Quantum Phases of the Shastry-Sutherland Kondo Lattice: Implications for the Global Phase Diagram of Heavy-Fermion Metals

Considerable recent theoretical and experimental effort has been devoted to the study of quantum criticality and novel phases of antiferromagnetic heavy-fermion metals. In particular, quantum phase transitions have been discovered in heavy-fermion compounds with geometrical frustration. These developments have motivated us to study the competition between the Ruderman-Kittel-Kasuya-Yosida and Kondo interactions on the Shastry-Sutherland lattice. We determine the zero-temperature phase diagram as a function of magnetic frustration and Kondo coupling within a slave-fermion approach. Pertinent phases include the valence bond solid and heavy Fermi liquid. In the presence of antiferromagnetic order, our zero-temperature phase diagram is remarkably similar to the global phase diagram proposed earlier based on general grounds. We discuss the implications of our results for the experiments on ${\mathrm{Yb}}_2{\mathrm{Pt}}_2\mathrm{Pb}$ and related compounds.

Figure 1

(a) Proposed global phase diagram of heavy-fermion metals. Here, ${\mathrm{AF}}_s$ and ${\mathrm{AF}}_L$ refer to antiferromagnetic states without or with static Kondo screening. $P_L$ is the paramagnetic heavy Fermi liquid, and $P_S$ refers to a paramagnetic phase without static Kondo screening. Adapted with permission from Ref. [7], Fig. 2, copyright © 2010, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim. We have sketched the proposed trajectory of ${\mathrm{Yb}}_2{\mathrm{Pt}}_2\mathrm{Pb}$ under magnetic field tuning. (b) Shastry-Sutherland lattice, denoting the Heisenberg exchange couplings $J_1$ on all the horizontal and vertical bonds, and $J_2$ along the diagonals. The unit cell is the dashed square, containing four sites $A$, $B$, $C$, $D$. (c) The bond singlet parameters.

Figure 2

Large-$N$ phase diagram as a function of frustration ($J_2/J_1$) and Kondo coupling ($J_K/t_1$), for a metallic filling $n_c=0.5$. The phases are described in the main text. The solid lines represent first-order transitions, and the dashed lines surrounding the grey area locate the boundaries of the intermediate phases that exhibit partial Kondo screening (PKS).

Figure 3

(a) The bond and Kondo singlet parameters at a fixed ratio $J_2/J_1=2.0$ as a function of $J_K$, displaying a first order transition from the SSL-VBS to the HFL phase. We show the three dimensionless independent quantities for the solution that breaks no lattice translational symmetry. Band structure along high symmetry directions in the reduced Brillouin zone in the SSL-VBS phase with $J_K=0$ and $J_2/J_1=2.0$ (b) and in the HFL phase with $J_K=2.1t_1$ and $J_2/J_1=2.0$ (c). The thick blue lines are the gapped spinon dispersion in the SSL-VBS phase.

Figure 4

Phase diagram of the Shastry-Sutherland Kondo lattice incorporating magnetic order for a metallic filling $n_c=0.5$. Thin (thick) lines represent first order (continuous [38]) transitions.