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

Abstract

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.

Published version; 18 pages, 20 figures

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Cited by in corpus (12)

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• Excitation spectra and correlation functions of quantum Su-Schrieffer-Heeger models
• Retardation effects in the Holstein-Hubbard chain at half-filling
• The quantum vs classical aspects of one dimensional electron-phonon systems revisited by the renormalization group method
• Nature of ground states in one-dimensional electron-phonon Hubbard models at half-filling
• Finite-size effects in Luther-Emery phases of Holstein and Hubbard models
• Density waves in strongly correlated quantum chains
• Dominant Superconducting Fluctuations in the One-Dimensional Extended Holstein-Extended Hubbard model
• On the Validity of the Tomonaga Luttinger Liquid Relations for the One-dimensional Holstein Model
• Phonons in Hubbard ladders studied within the framework of the one-loop renormalization group
• The one-dimensional Holstein model revisited
• Renormalization-group exponents for superconducting phases in two-leg ladders