on the spatial shape of the driving field and the range of the interaction.Comment: 7 pages, EURO-TeX, 3 figures, to appear in Europhysics Letter

How universal is the one-particle Green's function of a Luttinger liquid?

The one-particle Green's function of the Tomonaga-Luttinger model for one-dimensional interacting Fermions is discussed. Far away from the origin of the plane of space-time coordinates the function falls off like a power law. The exponent depends on the direction within the plane. For a certain form of the interaction potential or within an approximated cut-off procedure the different exponents only depend on the strength of the interaction at zero momentum and can be expressed in terms of the Luttinger liquid parameters $K_{\rho}$ and $K_{\sigma}$ of the model at hand. For a more general interaction and directions which are determined by the charge velocity $v_{\rho}$ and spin velocity $v_{\sigma}$ the exponents also depend on the smoothness of the interaction at zero momentum and the asymptotic behavior of the Green's function is not given by the Luttinger liquid parameters alone. This shows that the physics of large space-time distances in Luttinger liquids is less universal than is widely believed.Comment: 5 pages with 2 figure