Excitonic condensation of strongly correlated electrons: The case of ${\mathrm{Pr}}_{0.5}{\mathrm{Ca}}_{0.5}{\mathrm{CoO}}_3$

We use a combination of dynamical mean-field model calculations and LDA + U material specific calculations to investigate the low temperature phase transition in the compounds from the $\left({\mathrm{Pr}}_{1-y}R{}_y\right){}_x{\mathrm{Ca}}_{1-x}{\mathrm{CoO}}_3$ $\left(R=\text{Nd,}\text{Sm,}\text{Eu,}\text{Gd,}\text{Tb,}\text{Y}\right)$ family (PCCO). The transition, marked by a sharp peak in the specific heat, leads to an exponential increase of dc resistivity and a drop of the magnetic susceptibility, but no order parameter has been identified yet. We show that condensation of spin-triplet, atomic-size excitons provides a consistent explanation of the observed physics. In particular, it explains the exchange splitting on the Pr sites and the simultaneous Pr valence transition. The excitonic condensation in PCCO is an example of a general behavior expected in certain systems in the proximity of a spin-state transition.

Figure 1

The DMFT results for fixed particle density $n=2$. (a) The magnitude of the order parameter $\left|\varphi \right(T\left)\right|$. The inset shows specific heat $C\left(T\right)$. (b), (c) The spectral functions $A_{aa}\left(\omega \right)$ and $A_{bb}\left(\omega \right)$, respectively, at $T=1160,968,921,892,829,725,580,290$ K. (blue curves for $T<T_c$, the red ones for $T>T_c)$. The arrow marks the direction of increasing temperature. (e) The corresponding optical conductivity. The inset shows the dc resistivity. (d) The spin susceptibility ${\chi }_S\left(T\right)$ (circles with error bars) and ${\chi }_S\left(T\right)$ of the constrained normal phase solutions (dotted line).

Figure 2

(a) The magnitude of the order parameter $\left|\varphi \right(T\left)\right|$ for various fixed chemical potentials (The $\left|\varphi \right(T\left)\right|$ for $n=2$ taken from Fig. 1 is marked by black circles). (b) The corresponding particle densities $n$ as functions of temperature. The curves correspond to the doping of 0.03 (red), 0.06 (green), 0.09 (blue), and 0.12 (violet) holes per atom in the normal phase. (c) The susceptibility ${\chi }_S\left(T\right)$ for the 0.12 hole doping. The symbols have the same meaning as in Fig. 1.

Figure 3

The distribution of the collinear spin density (red and blue correspond to positive and negative signs respectively) around Co atoms in PCCO with O (blue), Ca (light blue), and Pr (gray).

Figure 4

The spectrum of the Pr $4f$ states: no EC order (black), the self-consistent LDA + U solution with the ${\sigma }_h$-odd order parameter (red), and with an artificial order parameter of the same magnitude containing a ${\sigma }_h$-even contribution (green). The inset shows the exchange splitting of the $4f$ levels for the same order parameters when spin-orbit coupling is not included.