Charge order in Kondo lattice systems

Charge order is a commonly observed phenomenon in strongly correlated materials. However, most theories are based on a repulsive intersite Coulomb interaction in order to explain charge order. Here we show that only due to local interactions, charge order is favorable in heavy fermion systems at quarter filling. The driving force is the Kondo effect, which leads to a nonlinear dependence on the filling of the lattice site for the energy gain. We use dynamical mean field theory combined with numerical renormalization group to demonstrate the existence of charge order at quarter filling for a Kondo lattice model.

Figure 1

Charge order parameter for a paramagnetic state at quarter filling for different temperatures and coupling strengths $J$. Lines are a guide for the eye.

Figure 2

Magnitude of the charge order parameter for different temperatures and coupling strengths.

Figure 3

Upper panels: Transition temperature over chemical potential for the CDW exactly at quarter filling. This plot illustrates the shrinking area of chemical potentials with increasing coupling strength, which stabilize the CDW at quarter filling. ${\mu }_c$ is the chemical potential at the center of the CDW phase at quarter filling. Lower panel: Charge order parameter for different interaction strengths.

Figure 4

Kinetic energy and $J\langle \vec{S}·\vec{s}\rangle$ (coupling energy between localized spin and conduction electrons) for two different interaction values $J/W$. By introducing a staggered potential for the sublattices A and B, we artificially create a metastable solution with different occupation numbers $n_A$ and $n_B$. For all solutions the system is kept at quarter filling.

Figure 5

Spectral function of the charge ordered state for A and B sublattices for two different coupling strengths. The Fermi energy corresponds to $\omega =0$.

Figure 6

Spin polarization (left panel) and charge order parameter (middle panel) calculated from approximately 300 data points for $J/W=0.35$, simultaneously allowing for charge and magnetic order in a two-site cluster. From these data the qualitative phase diagram (right panel) is drawn. The phase diagram comprises a pure ferromagnetic state at low temperatures, a transition region where charge and spin order can be found, a pure charge ordered state at intermediate temperatures, and a paramagnetic disordered state at high temperatures.