It is widely recognized that the effect of doping into a Mott insulator is complicated and unpredictable, as can be seen by examining the Hall coefficient in high T_c cuprates. The doping effect, including the electron–hole doping asymmetry, may be more straightforward in doped organic Mott insulators owing to their simple electronic structures. Here we investigate the doping asymmetry of an organic Mott insulator by carrying out electric-double-layer transistor measurements and using cluster perturbation theory. The calculations predict that strongly anisotropic suppression of the spectral weight results in the Fermi arc state under hole doping, while a relatively uniform spectral weight results in the emergence of a non-interacting-like Fermi surface (FS) in the electron-doped state. In accordance with the calculations, the experimentally observed Hall coefficients and resistivity anisotropy correspond to the pocket formed by the Fermi arcs under hole doping and to the non-interacting FS under electron doping.

We report the influence of the field effect on the dc resistance and Hall coefficient in the strain-induced Mott insulating state of an organic superconductor $\kappa \mathrm{\text{−}}(\mathrm{BEDT}\mathrm{\text{−}}\mathrm{TTF}{)}_2\mathrm{Cu}[\mathrm{N}(\mathrm{CN}{)}_2]\mathrm{Br}$. Conductivity obeys the formula for an activated transport ${\sigma }_{\square }={\sigma }_0\exp (-W/k_{B}T)$, where ${\sigma }_0$ is a constant and $W$ depends on the gate voltage. The gate-voltage dependence of the Hall coefficient shows that, unlike in conventional field-effect transistors, the effective mobility of dense hole carriers ($\sim 1.6\times {10}^{14}{\mathrm{cm}}^{-2}$) is enhanced by a positive gate voltage. This implies that carrier doping involves delocalization of intrinsic carriers that were initially localized due to electron correlation.

Simultaneous control of bandfilling and bandwidth reveals the two-dimensional ground-state phase diagram of a Mott transistor.

We report on the Shubnikov–de Haas (SdH) oscillations in the quasi-two-dimensional molecular conductor $\alpha \text{−}{\left(\mathrm{BETS}\right)}_2{\mathrm{I}}_3$ [BETS: bis(ethylenedithio)tetraselenafulvalene] laminated on polyimide films at 1.7 K. From the SdH phase factor we verified experimentally that the material is in the Dirac fermion phase under pressure. $\alpha \text{−}{\left(\mathrm{BETS}\right)}_2{\mathrm{I}}_3$ is in the vicinity of the phase transition between strongly correlated insulating and Dirac fermion phases, and is a possible candidate for an ambient-pressure molecular Dirac fermion system. However, the SdH oscillations indicate that the Berry phase is zero at ambient pressure. Under pressure, a $\pi$ Berry phase emerges when the metal-insulator crossover is almost suppressed at $\sim 0.5$ GPa. The results contrast with those for the pioneering molecular Dirac fermion system $\alpha \text{−}{\left(\mathrm{BEDT}\text{−}\mathrm{TTF}\right)}_2{\mathrm{I}}_3$ [BEDT-TTF: bis(ethylenedithio)tetrathiafulvalene] in which Dirac fermions and semiconducting behavior are simultaneously observed.

The physics of quantum many-body systems have been studied using bulk correlated materials, and recently, moiré superlattices formed by atomic bilayers have appeared as a novel platform in which the carrier concentration and the band structures are highly tunable. In this brief review, we introduce an intermediate platform between those systems, namely, a band-filling- and bandwidth-tunable electric double-layer transistor based on a real organic Mott insulator κ-(BEDT-TTF)₂Cu[N(CN)₂]Cl. In the proximity of the bandwidth-control Mott transition at half filling, both electron and hole doping induced superconductivity (with almost identical transition temperatures) in the same sample. The normal state under electric double-layer doping exhibited non-Fermi liquid behaviors as in many correlated materials. The doping levels for the superconductivity and the non-Fermi liquid behaviors were highly doping-asymmetric. Model calculations based on the anisotropic triangular lattice explained many phenomena and the doping asymmetry, implying the importance of the noninteracting band structure (particularly the flat part of the band).