Influence of magnetism and correlation on the spectral properties of doped Mott insulators

Unraveling the nature of the doping-induced transition between a Mott insulator and a weakly correlated metal is crucial to understanding novel emergent phases in strongly correlated materials. For this purpose, we study the evolution of spectral properties upon doping Mott insulating states by utilizing the cluster perturbation theory on the Hubbard and $t–J$-like models. Specifically, a quasifree dispersion crossing the Fermi level develops with small doping, and it eventually evolves into the most dominant feature at high doping levels. Although this dispersion is related to the free-electron hopping, our study shows that this spectral feature is, in fact, influenced inherently by both electron-electron correlation and spin-exchange interaction: the correlation destroys coherence, while the coupling between spin and mobile charge restores it in the photoemission spectrum. Due to the persistent impact of correlations and spin physics, the onset of gaps or the high-energy anomaly in the spectral functions can be expected in doped Mott insulators.

Figure 1

Spectral function $A(\mathbf{k},\omega )$ of the Hubbard model calculated by cluster perturbation theory (CPT) on a $4\times 4$ square lattice at (a) half filling and (b) 37.5% hole doping. The spectral features at half filling are dominated by the spin physics, including the spin-polaron and three-site term dispersions. The 37.5% doped system shows a cosinelike quasifree dispersion (the dashed gray line) described by a 2D nearest-neighbor tight-binding model with renormalized hopping $t^{*}=0.66t$. The calculations adopt an on-site Hubbard interaction $U=8t$ and a Lorentzian broadening $\mathrm{\Gamma }=0.15t$. The horizontal dashed lines denote the Fermi level. The insets sketch the density of states for a Mott insulator and a metal.

Figure 2

Spectral function $A(\mathbf{k},\omega )$ calculated by CPT at 12.5% (left), 25% (middle), and 37.5% (right) hole doping for (a1)–(a3) the Hubbard model, (b1)–(b3) the $t–J$ model, and (c1)–(c3) the normalized $t–J–3s$ model. Spin exchange $J=4t^2/U=0.5t$ is adopted for the $t–J$ and $t–J–3s$ models. The horizontal dashed lines denote the Fermi level $E_F$.

Figure 3

Spectral function $A(\mathbf{k},\omega )$ calculated by CPT for the $t–J$ model at 12.5% (left), 25% (middle), and 37.5% (right) hole dopings with (a1)–(a3) $J=0t$, (b1)–(b3) $J=0.1t$, and (c1)–(c3) $J=t$. The dashed curves show the 2D nearest-neighbor tight-binding dispersions with a renormalized hopping $t^{*}=g_{t}t$, where $g_t$ is the doping-dependent Gutzwiller factor in the Gutzwiller mean-field approximation [72]. The horizontal dashed lines denote the Fermi level.

Figure 4

Cartoons illustrating the motion of a photodoped hole in the $t–J$ model with $J=0$ and a finite density of holes in the ground state: (a) the coherent motion of a photodoped hole allowed due to the existence of ferromagnetic clusters in the ground state $|G\rangle$ of a hole-doped $t–J$ model, (b) the coherent motion of a photodoped hole allowed due to the existence of empty sites in the ground state $|G\rangle$ of a hole-doped $t–J$ model, and (c) incoherent motion of a photodoped hole along the retraceable paths (here of one lattice spacing). The photoemission spectrum is related to the imaginary part of the Green's function $\langle {\phi }_3|{\phi }_1\rangle$. For simplicity, the cartoons show only hole motion along a 1D path in a 2D lattice.

Figure 5

Energy-dependent cuts of the $t–J$ model spectral functions at the 12.5% doping level and for three distinct values of spin exchange $J$ at four distinct momenta $\mathbf{k}$: (a) $\mathrm{\Gamma }$, (b) $M$, (c) $X$, and (d) $Q$. The insets show the variance $\sigma \left(\mathbf{k}\right)$ of the most intensive peak at each momentum calculated as a function of $J$ with $\mathrm{\Delta }\omega =4t$. The shaded blue curves denote the canonical $J=0.5$ scenario.

Figure 6

Spectral function $A(\mathbf{k},\omega )$ calculated by CPT for the $t–J^z$ model (i.e., the $t–J$ model without quantum spin fluctuations) with $J^z=0.5t$ at 12.5% hole doping. The horizontal dashed line denotes the Fermi level.

Figure 7

Cartoons illustrating another channel for the coherent motion of a photodoped hole in the $t–J$ model with a finite density of holes in the ground state. This channel contributes only when $J\ne 0$. The hole can move coherently as the spin-exchange process $\propto J$ may repair the “defects” made by the hole motion, so that a “kinetically relaxed spin polaron” can form. The photoemission spectrum is related to the imaginary part of the Green's function $\langle {\phi }_3|{\phi }_1\rangle$. For simplicity, the cartoons show only hole motion along a 1D path in a 2D lattice.