Pseudogap in Doped Mott Insulators is the Near-Neighbor Analogue of the Mott Gap

We show that the strong-coupling physics inherent to the insulating Mott state in 2D leads to a jump in the chemical potential upon doping and the emergence of a pseudogap in the single-particle spectrum below a characteristic temperature. The pseudogap arises because any singly occupied site not immediately neighboring a hole experiences a maximum energy barrier for transport equal to $t^2/U$, $t$ the nearest-neighbor hopping integral and $U$ the on-site repulsion. The resultant pseudogap cannot vanish before each lattice site, on average, has at least one hole as a near neighbor. The ubiquity of this effect in all doped Mott insulators suggests that the pseudogap in the cuprates has a simple origin.

Figure 1

Doping dependence of the chemical potential in the 2D Hubbard model computed using the local cluster approach for $T=0.15t$ (dashed line) and $T=0.07t$ (solid line). The inset on the left shows the imaginary part of the self-energy evaluated at a Fermi momentum ($0.3,2.10$) for $n=0.97$, ($0.3,1.84$) for $n=0.8$, and ($0.3,1.06$) for $n=0.3$, whereas the inset on the right contains the density of states for $n=0.95$ for $U=4t$, $U=8t$, and $U=12t$.

Figure 2

Electron spectral function for $U=8t$, $T=0.07t$, and $n=0.97$ and $0.60$ along a path in the first Brillouin zone from top to bottom: $(k_x,k_y)=(0,0)\to (\pi ,\pi )\to (\pi ,0)\to (0,0)$.

Figure 3

Density of single particle states for $T=0.25t$ and $T=0.07t$, $U=8t$ for the fillings shown. No pseudogap exists at high temperature. At low $T$, a pseudogap emerges and remains pinned at the Fermi level but moves above at an intermediate doping level. In the overdoped regime, the pseudogap vanishes entirely and a noninteracting system is recovered.

Figure 4

High ($W_H$) and low ($W_L$) spectral weight as a function of filling. $W_{\mathrm{N}\mathrm{I}}$ is the spectral weight in the noninteracting system.