Breakdown of Hooke's law of elasticity at the Mott critical endpoint in an organic conductor

Abstract

The Mott metal-insulator transition, a paradigm of strong electron-electron correlations, has been considered as a source of intriguing phenomena. Despite its importance for a wide range of materials, fundamental aspects of the transition, such as its universal properties, are still under debate. We report detailed measurements of relative length changes ΔL/L as a function of continuously controlled helium-gas pressure P for the organic conductor κ-(BEDT-TTF)₂Cu[N(CN)₂]Cl across the pressure-induced Mott transition. We observe strongly nonlinear variations of ΔL/L with pressure around the Mott critical endpoint, highlighting a breakdown of Hooke's law of elasticity. We assign these nonlinear strain-stress relations to an intimate, nonperturbative coupling of the critical electronic system to the lattice degrees of freedom. Our results are fully consistent with mean-field criticality, predicted for electrons in a compressible lattice with finite shear moduli. We argue that the Mott transition for all systems that are amenable to pressure tuning shows the universal properties of an isostructural solid-solid transition.

Keywords: Mott metal-insulator-transiton; Strongly correlated electron systems; coupling of electrons to lattice degrees of freedom; critical phenomena; effects of hydrostatic pressure; organic charge-transfer salts; thermal expansion; thermodynamic studies.

Fig. 1. Generic phase diagram for a pressure-tuned Mott transition and structure of κ-(BEDT-TTF)₂Cu[N(CN)₂]Cl.

(A) Generic temperature-pressure phase diagram predicted for the Mott metal-insulator transition in a real material. The red solid line represents the first-order transition line that ends in a second-order critical endpoint (open red circle). The Widom line (red dotted line) corresponds to a smooth extrapolation of the first-order line. Blue broken lines (blue-shaded area) represent the predicted crossover lines (crossover regime) that emanate from the critical endpoint (for details, see text). In a distinct region around the critical endpoint, critical elasticity with mean-field (MF) behavior is expected (yellow circle). Further away from the endpoint (light blue circle), within a radius given by the Ginzburg criterion, nontrivial critical exponents of the Mott transition prevail. Outside of this range (white area), the critical properties can be described by a mean-field theory. The pink-shaded area indicates the finite width of the first-order transition due to the presence of some disorder in real systems. (B) Structure of κ-(BEDT-TTF)₂Cu[N(CN)₂]Cl along the out-of-plane b axis. For simplicity, the hydrogen atoms are omitted. (C) View on the BEDT-TTF plane (ac plane). Circles represent one dimer consisting of two BEDT-TTF molecules. The dimers are arranged on a triangular lattice with hopping parameters t and t′ (dotted lines). a′ accounts for a small tilt of the a axis with respect to the b axis due to the inclination of the BEDT-TTF molecules.

Fig. 2. Relative length changes as a function of pressure.

Relative length changes, ΔL_i/L_i, as a function of applied pressure at constant temperatures between 30 and 55 K. Measurements have been performed along the i = a (A) and b axes (B). The data have been offset for clarity. The broken lines close to the data at 43 K, that is, distinctly above T_c ≈ 36.5 K of the critical endpoint, are guides to the eyes and serve to estimate the pressure-induced changes in the compressibilities. The strong nonlinearities, which are observed here, reflecting nonlinear strain-stress relations, highlight a breakdown of Hooke’s law of elasticity.

Fig. 3. Experimentally determined temperature-pressure phase diagram for κ-(BEDT-TTF)₂Cu[N(CN)₂]Cl.

Full (open) red squares represent the first-order transition line (Widom line). The open red circle indicates the critical endpoint. Full (open) cyan points show the position of maximum response, α_max, of the coefficient of thermal expansion, α(T) = L⁻¹dL/dT, which can be assigned to a first-order transition line (crossover line). Red- and blue-shaded areas delimited by the broken lines in the same color code indicate the experimentally determined width of the features along the b axis and can be assigned to the disorder-related (red) and the criticality-related (blue) crossover regimes, respectively. The broken lines represent, within the error margins, the full width at half maximum of the peaks in κ_i. The yellow ellipse indicates the range where critical elasticity, characterized by mean-field critical exponents, dominates.

Fig. 4. Modeling of relative length changes.

Measurements of the relative length change ΔL_b(P)/L_b at various constant temperatures around T_c ≈ 36.5 K as a function of pressure (black symbols) along the b axis, together with a fit of the mean-field solution based on Eq. 1 (red solid line; for details, see text).