Charged Particles on a Two-Dimensional Lattice Subject to Anisotropic Jahn-Teller Interactions

The properties of a system of charged particles on a 2D lattice, subject to an anisotropic Jahn-Teller-type interaction and 3D Coulomb repulsion, are investigated. In the mean-field approximation without Coulomb interaction, the system displays a phase transition of first order. When the long-range Coulomb interaction is included, Monte Carlo simulations show that the system displays very diverse mesoscopic textures, ranging from spatially disordered pairs to ordered arrays of stripes, or charged clusters, depending only on the ratio of the two interactions (and the particle density). Remarkably, charged objects with an even number of particles are more stable than with an odd number of particles. We suggest that the diverse functional behavior—including superconductivity—observed in oxides can be thought to arise from the self-organization of this type.

Figure 1

(a) The phase diagram generated by $H_{\mathrm{JT}}$ (2) with and without the Coulomb repulsion (CR). The dashed line is the MF critical temperature, while the full triangles ($▴$) represent the MC critical temperature, $t_{\mathrm{crit}}$, without CR. The open circles ($◯$) represent $t_{cl}$ without CR. The open triangles ($△$) represent $t_{cl}$ while the diagonal crosses ($\times$) represent the onset of clustering, $t_0$, in presence of CR. The cluster-ordering temperature (see text), $t_{co}$, (also including CR) is shown as crosses ($+$). The size of the symbols corresponds to the error bars. (b) Typical temperature dependencies of the nearest neighbor density correlation function $g_{\rho L}$ for $n=0.18$ in absence of CR ($●$) and in presence of CR ($▿$). Arrows indicate the characteristic temperatures.

Figure 2

(a) Snapshots of clusters ordering at $t=0.04$, $n=0.2$, and $v_l(1,0)=-1$ for different diagonal $v_l(1,1)$ (given in each figure). Grey and black dots represent particle clusters in state $S_i^z=1$ and states $S_i^z=-1$, respectively. The preference for even-particle-number clusters in certain cases is clearly observed, for example, for $v_l(1,1)=-0.2$. (b) Snapshots of the particle distribution for two densities at two different temperatures $t=0.64$ and $t=0.1$, respectively.

Figure 3

The temperature dependence of the cluster-size distribution function $x_L(j)$ (for the smallest cluster sizes) as a function of temperature at two different average densities $n=0.08$ (a) and $n=0.18$ (b). $x_L(j)$ as a function of $n$ at the temperature between $t_0$ and $t_{cl}$ (c), and near $t_{co}$ (d). The ranges of the density where pairs prevail are very clearly seen in (d). Error bars represent the standard deviation.