Evolution of the Fermi Surface across a Magnetic Order-Disorder Transition in the Two-Dimensional Kondo Lattice Model: A Dynamical Cluster Approach

We use the dynamical cluster approximation, with a quantum Monte Carlo cluster solver on clusters of up to 16 orbitals, to investigate the evolution of the Fermi surface across the magnetic order-disorder transition in the two-dimensional doped Kondo lattice model. In the paramagnetic phase, we observe the generic hybridized heavy-fermion band structure with large Luttinger volume. In the antiferromagnetic phase, the heavy-fermion band drops below the Fermi surface giving way to hole pockets centered around $\mathbf{k}=(\pi /2,\pi /2)$ and equivalent points. In this phase Kondo screening does not break down, but the topology of the resulting Fermi surface is that of a spin-density wave approximation in which the localized spins are frozen.

Figure 1

(a) Definition of the real space basis vectors, unit cell and orbital indices. (b) The reduced Brillouin zone and $k$-space patching for a cluster with $N_c^{\mathrm{AFM}}=4$.

Figure 2

Comparison of the single-particle spectral function of the KLM at half-filling ($t^{\prime }/t=0$ and $⟨n_c⟩=1$) and with coupling $J/t=1.2$ from (left) $12\times 12$-lattice QMC results as obtained with the projective auxiliary field algorithm of Ref. 12 and (right) DCA results with cluster size $N_c^{\mathrm{AFM}}=1$ and $\beta t=40.0$.

Figure 3

Bottom: Magnetic phase diagram of the hole-doped KLM showing simulation results for the staggered magnetization $m_z^f$ (color-coded circles) as a function of coupling $J/t$ and conduction electron occupancy $⟨n_c⟩$. Shading of AFM and PM regions is a guide to the eye. Here $t^{\prime }/t=-0.3$ and the calculations are carried out with the $N_c^{\mathrm{AFM}}=1$ cluster. Top: $m_z^f$ as a function of $⟨n_c⟩$ at constant coupling $J/t=1$.

Figure 4

Top: DCA single-particle spectrum for simulation A (see Fig. 3) in the PM region ($J/t=1.0$, $⟨n_c⟩=0.855$ and $\beta t=40.0$). The bottom right plot is a close-up of the main plot for energies around the Fermi energy along the path (0,0) to $(\pi ,\pi )$. The bottom left plot shows the resultant Fermi surface, plotted here via a large-$N$ mean-field modeling of the DCA data (see text).

Figure 5

Top: DCA result for the single-particle spectrum with $N_c^{\mathrm{AFM}}=4$, $J/t=1.0$, $⟨n_c⟩=0.977$ and $\beta t=40.0$ in the AFM region (point B in Fig. 3). The bottom right plot is a close-up of the main plot for energies around the Fermi energy along the path (0,0) to $(\pi ,\pi )$. The bottom left plot shows the resultant Fermi surface plotted here by fitting to the DCA spectrum using the mean-field form of Eq. (2).