Ladder physics in the spin fermion model

A link is established between the spin fermion (SF) model of the cuprates and the approach based on the analogy between the physics of doped Mott insulators in two dimensions and the physics of fermionic ladders. This enables one to use nonperturbative results derived for fermionic ladders to move beyond the large-$N$ approximation in the SF model. It is shown that the paramagnon exchange postulated in the SF model has exactly the right form to facilitate the emergence of the fully gapped $d$-Mott state in the region of the Brillouin zone at the hot spots of the Fermi surface. Hence, the SF model provides an adequate description of the pseudogap.

Figure 1

A sketch of a part of the Fermi surface with four hot spots. The dashed curves correspond to the Fermi surface of noninteracting electrons. It is energetically advantageous for the interactions to deform the Fermi surface by making it flat at the hot spots to facilitate nesting of the opposite parts of the FS (drawn by the solid lines). The right (left) moving fermions are located near the flat portions of the Fermi surface and are marked by $R_1,R_{-1}$ ($L_1,L_{-1}$). Hot spots with the same number are connected by the wave vector $(\pi ,\pi )$. The ones connected by $(\pi ,-\pi )$ are not shown. The line with an arrow corresponds to the coordinate axis of $x$.