One-dimensional Interacting Electron Gas Research Articles

Fragile versus stable two-dimensional fermionic quasiparticles

We provide a comprehensive theoretical investigation of the Fermi liquid quasiparticle description in two-dimensional electron gas interacting via the long-range Coulomb interaction by calculating the electron self-energy within the leading-order approximation, which is exact in the high-density limit. We find that the quasiparticle energy is larger than the imaginary part of the self-energy up to very high energies, implying that the basic Landau quasiparticle picture is robust up to far above the Fermi energy. We find, however, that the quasiparticle picture becomes fragile in a small discrete region around a critical wave vector where the quasiparticle spectral function strongly deviates from the expected quasiparticle Lorentzian line shape with a vanishing renormalization factor. We show that such a non-Fermi liquid behavior arises due to the coupling of quasiparticles with the collective plasmon mode. This situation is somewhat intermediate between the one-dimensional interacting electron gas (i.e., Luttinger liquid), where the Landau Fermi liquid theory completely breaks down since only bosonic collective excitations exist, and three-dimensional electron gas, where quasiparticles are well-defined and more stable against interactions than in one and two dimensions. We use a number of complementary definitions for a quasiparticle to examine the interacting spectral function, contrasting two-dimensional and three-dimensional situations critically.

Luttinger liquid with strong spin-orbital coupling and Zeeman splitting in quantum wires

We study a one-dimensional interacting electron gas with the strong Rashba spin-orbit coupling and Zeeman splitting in a quantum well. A bosonization theory is developed for this system. The tunneling current may deviate from a simple power law which is that in an ordinary Luttinger liquid. The microscopic interacting coupling and the spin-orbital parameter may be measured by varying the external magnetic field in the tunneling experiment.

Josephson Current through a One-Dimensional Interacting Electron Gas

The Josephson current through a one-dimensional (1D) interacting electron system of length L coupled with two superconductors is studied in the presence of a barrier potential at the junction interfaces. The 1D system is treated within the framework of the Tomonaga-Luttinger liquid, in which the interaction is characterized by correlation exponents K ρ and K σ . We pay attention to the influence of Andreev reflection, which modifies the low-energy property of the 1D electron system near the junction interfaces. It is found that the critical current at low temperatures decays with increasing L as j c ∝(1/ L ) 2/ K ρ -1 , which is in striking contrast to the previous result j c ∝(1/ L ) 1/ K ρ + K σ -1 , obtained by Fazio et al. taking no account of the influence of Andreev reflection.

Andreev Conductance of a One-Dimensional Interacting Electron Gas Coupled with a Superconductor

Andreev reflection in a one-dimensional interacting electron gas coupled with a bulk superconductor is studied theoretically. In the case of weak interaction we calculate the renormalized Andreev-reflection amplitude using a poor man's renormalization group approach, taking account of both the forward and backward scatterings due to the electron-electron interaction. The conductance as a function of temperature is obtained for arbitrary strength of the barrier potential at the normal-superconductor interface. We show that the resulting temperature dependence is stronger than that of single-barrier conductance in the one-dimensional interacting electron gas. It is also shown that any logarithmic temperature dependence does not appear in the Andreev conductance despite the presence of the backward scattering.

Superconducting Proximity Effect on a One-Dimensional Interacting Electron Gas

A one-dimensional interacting electron gas (N) in contact with a bulk superconductor (S) is studied theoretically using a bosonization method. We calculate various correlation functions in the case of the complete Andreev reflection at zero temperature. It is found that a tendency towards singlet superconductivity is enhanced in the vicinity of the NS interface, while spin-density-wave correlation is shown to be suppressed. We calculate the conductance of the NS interface in the presence of a barrier potential. This interface conductance shows relatively strong temperature dependence compared with conductance through a single barrier in the absence of the proximity effect. This is a manifestation of interplay between the proximity effect and the mutual interaction.

Tunneling in quantum wires: A boundary conformal field theory approach

Tunneling through a localized barrier in a one-dimensional interacting electron gas has been studied recently using Luttinger liquid techniques. Stable phases with zero or unit transmission occur, as well as critical points with universal fractional transmission whose properties have only been calculated approximately, using a type of “ϵ-expansion”. It may be possible to calculate the universal properties of these critical points exactly using the recent boundary conformal field theory technique, although difficulties arise from the infinite number of conformal towers in this c = 4 theory and the absence of any apparent “fusion” principle. Here, we formulate the problem efficiently in this new language, and recover the critical properties of the stable phases.

Single-electron oscillations in the one-dimensional interacting electron gas.

