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

Exact-exchange density-functional theory for quasi-two-dimensional electron gases

A simple exact-exchange density-functional method for a quasi-two-dimensional electron gas with variable density is presented. An analytical expression for the exact-exchange potential with only one occupied subband is provided, without approximations. When more subbands are occupied the exact-exchange potential is obtained numerically. The theory shows that, in contradiction with LDA, the exact-exchange potential exhibits discontinuities and the system suffers a zero-temperature first-order transition each time a subband is occupied. Results suggesting that the translational symmetry might be spontaneously broken at zero temperature are presented. An extension of the theory to finite temperatures allows to describe a drop in the intersubband spacing in good quantitative agreement with recent experiments.Comment: 14 pages, 3 figure

Coulomb Gaps in One-Dimensional Spin-Polarized Electron Systems

We investigate the density of states (DOS) near the Fermi energy of one-dimensional spin-polarized electron systems in the quantum regime where the localization length is comparable to or larger than the inter-particle distance. The Wigner lattice gap of such a system, in the presence of weak disorder, can occur precisely at the Fermi energy, coinciding with the Coulomb gap in position. The interplay between the two is investigated by treating the long-range Coulomb interaction and the random disorder potential in a self-consistent Hartree-Fock approximation. The DOS near the Fermi energy is found to be well described by a power law whose exponent decreases with increasing disorder strength.Comment: 4 pages, revtex, 4 figures, to be published in Phys. Rev. B as a Rapid Communicatio

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

Tomonaga-Luttinger features in the resonant Raman spectra of quantum wires

The differential cross section for resonant Raman scattering from the collective modes in a one dimensional system of interacting electrons is calculated non-perturbatively using the bosonization method. The results indicate that resonant Raman spectroscopy is a powerful tool for studying Tomonaga-Luttinger liquid behaviour in quasi-one dimensional electron systems.Comment: 4 pages, no figur

DC and AC Josephson Effect in a Superconductor-Luttinger Liquid-Superconductor System

We calculate both the DC and the AC Josephson current through a one-dimensional system of interacting electrons, connected to two superconductors by tunnel junctions. We treat the (repulsive) Coulomb interaction in the framework of the one-channel, spin-$1/2$ Luttinger model. The Josephson current is obtained for two geometries of experimental relevance: a quantum wire and a ring. At zero temperature, the critical current is found to decay algebraically with increasing distance $d$ between the junctions. The decay is characterized by an exponent which depends on the strength of the interaction. At finite temperatures $T$, lower than the superconducting transition temperature $T_c$, there is a crossover from algebraic to exponential decay of the critical current as a function of $d$, at a distance of the order of $\hbar v_F/k_B T$. Moreover, the dependence of critical current on temperature shows non-monotonic behavior. If the Luttinger liquid is confined to a ring of circumference $L$, coupled capacitively to a gate voltage and threaded by a magnetic flux, the Josephson current shows remarkable parity effects under the variation of these parameters. For some values of the gate voltage and applied flux, the ring acts as a $\pi$-junction. These features are robust against thermal fluctuations up to temperatures on the order of $\hbar v_F/k_B L$. For the wire-geometry, we have also studied the AC-Josephson effect. The amplitude and the phase of the time-dependent Josephson current are affected by electron-electron interactions. Specifically, the amplitude shows pronounced oscillations as a function of the bias voltage due to the difference between the velocities of spin and charge excitations in the Luttinger liquid. Therefore, the AC Josephson effect can be used as a tool for the observation o

Revival of the spin-Peierls transition in Cu_xZn_(1-x)GeO_3 under pressure

Pressure and temperature dependent susceptibility and Raman scattering experiments on single crystalline Cu_xZn_(1-x)GeO_3 have shown an unusually strong increase of the spin-Peierls phase transition temperature upon applying hydrostatic pressure. The large positive pressure coefficient (7.5 K/GPa) - almost twice as large as for the pure compound (4.5 K/GPa) - is interpreted as arising due to an increasing magnetic frustration which decreases the spin-spin correlation length, and thereby weakens the influence of the non-magnetic Zn-substitution.Comment: LaTeX, 15 pages, 5 eps figures, Phys. Rev. B, to appea

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

Band structure and optical anisotropy in V-shaped and T-shaped semiconductor quantum wires

We present a theoretical investigation of the electronic and optical properties of V- and T-shaped quantum wires. Valence-band mixing as well as realistic sample geometries are fully included through an accurate and efficient approach that is described here in detail. We investigate the resulting valence-band structure, which shows some significant peculiarities, such as an anomalously large spin splitting in the lowest heavy-hole subband of T-shaped wires. For both classes of wires we obtain good agreement between calculated optical absorption and recent experimental spectra, and we demonstrate that the analysis of optical anisotropy can be used as an effective tool to extract information on valence states, which is usually very difficult to obtain otherwise