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Register a new userInterpolative approach for electron-electron and electron-phonon interactions: from the Kondo to the polaronic regime
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Added by
Alvaro Martin-Rodero
Publication date
2008
fields
Physics
and research's language is
English
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We present a theoretical approach to determine the electronic properties of nanoscale systems exhibiting strong electron-electron and electron-phonon interactions and coupled to metallic electrodes. This approach is based on an interpolative ansatz for the electronic self-energy which becomes exact both in the limit of weak and strong coupling to the electrodes. The method provides a generalization of previous interpolative schemes which have been applied to the purely electronic case extensively. As a test case we consider the single level Anderson-Holstein model. The results obtained with the interpolative ansatz are in good agreement with existing data from Numerical Renormalization Group calculations. We also check our results by considering the case of the electrodes represented by a few discrete levels which can be diagonalized exactly. The approximation describes properly the transition from the Kondo regime where electron-electron interactions dominate to the polaronic case characterized by a strong electron-phonon interaction.
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This work presents a method of grouping the electron spinors and the acoustic phonon modes of polar crystals such as metal oxides into an SU(2) gauge theory. The gauge charge is the electron spin, which is assumed to couple to the transverse acoustic phonons on the basis of spin ordering phenomena in crystals such as V$_{2}$O$_{3}$ and VO$_{2}$, while the longitudinal mode is neutral. A generalization the Peierls mechanism is presented based on the discrete gauge invariance of crystals and the corresponding Ward-Takahashi identity. The introduction of a band index violates the Ward-Takahashi identity for interband transitions resulting in a longitudinal component appearing in the upper phonon band. Thus both the spinors and the vector bosons acquire mass and a crystal with an electronic band gap and optical phonon modes results. In the limit that the coupling of bosons charged under the SU(2) gauge group goes to zero, breaking the electron U(1) symmetry recovers the BCS mechanism. In the limit that the neutral boson decouples, a Cooper instability mediated by spin-wave exchange results from symmetry breaking, i.e. unconventional superconductivity mediated by magnetic interactions.
We investigate the effect of tuning the phonon energy on the correlation effects in models of electron-phonon interactions using DMFT. In the regime where itinerant electrons, instantaneous electron-phonon driven correlations and static distortions c
ompete on similar energy scales, we find several interesting results including (1) A crossover from band to Mott behavior in the spectral function, leading to hybrid band/Mott features in the spectral function for phonon frequencies slightly larger than the band width. (2) Since the optical conductivity depends sensitively on the form of the spectral function, we show that such a regime should be observable through the low frequency form of the optical conductivity. (3) The resistivity has a double kondo peak arrangement
Existing Quantum Monte Carlo studies have investigated the properties of fermions on a Lieb (CuO$_2$) lattice interacting with an on-site, or near-neighbor electron-electron coupling. Attention has focused on the interplay of such interactions with the macroscopic degeneracy of local zero energy modes, from which Bloch states can be formed to produce a flat band in which energy is independent of momentum. The resulting high density of states, in combination with the Stoner criterion, suggests that there should be pronounced instabilities to ordered phases. Indeed, a theorem by Lieb rigorously establishes the existence of ferrimagnetic order. Here we study the charge density wave phases induced by electron-phonon coupling on the Lieb lattice, as opposed to previous work on electron-electron interactions. Our key result is the demonstration of charge density wave (CDW) phases at one-third and two-thirds fillings, characterized by long-range density density correlations between doubly occupied sites on the minority or majority sublattice, and an accompanying gap. We also compute the transition temperature to the ordered phase as a function of the electron-phonon coupling.
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