Breakup of the Fermi Surface Near the Mott Transition in Low-Dimensional Systems

We investigate the Mott transition in weakly coupled one-dimensional (1D) fermionic chains. Using a generalization of dynamical mean field theory, we show that the Mott gap is suppressed at some critical hopping $t_{\perp }^{c2}$. The transition from the 1D insulator to a 2D metal proceeds through an intermediate phase where the Fermi surface is broken into electron and hole pockets. The quasiparticle spectral weight is strongly anisotropic along the Fermi surface, both in the intermediate and metallic phases. We argue that such pockets would look like “arcs” in photoemission experiments.

Figure 1

Left panels: Self-energy on the imaginary-frequency axis for $k$ between 0 and $\pi /2$ at $V=4$, $t_{\perp }=0.5$, and $T=0.04$. The dots show the numerical data and the lines are guides to the eye. The number of imaginary-time slices was $L=60$. Right panels: Fit of the numerical data to a trial self-energy (see text). All energies are in units of $t$.

Figure 2

(a)–(c) Real part of the ch-DMFT self-energy as a function of $k$ at the lowest Matsubara frequency for $V=2.5$, $T=0.1$, and increasing $t_{\perp }$ (red points). The red and blue lines show the fit of the data to the function ${\Sigma }_{\Delta }+{\Sigma }_{\mathrm{int}}$ at $\omega =i{\omega }_0$, $T=0.1$, and at $\omega =i{0}^{+}$, $T=0$, respectively. The shaded areas show the domain covered by the free dispersion ${\xi }_k-2t_{\perp }\cos (k_{\perp })$ in Eq. (4). The Fermi surfaces corresponding to (b) and (c) are shown in (b′) and (c′). The dotted lines indicate the noninteracting Fermi surfaces, and the $+$ and $-$ show the sign of $\mathrm{Re}G(\mathit{k},0)$.

Figure 3

(a) Evolution of the quasiparticle residue $Z$ along the Fermi surface for different interchain couplings $t_{\perp }$. When FS pockets are present there are two values of $Z$ for each $k_{\perp }$, the lowest value corresponding to the region of the pocket closest to $k=\pi /2$. (b) Parameters of the model self-energy determined from fits to the ch-DMFT numerical data.

Figure 4

Comparison of the zero-energy spectral function $A(\mathit{k},0)$ at $T=0$ with the expected ARPES intensity $I(\mathit{k})$ calculated assuming a $k$-space resolution of $0.04\pi$, an energy resolution $0.004t$, and an energy integration window $\delta E=0.01t$. The self-energy parameters are taken from Fig. 3b for $t_{\perp }=0.42$ (a) and $t_{\perp }=0.46$ (b).