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Springer series in solid-state sciences

Instability of a 2-Dimensional Landau-Fermi Liquid Due to Umklapp Scattering

Nobuo Furukawa, Thomas Maurice Rice

Published Jan 1, 1999• 0 citations
Publisher
DOI
10.1007/978-3-642-60041-8_21

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We study the renormalization-group (RG) flow of interactions in the two-dimensional ${t\ensuremath{-}t}^{\ensuremath{'}}$ Hubbard model near half-filling in an N-patch representation of the whole Fermi surface. Starting from weak to intermediate couplings the flows are to strong coupling, with different characters depending on the choice of parameters. In a large parameter region elastic umklapp scatterings drive an instability which on parts of the Fermi surface exhibits the key signatures of an insulating spin liquid (ISL), as proposed by Furukawa, Rice, and Salmhofer [Phys. Rev. Lett. 81, 3195 (1998)] rather than a conventional symmetry-broken state. The ISL is characterized by both strong d-wave pairing and antiferromagnetic correlations; however, it is insulating due to the vanishing local charge compressibility and a spin liquid because of the spin gap arising from the pairing correlations. We find that the unusual RG flow, which we interpret in terms of an ISL, is a consequence of a Fermi surface close to the saddle points at the Brillouin-zone boundaries which provides an intrinsic and mutually reinforcing coupling between pairing and umklapp channels.
We examine a two-dimensional Fermi liquid with a Fermi surface which touches the Umklapp surface first at the four points as the electron density is increased. Umklapp processes at the four patches near lead the renormalization group equations to scale to strong coupling, resembling the behaviour of a two-leg ladder at half-filling. The incompressible character of the fixed point causes a breakdown of Landau theory at these patches. A further increase in density spreads the incompressible regions so that the open Fermi surface shrinks to four disconnected segments. This non-Landau state, in which parts of the Fermi surface are truncated to form an insulating spin liquid, has many features in common with phenomenological models recently proposed for the cuprate superconductors.