Disorder unveils Mott quantum criticality behind a first-order transition in the quasi-two-dimensional organic conductor $\kappa \text{−}\left(\text{ET}\right){}_2\text{Cu}\left[\text{N}\right(\text{CN}{)}_2]\text{Cl}$

We show the significant impact of weak disorder on the Mott transition by investigating electronic transport in a systematically x-ray-irradiated layered organic conductor under continuous pressure control. The critical end point of the first-order Mott transition is dramatically suppressed by such weak disorder that causes only a minor reduction in the transition temperature of disorder-sensitive nodal superconductivity. Instead, quantum critical scaling of resistance holds at lower temperatures and Fermi-liquid coherence temperature on the metallic side is lowered. Introducing disorder unveils the interaction-induced quantum criticality hidden behind the first-order transition.

Figure 1

(a)–(c) Resistance in the $P\text{−}T$ planes. The range of color indicates the compressibility of the conductance $\left|\right(1/G)\partial G/\partial P|$, and the open circles represent the crossover points corresponding to maxima in $\left|\right(1/G)\partial G/\partial P|$. The solid star corresponds to $T_{\mathrm{ep}}$. (d)–(f) Phase diagrams. “Ins.,” “Fermi Liq.,” and “SC” represent insulator, Fermi liquid, and superconductivity, respectively. The solid and open circles represent points at which major resistance jumps (first-order transitions) and the crossover points appear, respectively. The solid triangles and crosses are the superconducting transition temperatures $T_{\mathrm{SC}}$ and the coherence temperatures $T^{*}$, respectively (see also the Supplemental Material [22]). We took the set of $T^{*}$ for $t_{\mathrm{irr}}=0$ h from Ref. [16].

Figure 2

(a)–(c) Pressure dependence of $\left|\right(1/G)\partial G/\partial P|$ at fixed temperatures. The curve at 15.3 K in (c) was determined under a perpendicular magnetic field of 9 T, which was applied to suppress the possible superconducting fluctuations (see also the Supplemental Material [22]). (d) Temperature dependence of the inverse of the peak value in $\left|\right(1/G)\partial G/\partial P|$. The solid lines are guides for the eye. The dashed lines and thick arrows indicate $T_{\mathrm{ep}}$ and $T_{\mathrm{ep}}^{*}$, respectively, for each irradiation time.

Figure 3

(a)–(d) Temperature dependence of the resistance. The arrows indicate $T^{*}$. (e) Residual resistance $R_0$ and coefficient $A$ against the irradiation time. The values of $R_0$ and $A$ plotted here are those at $P-P_{\mathrm{c}}\sim 20$ MPa (see also the Supplemental Material [22]). (f) Plot of $T_{\mathrm{SC}}$ versus $R_0$ at $P-P_{\mathrm{c}}\sim 20$ MPa.

Figure 4

(a)–(c) Quantum critical scaling of renormalized resistance $R/R_{\mathrm{c}}$. (d)–(f) Plots of ${log}_{10}\left|{log}_{10}(R/R_{\mathrm{c}})\right|$ versus $T/T_0$. Top and bottom panels show insulating and metallic branches, respectively. Solid lines represent the quantum critical behavior $R/R_{\mathrm{c}}=exp[\pm {(T/T_0)}^{-1/z\nu }]$. (g)–(i) Color plots of $|{log}_{10}(R/R_{\mathrm{c}})|$ in the $\delta P\text{−}T$ plane. The thick gray lines and black curves represent the first-order transition lines and $T_0$, respectively. The point of $(\delta P,T)=(0,0)$, the origin of the $T_0$ curve (indicated by a dashed curve), is a hypothetical quantum critical point.