Dynamic correlations of the Coulomb Luttinger liquid

The dynamic density response function, form-factor, and spectral function of a Luttinger liquid with Coulomb electron-electron interaction are studied with the emphasis on the short-range electron correlations. The Coulomb interaction changes dramatically the density response function as compared to the case of the short-ranged interaction. The form of the density response function is smoothing with time, and the oscillatory structure appears. However, the spectral functions remain qualitatively the same. The dynamic form-factor contains the $\delta$-peak in the long-wave region, corresponding to one-boson excitations. Besides, the multi-boson-excitations band exists in the wave-number region near to $2k_F$. The dynamic form-factor diverges at the edges of this band, while the dielectric function goes to zero there, which indicates the appearance of a soft mode. We develop a method to analyze the asymptotics of the spectral functions near to the edges of the multi-boson-excitations band.Comment: 11 pages, 3 figures, submitted to PR

Plasmon-pole approximation for semiconductor quantum wire electrons

We develop the plasmon-pole approximation for an interacting electron gas confined in a semiconductor quantum wire. We argue that the plasmon-pole approximation becomes a more accurate approach in quantum wire systems than in higher dimensional systems because of severe phase-space restrictions on particle-hole excitations in one dimension. As examples, we use the plasmon-pole approximation to calculate the electron self-energy due to the Coulomb interaction and the hot-electron energy relaxation rate due to LO-phonon emission in GaAs quantum wires. We find that the plasmon-pole approximation works extremely well as compared with more complete many-body calculations.Comment: 16 pages, RevTex, figures included. Also available at http://www-cmg.physics.umd.edu/~lzheng

Orthorhombically Mixed s and dx2−y2_{x^2-y^2} Wave Superconductivity and Josephson Tunneling

The effect of orthorhombicity on Josephson tunneling in high T$_c$ superconductors such as YBCO is studied for both single crystals and highly twinned crystals. It is shown that experiments on highly twinned crystals experimentally determine the symmetry of the superconducting twin boundaries (which can be either even or odd with respect to a reflection in the twinning plane). Conversely, Josephson experiments on highly twinned crystals can not experimentally determine whether the superconductivity is predominantly $s$-wave or predominantly $d$-wave. The direct experimental determination of the order-parameter symmetry by Josephson tunneling in YBCO thus comes from the relatively few experiments which have been carried out on untwinned single crystals.Comment: 5 pages, RevTeX file, 1 figure available on request ([email protected]

Phase-Sensitive Tetracrystal Pairing-Symmetry Measurements and Broken Time-Reversal Symmetry States of High Tc Superconductors

A detailed analysis of the symmetric tetracrystal geometry used in phase-sensitive pairing symmetry experiments on high Tc superconductors is carried out for both bulk and surface time-reversal symmetry-breaking states, such as the d+id' and d+is states. The results depend critically on the substrate geometry. In the general case, for the bulk d+id' (or d+is) state, the measured flux quantization should in general not be too different from that obtained in the pure d-wave case, provided |d'| << |d| (or |s| << |d|). However, in one particular high symmetry geometry, the d+id' state gives results that allow it to be distinguished from the pure d and the d + is states. Results are also given for the cases where surface d+is or d+id' states occur at a [110] surface of a bulk d-wave superconductor. Remarkably, in the highest symmetry geometry, a number of the broken time-reversal symmetry states discussed above give flux quantization conditions usually associated with states not having broken time- reversal symmetry.Comment: 6 page

Luttinger Parameter g for Metallic Carbon Nanotubes and Related Systems

The random phase approximation (RPA) theory is used to derive the Luttinger parameter g for metallic carbon nanotubes. The results are consistent with the Tomonaga-Luttinger models. All metallic carbon nanotubes, regardless if they are armchair tubes, zigzag tubes, or chiral tubes, should have the same Luttinger parameter g. However, a (10,10) carbon peapod should have a smaller g value than a (10,10) carbon nanotube. Changing the Fermi level by applying a gate voltage has only a second order effect on the g value. RPA theory is a valid approach to calculate plasmon energy in carbon nanotube systems, regardless if the ground state is a Luttinger liquid or Fermi liquid. (This paper was published in PRB 66, 193405 (2002). However, Eqs. (6), (9), and (19) were misprinted there.)Comment: 2 figure

