Non-Fermi-liquid behavior and doping asymmetry in an organic Mott insulator interface

High-$T_{\mathrm{C}}$ superconductors show anomalous transport properties in their normal states, such as the bad-metal and pseudogap behaviors. To discuss their origins, it is important to speculate whether these behaviors are material-dependent or universal phenomena in the proximity of the Mott transition by investigating similar but different material systems. An organic Mott transistor is suitable for this purpose owing to the adjacency between the two-dimensional Mott insulating and superconducting states, simple electronic properties, and high doping/bandwidth tunability in the same sample. Here we report the temperature dependence of the transport properties under electron and hole doping in an organic Mott electric-double-layer transistor. At high temperatures, the bad-metal behavior widely appears except at half filling, regardless of the doping polarity. At lower temperatures, the pseudogap behavior is observed only under hole doping, while the Fermi-liquid-like behavior is observed under electron doping. The bad-metal behavior seems a universal high-energy-scale phenomenon, while the pseudogap behavior is based on lower-energy-scale physics that can be influenced by details of the band structure.

Figure 1

Unit cells, Brillouin zones, band structure, and single-particle spectral function of $\kappa$-Cl. Note that the calculations are based on the one-band model. However, the band structure and spectral functions are shown in the two-site Brillouin zone [blue shaded area in (b)] because the adjacent BEDT-TTF dimers are not completely equivalent in the material. Accordingly, the $X, Z$, and $M$ points in (c) and (d) correspond to the points ($\pi /2, -\pi /2$), ($\pi /2, \pi /2$), and ($\pi$, 0) in the Brillouin zone of the one-site unit cell. (a) Schematic of the anisotropic triangular lattice of $\kappa$-Cl. The translational vectors ${\mathbf{e}}_{\mathbf{1}}$ and ${\mathbf{e}}_{\mathbf{2}}$ ($\mathbf{a}$ and $\mathbf{c}$) are represented by the red (blue) arrows. The red (blue) shaded region represents the unit cell containing one site (two sites). The ellipses on the sites denote the conducting BEDT-TTF dimers. (b) The momentum space for the anisotropic triangular lattice. The Brillouin zones of the one- (two-) site unit cell are represented by the red (blue) shaded region bounded by the red solid (blue dashed) lines. (c) Noninteracting tight-binding band structure along highly symmetric momenta and density of states (DOS) of $\kappa$-Cl ($t^{\prime }/t=-0.44$ with $t=65\mathrm{meV}$). The Fermi level for half filling is set to zero and denoted by dashed lines. (d) Single-particle spectral functions and DOS of $\kappa$-Cl at half filling in an antiferromagnetic state at zero temperature, calculated by variational cluster approximation [9]. The Fermi level is denoted by dashed lines at zero energy. The momentum path along $\mathrm{\Gamma }-Z-M-X-\mathrm{\Gamma }-M$ used in (c) and (d) is indicated by arrows in (b).

Figure 2

Hall measurements in sample 2. (a) Temperature dependence of $R_{\mathrm{Hs}}$. The dashed line indicates $1/e{n}_{\mathrm{HF}}$, where $n_{\mathrm{HF}}$ is the hole density per unit cell at the charge neutrality point. (b) Same as (a), but for $R_{\mathrm{Hs}}$ vs $1/T$ plots. (c) CPT calculations of the Fermi surface for 17% hole doping at 0 K (left) and 100 K (right). (d) Hall angle at 1 T vs $T^2$ plots.

Figure 3

Temperature $T$ dependence of surface resistivity ${\rho }_{\mathrm{s}}$ along the $a$ axis in sample 1 under (a) electron doping and (b) hole doping. (c) ${\rho }_{\mathrm{s}}$ vs $T^2$ plots below 20 K for $V_{\mathrm{G}}=+0.5, +0.55$, and $+0.6$ V. The orange solid lines denote ${\rho }_{\mathrm{s}}\propto T^2$ lines. (d) Log-log plots of ${\rho }_{\mathrm{s}}-{\rho }_0$ vs $T$ for $V_{\mathrm{G}}=+0.5$ and $+0.6$ V. The plot for $-0.6$ V is also shown as a reference, where ${\rho }_0$ at $+0.6$ V is assumed. (e) Color plots of surface resistivity under electron doping. The original data (52 temperature cycles at different $V_{\mathrm{G}}$ values) are shown in Fig. S3 in the Supplemental Material [13]. The orange solid line indicates the contour line ${\rho }_{\mathrm{MIR}}$. The right panel shows the results of DMFT calculations in Ref. [20], where the temperature is normalized by $T_{\mathrm{MIR}}$, the temperature at which the resistivity reaches ${\rho }_{\mathrm{MIR}}$ for $\delta =20\%$.

Figure 4

Temperature dependence of in-plane anisotropy of surface resistivity in sample 1 (note that both $a$ and $c$ axes are parallel to the conducting plane in this material). The black dots denote the data points in both panels. The left panel shows the height profile at 140 K where IBMC (indicated by red arrows) and IMC (blue arrow) denote insulator-to-BM crossover and insulator-to-metal crossover, respectively. Data are missing at low temperatures and low doping (white region in the right panel) due to the high resistance.

Figure 5

Phase diagram drawn from the transport properties of sample 1. PG, AFI, and FL denote pseudogap, antiferromagnetic insulator, and Fermi liquid, respectively. Black lines indicate temperatures where $d{\rho }_{\mathrm{s}}/dT=0$. Above this temperature, the conductivity is metalliclike. Orange lines indicate temperatures and $V_{\mathrm{G}}$ where ${\rho }_{\mathrm{s}}={\rho }_{\mathrm{MIR}}$. The surface resistivity is quadratic in temperature below the white dashed line on the electron-doped side. The surface resistivity ${\rho }_{\mathrm{s}}$ is shown as a color plot.