Explanation of the phase diagram ofβ-di[bis(ethylenedithio)tetrathiafulvalene]triiodide based on the two configurations of the organic molecule

The organic superconductor β-di[bis(ethylenedithio)tetrathiafulvalene]triiodide, β-(BEDT-TTF${)}_2$ ${\mathrm{I}}_3$, shows an unusual phase diagram in temperature (T) and pressure (P) with large metastability domains for the stabilization of an incommensurate modulation. This behavior is related to the T-P cycling around a tricritical point. The superconducting properties are drastically affected by the nature of the structural ground state. In this paper, we present a simple microscopic mean-field model that satisfactorily explains the experimental phase diagram of β-(BEDT-TTF${)}_2$ ${\mathrm{I}}_3$. This model takes explicitly into account the two nonsymmetrical configurations of one of the two ethylene groups of the BEDT-TTF molecule, under the form of pseudospins linearly coupled to the vibrational degrees of freedom involved in the structural modulation. The calculations are performed as a function of the reduced interaction v=V/$k_B$ $T_c$, where V is half the energy difference between the two ethylene group configurations and $k_B$ $T_c$ is the coupling energy between the vibrational degrees of freedom. The antiferrodistortive (commensurate) case is first treated; then the incommensurate case is solved. The phase diagram obtained as a function of v exhibits a tricritical point and large metastability domains. The experimental phase diagram is well accounted for by assuming a linear temperature and pressure dependence of V in the vicinity of the tricritical point. The origin of the incommensurate modulation of β-(BEDT-TTF${)}_2$ ${\mathrm{I}}_3$ is briefly discussed.