Intrasubband and Intersubband Electron Relaxation in Semiconductor Quantum Wire Structures

We calculate the intersubband and intrasubband many-body inelastic Coulomb scattering rates due to electron-electron interaction in two-subband semiconductor quantum wire structures. We analyze our relaxation rates in terms of contributions from inter- and intrasubband charge-density excitations separately. We show that the intersubband (intrasubband) charge-density excitations are primarily responsible for intersubband (intrasubband) inelastic scattering. We identify the contributions to the inelastic scattering rate coming from the emission of the single-particle and the collective excitations individually. We obtain the lifetime of hot electrons injected in each subband as a function of the total charge density in the wire.Comment: Submitted to PRB. 20 pages, Latex file, and 7 postscript files with Figure

Energy relaxation of an excited electron gas in quantum wires: many-body electron LO-phonon coupling

We theoretically study energy relaxation via LO-phonon emission in an excited one-dimensional electron gas confined in a GaAs quantum wire structure. We find that the inclusion of phonon renormalization effects in the theory extends the LO-phonon dominated loss regime down to substantially lower temperatures. We show that a simple plasmon-pole approximation works well for this problem, and discuss implications of our results for low temperature electron heating experiments in quantum wires.Comment: 10 pages, RevTex, 4 figures included. Also available at http://www-cmg.physics.umd.edu/~lzheng

Mixed symmetry superconductivity in two-dimensional Fermi liquids

We consider a 2D isotropic Fermi liquid with attraction in both $s$ and $d$ channels and examine the possibility of a superconducting state with mixed $s$ and $d$ symmetry of the gap function. We show that both in the weak coupling limit and at strong coupling, a mixed $s+id$ symmetry state is realized in a certain range of interaction. Phase transitions between the mixed and the pure symmetry states are second order. We also show that there is no stable mixed $s+d$ symmetry state at any coupling.Comment: 3 figures attached in uuencoded gzipped file

Tomonaga-Luttinger parameters for quantum wires

The low-energy properties of a homogeneous one-dimensional electron system are completely specified by two Tomonaga-Luttinger parameters $K_{\rho}$ and $v_{\sigma}$. In this paper we discuss microscopic estimates of the values of these parameters in semiconductor quantum wires that exploit their relationship to thermodynamic properties. Motivated by the recognized similarity between correlations in the ground state of a one-dimensional electron liquid and correlations in a Wigner crystal, we evaluate these thermodynamic quantities in a self-consistent Hartree-Fock approximation. According to our calculations, the Hartree-Fock approximation ground state is a Wigner crystal at all electron densities and has antiferromagnetic order that gradually evolves from spin-density-wave to localized in character as the density is lowered. Our results for $K_{\rho}$ are in good agreement with weak-coupling perturbative estimates $K_{\rho}^{pert}$ at high densities, but deviate strongly at low densities, especially when the electron-electron interaction is screened at long distances. $K_{\rho}^{pert}\sim n^{1/2}$ vanishes at small carrier density $n$ whereas we conjecture that $K_{\rho}\to 1/2$ when $n\to 0$, implying that $K_{\rho}$ should pass through a minimum at an intermediate density. Observation of such a non-monotonic dependence on particle density would allow to measure the range of the microscopic interaction. In the spin sector we find that the spin velocity decreases with increasing interaction strength or decreasing $n$. Strong correlation effects make it difficult to obtain fully consistent estimates of $v_{\sigma}$ from Hartree-Fock calculations. We conjecture that v_{\sigma}/\vf\propto n/V_0 in the limit $n\to 0$ where $V_0$ is the interaction strength.Comment: RevTeX, 23 pages, 8 figures include