Phases of the interacting one-dimensional electron gas coupled to phonons

A one-dimensional electron gas problem is investigated within the framework of the Luttinger model incorporating both the electron-acoustic-phonon interaction and the electron-optical-phonon interaction together with the electron-electron interaction. It is shown that this model is exactly soluble and the energy spectrum is constituted by bosonic excitations. It is also shown that for certain values of the coupling parameters the system exhibits an instability indicating the possibility of a phase transition.A one-dimensional electron gas problem is investigated within the framework of the Luttinger model incorporating both the electron-acoustic-phonon interaction and the electron-optical-phonon interaction together with the electron-electron interaction. It is shown that this model is exactly soluble and the energy spectrum is constituted by bosonic excitations. It is also shown that for certain values of the coupling parameters the system exhibits an instability indicating the possibility of a phase transition.

Journal of Physics Condensed MatterOct 30, 20012 citations

Phase diagram and isotope effects of the quasi-one-dimensional electron gas coupled to phonons

Ian P. Bindloss

Using a multistep renormalization group method, we study the low-temperature phases of the interacting one-dimensional (1D) electron gas coupled to phonons. We obtain analytic expressions for the weak-coupling quantum phase boundaries of the 1D extended Holstein-Hubbard model and the 1D extended Peierls-Hubbard model for general band-filling and phonon frequency. Away from half-filling, the phase diagrams are characterized by a delicate competition between spin density wave, charge density wave, and superconducting orders. We study the dependence of the ground state on the electron-phonon (el-ph) and electron-electron (el-el) coupling strengths, the screening length, electron bandwidth, phonon frequency, doping, and type of phonon. Unlike the case in Fermi liquids, in 1D the el-ph coupling is strongly renormalized, often to stronger values. Even when the bare phonon-induced attraction is weak compared to the bare el-el repulsion, a small amount of retardation can cause the renormalized el-ph interaction to dominate the problem. We find cases in which a repulsive el-el interaction enhances the superconducting susceptibility in the presence of a retarded el-ph interaction. The spin gap and superconducting susceptibility are found to be strongly dependent on the deviation from half-filling (doping). In some cases, the superconducting susceptibility varies nonmonotonically with doping and exhibits a maximum at a particular doping. For a quasi-1D array of weakly coupled, fluctuating 1D chains, the superconducting transition temperature ${T}_{c}$ also exhibits a maximum as a function of doping. The effect of changing the ion mass (isotope effect) on ${T}_{c}$ is found to be largest near half-filling and to decrease rapidly with doping.Using a multistep renormalization group method, we study the low-temperature phases of the interacting one-dimensional (1D) electron gas coupled to phonons. We obtain analytic expressions for the weak-coupling quantum phase boundaries of the 1D extended Holstein-Hubbard model and the 1D extended Peierls-Hubbard model for general band-filling and phonon frequency. Away from half-filling, the phase diagrams are characterized by a delicate competition between spin density wave, charge density wave, and superconducting orders. We study the dependence of the ground state on the electron-phonon (el-ph) and electron-electron (el-el) coupling strengths, the screening length, electron bandwidth, phonon frequency, doping, and type of phonon. Unlike the case in Fermi liquids, in 1D the el-ph coupling is strongly renormalized, often to stronger values. Even when the bare phonon-induced attraction is weak compared to the bare el-el repulsion, a small amount of retardation can cause the renormalized el-ph interaction to dominate the problem. We find cases in which a repulsive el-el interaction enhances the superconducting susceptibility in the presence of a retarded el-ph interaction. The spin gap and superconducting susceptibility are found to be strongly dependent on the deviation from half-filling (doping). In some cases, the superconducting susceptibility varies nonmonotonically with doping and exhibits a maximum at a particular doping. For a quasi-1D array of weakly coupled, fluctuating 1D chains, the superconducting transition temperature ${T}_{c}$ also exhibits a maximum as a function of doping. The effect of changing the ion mass (isotope effect) on ${T}_{c}$ is found to be largest near half-filling and to decrease rapidly with doping.

arXiv:cond-mat/0404154Physical Review BMay 27, 200513 citations

One-dimensional electron-phonon system at arbitrary coupling constant

Larissa S. Brizhik, A. A. Eremko

Zeitschrift für Physik B Condensed MatterDec 1, 19979 citations

Two-cutoff scaling for the one-dimensional electron gas

Gary S. Grest, Elihu Abrahams, S. T. Chui +2 more

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.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.

Physical review. B, Solid stateAug 1, 197637 citations

Dynamics of one-dimensional electron-phonon systems at low temperatures

S. Brazovskiǐ, I. E. Dzyaloshinskiǐ

Journal of Experimental and Theoretical PhysicsDec 1, 19760 citations

{T}_{c}

also exhibits a maximum as a function of doping. The effect of changing the ion mass (isotope effect) on

{T}_{c}

is found to be largest near half-filling and to decrease rapidly with doping.

{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.