Effects of Umklapp Scattering on Electronic States in One Dimension

Details Effects of Umklapp Scattering on Electronic States in One Dimension Effects of Umklapp Scattering on Electronic States in One Dimension

1997-04-07

arxiv.org/abs/cond-mat/9704049v4

J. Phys. Soc. Jpn. 66 (1997) 2399

Physics

Condensed Matter

Strongly Correlated Electrons

22 pages, LaTeX, 17 figures included, uses jpsj.sty

Scientific paper

10.1143/JPSJ.66.2399

The effects of Umklapp scattering on electronic states are studied in one spatial dimension at absolute zero. The model is basically the Hubbard model, where parameters characterizing the normal ($U$) and Umklapp ($V$) scattering are treated independently. The density of states is calculated in the t-matrix approximation by taking only the forward and Umklapp scattering into account. It is found that the Umklapp scattering causes the global splitting of the density of states. In the presence of sufficiently strong Umklapp scattering, a pole in the t-matrix appears in the upper half plane, signalling an instability towards the '$G/2-$pairing' ordered state ($G$ is the reciprocal lattice vector), whose consequences are studied in the mean field approximation. It turns out that this ordered state coexists with spin-density-wave state and also brings about Cooper-pairs. A phase diagram is determined in the plane of $V$ and electron filling $n$.

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