We have shown that the one-dimensional interacting electron gas carrying dc current I should exhibit single-electron singularities at frequency ${\mathrm{\ensuremath{\omega}}}_{\mathit{s}}$=2\ensuremath{\pi}I/e for arbitrary strength of electron-electron interaction. These singularities arise due to Coulomb or Fermi correlations between electrons in the gas. Depending on the strength of the interaction the frequency ${\mathrm{\ensuremath{\omega}}}_{\mathit{s}}$ can be interpreted either as a frequency of the single-electron oscillations or the cutoff frequency of the shot noise associated with the current I.

Anderson localization and interactions in one-dimensional metals.

A one-dimensional interacting electron gas in a random potential exhibits a localized-delocalized transition for increasingly attractive interactions. We develop here a renormalization-group approach to study this transition. Our treatment allows us to obtain the phase diagram and the exponents of the correlation functions in the delocalized regime. The boundary between the two regimes is found to depend both on disorder and the strength of the interactions. For (nearly) spin-isotropic interactions the delocalized phase is dominated by superconducting fluctuations of either singlet or triplet type. The temperature dependence of the conductivity in the delocalized phase is also obtained and a nonuniversal power-law behavior is found. A description of the crossover towards the localized phase is given and the localization length is computed. An analogous description is developed for the localized-superfluid transition of a one-dimensional boson gas. In this case the transition to the localized regime occurs for increasingly repulsive interactions. We suggest a phase diagram with two different localized phases. Finally, we discuss some possible implications of our model for real quasi-one-dimensional metals.

On the instabilities of the one-dimensional interacting electron gas

The model Hamiltonian of the one-dimensional electron gas with different types of interaction (forward and backward scattering, Umklapp processes) is studied by assuming a sharp bandwidth cut-off. Exact equalities among different response functions are obtained for specific values of coupling constants from simple symmetry considerations. The ground-state energy derived in mean-field approximation and the asymptotic behaviour of response functions as calculated by various authors are discussed with respect to these exact relations. The agreement of phase diagrams as obtained with different methods is traced back to the underlying symmetry. Giving up this symmetry, e.g. by assuming different cut-offs above and below the Fermi energy, changes the phase diagram. Furthermore this allows one to construct a mean-field ground state where superconductivity and density waves coexist in a finite region of coupling space. If the electron-phonon interaction is also taken into account it follows that the charge-density wave instability (together with a periodic lattice distortion) is favoured.

Order in metallic chains. I. The single chain

The nature of the order as $T\ensuremath{\rightarrow}0$ in the one-dimensional interacting electron gas is investigated. We consider both low-momentum-transfer (${g}_{2}$ and ${g}_{4}$) and large-momentum-transfer (${g}_{1}$ and ${g}_{3}$) electron-electron interactions, focusing upon the particular value of ${g}_{1}$ for which Luther and Emery have recently found an exact solution. For this value of ${g}_{1}=\ensuremath{-}\frac{6}{5\ensuremath{\pi}{\ensuremath{\nu}}_{F}}$, we calculate the low-frequency behavior of the zero-temperature response functions explicitly. For the singlet superconducting and charge-density-wave responses, our results are consistent with those of Luther and Emery, implying that these response functions are divergent as $\ensuremath{\omega}\ensuremath{\rightarrow}0$ for certain values of ${g}_{2}$. For the triplet superconducting and spin-density-wave responses, however, our results differ from those of Luther and Emery, as we show explicitly that these responses have a gap for low frequencies, as was predicted by Lee. Furthermore, they do not diverge at the gap edge for any value of ${g}_{2}$. We also consider the effect of interactions between electrons on the same side of the Fermi surface, and find that the low-momentum-transfer process of that type (${g}_{4}$) does not change the response behavior qualitatively. For the large-momentum-transfer process between electrons on the same side of the Fermi surface (${g}_{3}$), we may solve the problem exactly for ${g}_{2}=0$ and ${g}_{1}=\ensuremath{-}\frac{6}{5\ensuremath{\pi}{\ensuremath{\nu}}_{F}}$, and find that the ground state of the system exhibits only long-range charge-density-wave order. By a mapping onto the classical two-dimensional Coulomb gas problem, we may extend those results for ${g}_{3}\ensuremath{\ne}0$ to the region ${g}_{1}l0$ and ${g}_{1}\ensuremath{-}2{g}_{2}l|{g}_{3}|$.

Two-cutoff scaling for the one-dimensional electron gas

We discuss a variety of renormalization-group methods for treating the one-dimensional interacting electron gas when the cutoff for the energy transfer is a phonon frequency ${\ensuremath{\omega}}_{D}$, while the electron bandwidth is of order ${E}_{F}$, with ${\ensuremath{\omega}}_{D}<{E}_{F}$. Our results, consistent only in the region of weak coupling, give the scaling trajectories for the coupling constants and cutoffs. The relationship to the conventional one-cutoff renormalization-group approach is discussed.