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Phase evolution of the two-dimensional Kondo lattice model near half-filling

Within a mean-field approximation, the ground state and finite temperature phase diagrams of the two-dimensional Kondo lattice model have been carefully studied as functions of the Kondo coupling $J$ and the conduction electron concentration $n_{c}$. In addition to the conventional hybridization between local moments and itinerant electrons, a staggered hybridization is proposed to characterize the interplay between the antiferromagnetism and the Kondo screening effect. As a result, a heavy fermion antiferromagnetic phase is obtained and separated from the pure antiferromagnetic ordered phase by a first-order Lifshitz phase transition, while a continuous phase transition exists between the heavy fermion antiferromagnetic phase and the Kondo paramagnetic phase. We have developed a efficient theory to calculate these phase boundaries. As $n_{c}$ decreases from the half-filling, the region of the heavy fermion antiferromagnetic phase shrinks and finally disappears at a critical point $n_{c}^{*}=0.8228$, leaving a first-order critical line between the pure antiferromagnetic phase and the Kondo paramagnetic phase for $n_{c}<n_{c}^{* }$. At half-filling limit, a finite temperature phase diagram is also determined on the Kondo coupling and temperature ($J$-$T$) plane. Notably, as the temperature is increased, the region of the heavy fermion antiferromagnetic phase is reduced continuously, and finally converges to a single point, together with the pure antiferromagnetic phase and the Kondo paramagnetic phase. The phase diagrams with such triple point may account for the observed phase transitions in related heavy fermion materials.