Signatures of the Fermi surface reconstruction of a doped Mott insulator in a slab geometry

TL;DR

This work demonstrates that hole-doped Mott insulators in a slab geometry exhibit a layer-dependent Fermi surface reconstruction driven by surface-enhanced correlations, with outer layers hosting hole-like pockets and inner layers developing electron-like surfaces. It introduces a real-space diagnostic S(T) and analyzes Friedel oscillations to identify FS topology changes without momentum-space periodization, revealing a Lifshitz-type transition that can occur within a single slab. The study shows that pseudogap behavior correlates with hole-like FS on a layer and that the self-energy indicates a coexistence of Fermi-liquid and non-Fermi-liquid characteristics across layers. Altogether, these findings provide practical tools for detecting FS topology changes and offer insights into surface-sensitive spectroscopic signatures in doped Mott systems.

Abstract

We investigate a hole-doped Mott insulator in a slab geometry using the dynamical cluster approximation. We show that the enhancement of the correlation strength at the surface results in the remarkable evolution of the layer-projected Fermi surface, which exhibits hole-like pockets in the superficial layers, but gradually evolves into a single electron-like surface in the innermost layers. We further analyze the behavior of the Friedel oscillations induced by the surface and identify distinct signatures of the Fermi surface reconstruction as function of hole-doping. In addition, we introduce a computationally tractable quantity that diagnoses the same Fermi surface variation by the concurrent breakdown of Luttinger's theorem. Both the latter quantity and the Friedel oscillations serve as reliable indicators of the change in Fermi surface topology, without the need for any periodization in momentum space.

Figures (16)

• Figure 1: Sketch of the slab geometry for N layers, which are stacked along $\mathbf{x}$ axis. The intra-layer sites are identified by the $\mathbf{R}$ vector coordinates.
• Figure 2: Left panel: sketch of the renormalized dispersion $r(\mathbf{k})={\epsilon}(\mathbf{k})-\mu+\text{Re} \Sigma(0,\mathbf{k})$ in the upper right quarter of the Brillouin zone for the scenario proposed by Ref. PhysRevB.74.125110 in the case of an hole-like Fermi surface with Fermi pockets. The red (lightblue) color indicates $r(\mathbf{k})>0$ ($r(\mathbf{k})<0$). The blue solid line represents the Fermi surface, while the dashed green line indicates the Luttinger surface. Right Panel: same as left panel but for an electron-like Fermi surface that satisfies Luttinger theorem.
• Figure 3: Left panel: Layer-dependent real part of the Green's function in patch $\mathbf{X}$ at the first Matsubara frequency for different $\Delta \mu=\mu-U/2$. The black dot-dashed line indicates the value at which the Fermi surface changes topology. We note that Fermi surfaces with different topology can coexist within the same slab. Right panel: Layer-dependent density profile upon changing $\Delta \mu$ as in the left panel. The horizontal lines represent the densities $n^*_{\ell}$ at which the Lifshitz transition occurs for the first 3 layers.
• Figure 4: Layer dependent renormalized dispersion (\ref{['rk-layer']}). The black line indicates the value of the Lifshitz transition. Although it is a fundamentally different quantity from $\text{Re} G(i \omega_0,\mathbf{X},\ell)$, $r(\mathbf{X},\ell)$ almost always gives the same prediction for the Fermi surface character.
• Figure 5: Layer dependence of $S(T)$ in (\ref{['ST']}) for different values of $\Delta\mu$.